Introduction to Fundamental Concepts of Chemistry
Atom
It is the smallest particle of an element which can exist with all the
properties of its own element but it cannot exist in atmosphere alone.
Molecule
When two or more than two atoms are combined with each other a
molecule is formed. It can exist freely in nature.
Formula Weight
It is the sum of the weights of the atoms present in the formula of a substance.
Molecular Weight
It is the sum of the atomic masses of all the atoms present in a molecule.
Chemistry
It is a branch of science which deals with the properties, composition
and the structure of matter.
Empirical Formula
Definition
It is the simplest formula of a chemical compound which represents the
element present of the compound and also represent the simplest ratio
between the elements of the compound.
Examples
The empirical formula of benzene is "CH". It indicates that the
benzene molecule is composed of two elements carbon and hydrogen and
the ratio between these two elements is 1:1.
The empirical formula of glucose is "CH2O". This formula represents
that glucose molecule is composed of three elements carbon, hydrogen
and oxygen. The ratio between carbon and oxygen is equal but hydrogen
is double.
Determination of Empirical Formula
To determine the empirical formula of a compound following steps are required.
1. To detect the elements present in the compound.
2. To determine the masses of each element.
3. To calculate the percentage of each element.
4. Determination of mole composition of each element.
5. Determination of simplest ratio between the element of the compound.
Illustrated Example of Empirical Formula
Consider an unknown compound whose empirical formula is to be
determined is given to us. Now we will use the above five steps in
order to calculate the empirical formula.
Step I - Determination of the Elements
By performing test it is found that the compound contains magnesium
and oxygen elements.
Step II - Determination of the Masses
Masses of the elements are experimentally determined which are given below.
Mass of Mg = 2.4 gm
Mass of Oxygen = 1.6 gm
Step III - Estimation of the Percentage
The percentage of an element may be determined by using the formula.
% of element = Mass of element / Mass of compound x 100
In the given compound two elements are present which are magnesium and
oxygen, therefore mass of compound is equal to the sum of the mass of
magnesium and mass of oxygen.
Mass of compound = 2.4 + 1.6 = 4.0 gm
% Mg = Mass of Mg / Mass of Compound x 100
= 2.4 / 4.0 x 100
= 60%
% O = Mass of Oxygen / Mass of Compound x 100
= 1.6 / 4.0 x 100
= 40%
Step IV - Determination of Mole Composition
Mole composition of the elements is obtained by dividing percentage of
each element with its atomic mass.
Mole ratio of Mg = Percentage of Mg / Atomic Mass of Mg
= 60 / 24
= 2.5
Mole ratio of Mg = Percentage of Oxygen / Atomic Mass of Oxygen
= 40 / 16
= 2.5
Step V - Determination of Simplest Ratio
To obtain the simplest ratio of the atoms the quotients obtained in
the step IV are divided by the smallest quotients.
Mg = 2.5 / 2.5 = 1
O = 2.5 / 2.5 = 1
Thus the empirical formula of the compound is MgO
Note
If the number obtained in the simplest ratio is not a whole number
then multiply this number with a smallest number such that it becomes
a whole number maintain their proportion.
Molecular Formula
Definition
The formula which shows the actual number of atoms of each element
present in a molecule is called molecular formula.
OR
It is a formula which represents the element ratio between the
elements and actual number of atoms of each type of elements present
per molecule of the compound.
Examples
The molecular formula of benzene is "C6H6". It indicates that
1. Benzene molecule is composed of two elements carbon and hydrogen.
2. The ratio between carbon and hydrogen is 1:1.
3. The number of atoms present per molecule of benzene are 6 carbon
and 6 hydrogen atoms.
The molecular formula of glucose is "C6H12O6". The formula represents that
1. Glucose molecule is composed of three elements carbon, hydrogen and oxygen.
2. The ratio between the atoms of carbon, hydrogen and oxygen is 1:2:1.
3. The number of atoms present per molecule of glucose are 6 carbon
atoms. 12 hydrogen atoms and 6 oxygen atoms.
Determination of Molecular Formula
The molecular formula of a compound is an integral multiple of its
empirical formula.
Molecular formula = (Empirical formula)n
Where n is a digit = 1, 2, 3 etc.
Hence the first step in the determination of molecular formula is to
calculate its empirical formula by using the procedure as explained in
empirical formula. After that the next step is to calculate the value
of n
n = Molecular Mass / Empirical Formula Mass
Example
The empirical formula of a compound is CH2O and its molecular mass is 180.
To calculate the molecular formula of the compound first of all we
will calculate its empirical formula mass
Empirical formula mass of CH2O = 12 + 1 x 2 + 16
= 30
n = Molecular Mass / Empirical Formula Mass
= 180 / 30
= 6
Molecular formula = (Empirical formula)n
= (CH2O)6
= C6H12O6
Molecular Mass
Definition
The sum of masses of the atoms present in a molecule is called as
molecular mass.
OR
It is the comparison that how mach a molecule of a substance is
heavier than 1/12th weight or mass of carbon atom.
Example
The molecular mass of CO2 may be calculated as
Molecular mass of CO2 = Mass of Carbon + 2 (Mass of Oxygen)
= 12 + 2 x 16
= 44 a.m.u
Molecular mass of H2O = (Mass of Hydrogen) x 2 + Mass of Oxygen
= 1 x 2 + 16
= 18 a.m.u
Molecular mass of HCl = Mass of Hydrogen + Mass of Chlorine
= 1 + 35.5
= 36.5 a.m.u
Gram Molecular Mass
Definition
The molecular mass of a compound expressed in gram is called gram
molecular mass or mole.
Examples
1. The molecular mass of H2O is 18. If we take 18 gm H2O then it is
called 1 gm molecular mass of H2O or 1 mole of water.
2. The molecular mass of HCl is 36.5. If we take 36.5 gm of HCl then
it is called as 1 gm molecular mass of HCl or 1 mole of HCl.
Mole
Definition
It is defined as atomic mass of an element, molecular mass of a
compound or formula mass of a substance expressed in grams is called
as mole.
OR
The amount of a substance that contains as many number of particles
(atoms, molecules or ions) as there are atoms contained in 12 gm of
pure carbon.
Examples
1. The atomic mass of hydrogen is one. If we take 1 gm of hydrogen, it
is equal to one mole of hydrogen.
2. The atomic mass of Na is 23 if we take 23 gm of Na then it is equal
to one mole of Na.
3. The atomic mass of sulphur is 32. When we take 32 gm of sulphur
then it is called one mole of sulphur.
From these examples we can say that atomic mass of an element
expressed in grams is called mole.
Similarly molecular masses expressed in grams is also known as mole e.g.
The molecular mass of CO2 is 44. If we take 44 gm of CO2 it is called
one mole of CO2 or the molecular mass of H2O is 18. If we take 18 gm
of H2O it is called one mole of H2O.
When atomic mass of an element expressed in grams it is called gram atom
While
The molecular mass of a compound expressed in grams is called gram molecule.
According to the definition of mole.
One gram atom contain 6.02 x 10(23) atoms
While
One gram molecule contain 6.02 x 10(23) molecules.
Avagadro's Number
An Italian scientist, Avagadro's calculated that the number of
particles (atoms, molecules) in one mole of a substance are always
equal to 6.02 x 10(23). This number is known as Avogadro's number and
represented as N(A).
Example
1 gm mole of Na contain 6.02 x 10(23) atoms of Na.
1 gm mole of Sulphur = 6.02 x 10(23) atoms of Sulphur.
1 gm mole of H2SO4 = 6.02 x 10(23) molecules H2SO4
1 gm mole of H2O = 6.02 x 10(23) molecules of H2O
On the basis of Avogadro's Number "mole" is also defined as
Mass of 6.02 x 10(23) molecules, atoms or ions in gram is called mole.
Determination Of The Number Of Atoms Or Molecules In The Given Mass Of
A Substance
Example 1
Calculate the number of atoms in 9.2 gm of Na.
Solution
Atomic mass of Na = 23 a.m.u
If we take 23 gm of Na, it is equal to 1 mole.
23 gm of Na contain 6.02 x 10(23) atoms
1 gm of Na contain 6.02 x 10(23) / 23 atoms
9.2 gm of Na contain 9.2 x 6.02 x 10(23) /23
= 2.408 x 10(23) atoms of Na
Determination Of The Mass Of Given Number Of Atoms Or Molecules Of A Substance
Example 2
Calculate the mass in grams of 3.01 x 10(23) molecules of glucose.
Solution
Molecular mass of glucose = 180 a.m.u
So when we take 180 gm of glucose it is equal to one mole So,
6.02 x 10(23) molecules of glucose = 180 gm
1 molecule of glucose = 180 / 6.02 x 10(23) gm
3.01 x 10(23) molecules of glucose = 3.01 x 10(23) x 180 / 6.02 x 10(23)
= 90 gm
Stoichiometry
(Calculation Based On Chemical Equations)
Definition
The study of relationship between the amount of reactant and the
products in chemical reactions as given by chemical equations is
called stoichiometry.
In this study we always use a balanced chemical equation because a
balanced chemical equation tells us the exact mass ratio of the
reactants and products in the chemical reaction.
There are three relationships involved for the stoichiometric
calculations from the balanced chemical equations which are
1. Mass - Mass Relationship
2. Mass - Volume Relationship
3. Volume - Volume Relationship
Mass - Mass Relationship
In this relationship we can determine the unknown mass of a reactant
or product from a given mass of teh substance involved in the chemical
reaction by using a balanced chemical equation.
Example
Calculate the mass of CO2 that can be obtained by heating 50 gm of limestone.
Solution
Step I - Write a Balanced Equation
CaCO3 ----> CaO + CO2
Step II - Write Down The Molecular Masses And Moles Of Reactant & Product
CaCO3 ----> CaO + CO2
Method I - MOLE METHOD
Number of moles of 50 gm of CaCO3 = 50 / 100 = 0.5 mole
According to equation
1 mole of CaCO3 gives 1 mole of CO2
0.5 mole of CaCO3 will give 0.5 mole of CO2
Mass of CO2 = Moles x Molecular Mass
= 0.5 x 44
= 22 gm
Method II - FACTOR METHOD
From equation we may write as
100 gm of CaCO3 gives 44 gm of CO2
1 gm of CaCO3 will give 44/100 gm of CO2
50 gm of CaCO3 will give 50 x 44 / 100 gm of CO2
= 22 gm of CO2
Mass - Volume Relationship
The major quantities of gases can be expressed in terms of volume as
well as masses. According to Avogardro One gm mole of any gas always
occupies 22.4 dm3 volume at S.T.P. So this law is applied in
mass-volume relationship.
This relationship is useful in determining the unknown mass or volume
of reactant or product by using a given mass or volume of some
substance in a chemical reaction.
Example
Calculate the volume of CO2 gas produced at S.T.P by combustion of 20 gm of CH4.
Solution
Step I - Write a Balanced Equation
CH4 + 2 O2 ----> CO2 + 2 H2O
Step II - Write Down The Molecular Masses And Moles Of Reactant & Product
CH4 + 2 O2 ----> CO2 + 2 H2O
Method I - MOLE METHOD
Convert the given mass of CH4 in moles
Number of moles of CH4 = Given Mass of CH4 / Molar Mass of CH4
From Equation
1 mole of CH4 gives 1 moles of CO2
1.25 mole of CH4 will give 1.25 mole of CO2
No. of moles of CO2 obtained = 1.25
But 1 mole of CO2 at S.T.P occupies 22.4 dm3
1.25 mole of CO2 at S.T.P occupies 22.4 x 1.25
= 28 dm3
Method II - FACTOR METHOD
Molecular mass of CH4 = 16
Molecular mass of CO2 = 44
According to the equation
16 gm of CH4 gives 44 gm of CO2
1 gm of CH4 will give 44/16 gm of CO2
20 gm of CH4 will give 20 x 44/16 gm of CO2
= 55 gm of CO2
44 gm of CO2 at S.T.P occupy a volume 22.4 dm3
1 gm of CO2 at S.T.P occupy a volume 22.4/44 dm3
55 gm of CO2 at S.T.P occupy a volume 55 x 22.4/44
= 28 dm3
Volume - Volume Relationship
This relationship determine the unknown volumes of reactants or
products from a known volume of other gas.
This relationship is based on Gay-Lussac's law of combining volume
which states that gases react in the ratio of small whole number by
volume under similar conditions of temperature & pressure.
Consider this equation
CH4 + 2 O2 ----> CO2 + 2 H2O
In this reaction one volume of CH4 gas reacts with two volumes of
oxygen gas to give one volume of CO2 and two volumes of H2O
Examples
What volume of O2 at S.T.P is required to burn 500 litres (dm3) of
C2H4 (ethylene)?
Solution
Step I - Write a Balanced Equation
C2H4 + 3 O2 ----> 2 CO2 + 2 H2O
Step II - Write Down The Moles And Volume Of Reactant & Product
C2H4 + 3 O2 ----> 2 CO2 + 2 H2O
According to Equation
1 dm3 of C2H4 requires 3 dm3 of O2
500 dm3 of C2H4 requires 3 x 500 dm3 of O2
= 1500 dm3 of O2
Limiting Reactant
In stoichiometry when more than one reactant is involved in a chemical
reaction, it is not so simple to get actual result of the
stoichiometric problem by making relationship between any one of the
reactant and product, which are involved in the chemical reaction. As
we know that when any one of the reactant is completely used or
consumed the reaction is stopped no matter the other reactants are
present in very large quantity. This reactant which is totally
consumed during the chemical reaction due to which the reaction is
stopped is called limiting reactant.
Limiting reactant help us in calculating the actual amount of product
formed during the chemical reaction. To understand the concept the
limiting reactant consider the following calculation.
Problem
We are provided 50 gm of H2 and 50 gm of N2. Calculate how many gm of
NH3 will be formed when the reaction is irreversible.
The equation for the reaction is as follows.
N2 + 3 H2 ----> 2 NH3
Solution
In this problem moles of N2 and H2 are as follows
Moles of N2 = Mass of N2 / Mol. Mass of N2
= 50 / 28
= 1.79
Moles of H2 = Mass of H2 / Mol. Mass of H2
= 50 / 2
= 25
So, the provided moles for the reaction are
nitrogen = 1.79 moles and hydrogen = 25 moles
But in the equation of the process 1 mole of nitrogen require 3 mole
of hydrogen. Therefore the provided moles of nitrogen i.e. 1.79
require 1.79 x 3 moles of hydrogen i.e. 5.37 moles although 25 moles
of H2 are provided but when nitrogen is consumed the reaction will be
stopped and the remaining hydrogen is useless for the reaction so in
this problem N2 is a limiting reactant by which we can calculate the
actual amount of product formed during the reaction.
N2 + 3 H2 ----> 2 NH3
1 mole of N2 gives 2 moles of NH3
1.79 mole of N2 gives 2 x 1.79 moles of NH3
= 3.58 moles of NH3
Mass of NH3 = Moles of NH3 x Mol. Mass
= 3.58 x 17
= 60.86 gm of NH3
THREE STATES OF MATTER.
Three States Of Matter
Matter
It is defined as any thing which has mass and occupies space is called matter.
Matter is composed of small and tiny particles called Atoms or
molecules. It exist in three different states which are gaseous,
liquid & solid.
Properties of Gas
1. It has no definite shape.
2. It has no definite volume, so it can be compressed or expanded.
3. A gas may diffuse with the other gas.
4. The molecules of a gas are in continuous motion.
Properties of Liquids
1. A liquid has no definite shape.
2. It has a fixed volume.
3. The diffusion of a liquid into the other liquid is possible if both
of the liquids are polar or non-polar.
4. It can be compressed to a negligible.
Properties of Solids
1. A solid has a definite shape.
2. It has a fixed volume.
3. The rate of diffusion of solid with each other is very slow.
4. It cannot be compressed easily.
Kinetic Theory of Gases
It was an idea of some scientist like Maxwell & Bolzmann that the
properties of gases are due to their molecular motion. This motion of
the molecules is related with the kinetic energy, so the postulates
give by the scientist about the behaviour of gases are collectively
known as kinetic molecular theory of gases.
The postulates of kinetic molecular theory are as follows.
1. All gases consists of very large number of tiny particles called molecules.
2. These molecules are widely separated from each other and are so
small that they are invisible.
3. The size of the molecules is very small as compared to the distance
between them.
4. There is no attractive or repulsive force between molecules so they
can move freely.
5. The molecules are very hard and perfectly elastic so when they
collide no loss of energy takes place.
6. The gas molecules are in continuous motion they move in a straight
path until they collide. The distance between two continuous
collision is called Mean Free Path.
7. During their motion these molecules are collided with one another
and with the walls of the container.
8. The collision of the molecules are perfectly elastic. When
molecules collide they rebound with perfect elasticity and
without loss or gain of energy.
9. The pressure of the gas is the result of collision of molecules on
the walls of the container.
10. The average kinetic energy of gas molecules depends upon the
absolute temperature. At any given temperature the molecules of
all gases have the same average kinetic energy (1/2 mv2).
Kinetic Theory of Liquids
This theory is bases on the following assumptions.
1. The particles of a liquid are very close to each other due to which
a liquid has fixed volume.
2. The particles in a liquid are free to move so they have no definite shape.
3. During the motion these molecules collides with each other and with
the walls of the container.
4. These molecules possess kinetic which is directly proportional to
its absolute temperature.
Kinetic Theory of Solids
The assumptions of kinetic theory for solids are as follows.
1. The particles in a solid are very closely packed due to strong
attractive forces between the molecules.
2. These molecules are present at a fixed position and are unable to move.
3. They have definite shape because the particles are arranged in a
fixed pattern.
4. They possess only vibrational energy.
Mean Free Path
The distance which a molecule of a gas travels before its collision
with the other molecule is called free path. This distance between the
collision of the molecules changes constantly so the average distance
which a molecule travels before its collision is called mean free
path.
Boyle's Law
A relationship of volume with external pressure was given by Boyle's
in the form of law. This law is known as Boyle's Law which states,
For a given mass of a gas the volume of the gas is inversely
proportional to its pressure provided the temperature is kept
constant.
Mathematically it may be written as
V 8 1 / P
Or V = K / P
Or PV = K
On the bases of the relation, Boyle's law can also be stated as
The product of the pressure and volume of a given mass of a gas is
always constant at constant temperature.
Explanation
Consider for a given mass a gas having volume V1 at pressure P1, so
according to Boyle's Law we may write as
P1V1 = K1 (constant)
If the pressure of the above system is changed from P1 to P2 then the
volume of the gas will also change from V1 to V2. For this new
condition of the gas we can write as,
P2V2 = K2 (constant)
But for the same mass of the gas.
K1 = K2
P1V1 = P2V2
This equation is known as Boyle's Equation.
Charle's Law
We know that everything expand on heating and contract cooling. This
change in volume is small in liquids and solids but gases exhibit
enormous changes due to the presence of large intermolecular spaces.
Change of volume of a gas with the change of temperature at constant
pressure was studied by Charles and was given in the form of a law.
which states,
Statement
For a given mass of a gas the volume of the gas is directly
proportional to its absolute temperature provided the pressure is kept
constant.
Mathematically this law may be written as
V 8 T
V = K T
OR
V / T = K
This relation shows that the ratio of volume of a given mass of a gas
to its absolute temperature is always constant provided the pressure
is kept constant. On this bases Charles Law may also be defined as,
If the pressure remains constant for each 1ºC change of temperature
the volume of the gas changes to 1/273 of its original volume.
On the bases of this statement
V1 / T = K & V2 / T2 = K
V1 / T1 = V2 / T2
This equation is known as Charle's equation.
The volume temperature relationship can be represented graphically.
When volume of a given mass of gas is plotted against temperature, a
straight line is obtained.
Absolute Scale Of Temperature
There are different scales for the measurement of temperature such as
Celsius ºC and Fahrenheit ºC. Similarly another scale known as
absolute scale or Kelvin scale is determined on the basis of Charle's
law.
On the basis of Charle's law we known that the volume of the gas
changes to 1/273 times of its original volume for each 1 ºC change of
temperature. It suggests that the volume of a gas would theoretically
be zero at -273ºC. But this temperature has never been achieved for
any gas because all the gases condense to liquid at a temperature
above this point. So the minimum possible temperature for a gaseous
system is to be -273ºC. This temperature is referred as absolute zero
or zero degree of the absolute scale or Kelvin scale.
To form an absolute scale thermometer if the equally spaced divisions
of centigrade thermometer are extended below zero and when the point
-273ºC is maked then this point is called as absolute zero and the
scale is called as absolute scale. It shows that for the conversion of
centigrade scale into Kelvin scale 273 is added to the degrees on the
centigrade scale.
K = 273 + ºC
Avogadro's Law
In 1811, a scientist Avogadro's established a relationship between the
volume and number of molecules of the gas, which is known as
Avogadro's law.
Statement
Equal volume of all gases contains equal number of molecules under the
same condition of temperature & pressure.
Mathematically it may be represented as
V 8 n
OR
V = K n
On the basis of the above statement we can say that
1 dm3 of O2 gas will contain the same number of molecules as 1 dm3 of
H2 or N2 or any other gas at same temperature and pressure.
It was also observed that 22.4 dm3 of any gas at S.T.P contain 1 mole
of that gas, so 22.4 dm3 volume at S.T.P is called as molar volume or
the volume of 1 mole of the gas and the mass present in 22.4 dm3 of
any gas will be equal to its molar mass or molecular mass. It can also
be explained on the basis of following figures.
Determination of Unknown Molecular Mass of a Gas With the Help of Avogadro's Law
Suppose we have two gases (i) Oxygen (ii) CO
The volume of these two gases are equal which are 1 dm3.
The mass of 1 dm3 of oxygen is 1.43 gm
The mass of 1 dm3 of Co is 1.25 gm
According to Avogadro's law we know that 1 dm3 of CO at S.T.P contain
the same number of molecules as 1 dm3 of O2 under similar condition.
Hence a molecule of CO has 1.25 / 1.43 times as much as a molecule of
O2 and we know that the molecular mass of oxygen is 32 so the
molecular mass of CO would be
1.25 / 1.43 x 32 = 28 g / mole
General Gas Equation (Ideal Gas Equation)
To give a relation between the volume, pressure and number of moles of
n gas, Boyle's law, Charle's law and Avogadro's law are used.
According to Boyle's law | V 8 1 / P
According to Charle's law | V 8 T
According to Avogadro's law | V 8 n
By combining these laws we get
V 8 1 / P x T x n
OR
V = R x 1 / P x T x P
OR
P V = n R T
This equation is known as general gas equation n is also known as
equation of state because when we specify the four variables =
pressure, temperature, volume and number of moles we define the state
for a gas.
In this equation "R" is a constant known as gas constant.
Value of R
1. When Pressure is Expressed in Atmosphere and Volume in Litres or dm3
According to general gas equation
P V = n R T
OR
R = PV / nT
For 1 mole of a gas at S.T.P we know that
V = 22.4 dm3 or litres
T = 273 K (standard temperature)
P = 1 atm (standard pressure)
So,
R = PV / nT
= 1 atm x 22.4 dm3 / 1 mole x 273 K
= 0.0821 dm3 K-1 mol0-1
2. When Pressure is Expressed in Newtons Per Square Metre and Volume
in Cubic Metres
For 1 mole of a gas at S.T.P
V = 0.0224 m3 .......... ( 1 dm3 = 10-3 m3)
n = 1 mole
T = 273 K
P = 101200 Nm-2
So,
R = PV / nT
= 101300 Nm-2 x 0.0224 m3 / 1 mole x 273 K
= 8.3143 Nm K-1 mole-1
= 8.3143 J K-1 mol-1
Derivation of Gas Equation
According to general gas equation
P V = n R T
For 1 mole of a gas n = 1
P V = R T
OR
P V / T = R
Consider for a known mass of a gas the volume of the gas is V1 at a
temperature T1 and pressure P1. Therefore for this gas we can write as
P1 V1 / T1 = R
If this gas is heated to a temperature T2 due to which the pressure is
changed to P2 and volume is changed to V2. For this condition we may
write as
P2 V2 / T2 = R
P1 V1 / T1 = P2 V2 / T2 = R
P1 V1 / T1 = P2 V2 / T2
This equation is known as gas equation.
Graham's Law of Diffusion
We know that gas molecules are constantly moving in haphazard
direction, therefore when two gases are placed separated by a porous
membrane, they diffuse through the membrane and intermix with each
other. The phenomenon of mixing of molecules of different gases is
called diffusion.
In 1881, Graham established a relationship between the rates of
diffusion of gases and their densities which is known as Graham's law
of diffusion.
Statement
The rate of diffusion of any gas is inversely proportional to the
square root of its density.
Mathematically it can be represented as
r 8 1 / vd
r = K / vd
Graham also studied the comparative rates of diffusion of two gases.
On this basis the law os defined as
The comparative rates of diffusion of two gases under same condition
of temperature and pressure are inversely proportional to the square
root of their densities.
If the rate of diffusion of gas A is r1 and its density is d1 then
according to Graham's law
r1 8 1 / vd1
OR
r1 = K / vd1
Similarly the rate of diffusion of gas B is r2 and its density is d2 then
r2 8 1 / vd2
OR
r2 = K / vd2
Comparing the two rates
r1 / r2 = (K / vd1) / (K / vd2)
r1 / r2 = vd2 / d1 ................... (A)
But density d = mass / volume
Therefore,
For d1 we may write as
d1 = m1 / v1
And for d2
d2 = m2 / v2
Substituting these values of d1 & d2 in equation (A)
r1 / r2 = v(m2 / v2) / (m1 / v1)
But v1 = v2 because both gases are diffusing in the same volume.
Therefore,
r1 / r2 = vm2 / m1
Hence Graham's law can also be stated as,
The comparative rates of diffusion of two gases are inversely
proportional to the square root of their masses under the same
condition of temperature and pressure.
It means that a lighter gas will diffuse faster than the heavier gas.
For example compare the rate of diffusion of hydrogen and oxygen.
Rate of diffusion of H2 / Rate of diffusion of O2 = vMass of O2 / Mass
of H2 = v32/ 2 = v16 = 4
It shows that H2 gas which is lighter gas than O2 will diffuse four
times faster than O2.
Dalton's Law of Partial Pressures
Partial Pressure
In a gaseous mixture the individual pressure oxerted by a gas is known
as partial pressure.
When two or more gases which do not react chemically are mixed in the
same container each gas will exert the same pressure as it would exert
if it alone occupy the same volume.
John Dalton in 1801 formulated a law which is known as Dalton's Law of
partial pressure and stated as.
Statement
The total pressure of a gaseous system is equal to the sum of the
partial pressures of all the gases present in the system.
Suppose in a system three gases A, B & C are present. The partial
pressure of these gases are
PA = Partial pressure of gas A
PB = Partial pressure of gas B
PC = Partial pressure of gas C
Then Dalton's law may be mathematically written as
PT = PA + PB + PC
Where PT is the total pressure of the system.
To calculate the individual pressures of gases in the above example
suppose the number of moles of A, B & C in the container are nA, nB
and nC. So the total number of moles in the container will be
n = nA + nB + nC
Apply the general gas equation
P V = n R T
PT = n R T / V
Since R, T and V are same for gases A, B and C, therefore the partial
pressure of these gases are as follows.
Partial pressure of gas A | PA = n(A)RT / V ......... (2)
Partial pressure of gas B | PB = n(B)RT / V ......... (3)
Partial pressure of gas C | PC = n(C)RT / V ......... (4)
Now divide equation (2) by (1)
PA / PT = (nA RT/V) / (nRT/V)
OR
PA / PT = nA / nT
Therefore,
P(gas) = P1 x n(gas) / n(total)
Application of Dalton's Law
In an inert mixture of gases the individual gas exerts its own
pressure due to collision of its molecules with the walls of the
container but the total pressure produced on the container wall will
be the sum of pressure of all the individual gases of the mixture.
On this basis the number of moles formed during a chemical reaction
can be measured. For this purpose a gas produced in a chemical
reaction is collected over water. The gas also contains some of water
vapours. So the pressure exerted by the gas would be the pressure of
pure gas and the pressure of water vapours.
Therefore the pressure of the system may be represented as
P(moist) = P(dry) + P(water vapour)
So,
P(dry) = P(moist) - P(water vapour)
In this way we can obtain the pressure of the gas and by using general
gas equation we can calculate the number of moles of the prepared gas.
Ideal Gas
A gas which obeys all the gas laws at all temperatures and pressures
is known as ideal gas.
It means that the product of pressure and volume must be constant at
all pressures.
Similarly the rate of V/T will remain constant for an ideal gas.
But there is no gas which is perfectly ideal because of the presence
of the force of attraction or repulsion between the molecules.
Gas Laws on the Basis of Kinetic Theory
Boyle's Law
According to Boyle's law the volume of a given mass of a gas is
inversely proportional to its pressure at constant temperature.
It means that when the volume of the gas is decreased the pressure of
the gas will increase.
According to kinetic molecular theory of gases the pressure exerted by
a gas is due to the collisions of the molecules with the walls of the
container. If the volume of a gas is reduced at constant temperature,
the average velocity of the gas molecules remains constant so they
collide more frequently wit the walls which causes higher pressure.
Charle's Law
According to Charles law the volume of a given mass of a gas is
directly proportional to its absolute temperature at constant
pressure.
According to kinetic molecular theory the average kinetic energy of
gas molecules is directly proportional to its absolute temperature so
if the temperature of the gas is increased the average kinetic energy
of the gas molecules is also increased due to which the sample of the
gas expanded to keep the pressure constant. It is accordance with the
law.
Graham's Law
According to Graham's Law
r1 / r2 = vm2 / m1
The rate of diffusion of a gas is directly proportional to the
velocity of the molecules so,
v1 / v2 = vm2 / m1
Liquefaction
According to kinetic theory, the kinetic energy of the molecules is
low for lower temperature. These slower moving molecules become
subject to inter molecular attraction. At a sufficiently low
temperature these attractive forces are capable of holding the
molecules with one another so the gas is changed into liquid and the
process is called liquefaction.
Liquid State
It is one of the state of matter. In this state, the kinetic energy of
the molecule is very high due to which the molecules of the liquid are
able to move but due to compact nature liquids are not compressible.
On this basis we can say that the volume of a liquid is always
constant but its shape can be changed.
Behaviour of Liquids
The main properties of liquids are as follows.
Diffusibility
The diffusion of one liquid into another liquid is possible but its
rate is slow as compared with the rate of diffusion of gases. Example
of diffusion of liquids is mixing of alcohol in water.
Explanation of Diffusion in Terms of Kinetic Energy
As the molecular of a liquid are in cluster form they are very close
to each other but these molecules are movable so they can mix with the
other molecules. Since the intermolecular distance are smaller due to
which the rate of diffusion of liquids is slow.
Compressibility
The space between liquid molecules are very small due to strong Van
der Waals forces. When the pressure is applied, they can be compressed
but to a very little extent.
Expansion
When a liquid is heated, the kinetic energy of its molecules also
increases so the attraction between the molecules becomes weaker due
to which they go further apart and hence the liquid expands.
Contraction
When a liquid is cooled its kinetic energy is lowered and the
attraction among the molecules becomes stronger so they comes close to
each other and hence the liquid contract.
Viscosity
Definition
The internal resistance in the flow of a liquid is called viscosity.
Liquids have the ability to flow, but different liquids have different
rates of flow. Some liquids like honey mobil oil etc. flow slowly and
are called viscous liquids while ether, gasoline etc. which flow
quickly are called less viscous.
Explanation
The viscosity of liquid can be understood by considering a liquid in a
tube, a liquid in a tube is considered as made up of a series of
molecular layer. The layer of the liquid in contact with the walls of
the tube remains stationary and the layer in the center of the tube
has highest velocity as shown.
Each layer exerts a drag on the next layer and causes resistance to flow.
Factors on Which Viscosity Depends
1. Size of Molecules
The viscosity of a liquid depends upon the size of its molecules. If
the size of the molecules is bigger the viscosity of the liquid is
high.
2. Shape of Molecules
Shape of the molecules affects the viscosity. If the shapes of the
molecules are spherical they can move easily but if the shapes of the
molecules are irregular such as linear or trigonal then the molecules
will move slowly and its viscosity will be high.
3. Intermolecular Attraction
If the force of attraction between the molecules of a liquid is
greater the viscosity of the liquid is also greater.
4. Temperature
Viscosity of a liquid decreases with the increase of temperature.
Units of Viscosity
Viscosity of a liquid is measured in poise, centipoise or millipoise & S.I unit.
1 poise = 1 N.s.m(-2)
1 centipoise = 10(-2) N.s.m(-2)
Surface Tension
Definition
The force acting per unit length on the surface of a liquid at right
angle direction is called surface tension.
Explanation
Consider a liquid is present in a beaker. The molecules inside the
liquid are surrounded by the other molecules of the liquid. So the
force of attraction on a molecule is balanced from all direction. But
the force of attraction acting on the molecules of the surface from
the lower layer molecules is not balanced.
The molecules lying on the surface are attracted by the molecules
present below the surface Due to this downward pull the surface of the
liquid behave as a membrane which tends to contract to a smaller area
and causes a tension on the surface of the liquid known as surface
tension.
Factors on Which Surface Tension Depends
1. Molecular Structure of the Liquid
If the force of attraction between the molecules is greater, the
surface tension of the liquid is also greater. Those liquids in which
hydrogen bond formation take place will have more surface tension.
2. Temperature
Surface tension of a liquid is inversely proportional to the temperature.
Units
1. Dynes / cm
2. Ergs / cm2
Capillary Action
The fall or rise of a liquid in a capillary tube is called capillary action.
When a capillary tube is dipped in a liquid which wets the wall of the
tube, the liquid will rise in the capillary tube, to decrease the
surface area due to surface tension. The liquid will rise in the
capillary tube until the upward force due to surface tension is just
balanced by the downward gravitational pull. This is called capillary
action.
Vapour Pressre
Definition
The pressure exerted by the vapours of a liquid in its equilibrium
state with the pure liquid at a given temperature is called vapour
pressure.
Explanation
Consider a liquid is present in a bottle as shown.
In the beginning the atmosphere above the surface of liquid is
unsaturated but due to continuous evaporation the molecule of the
liquid are trapped in the bottle and the air present above the surface
of the liquid is becomes saturated and after it the molecules present
in the vapour state may hit the liquid again and rejoin it by
condensing into liquid. Thus in this closed vessel two process are
going on simultaneously which are evaporation and condensation of
vapours. When the rates of these two processes becomes equal at this
point the pressure exerted by vapours is called vapour pressure.
Units of Vapour Pressure
The units for vapour pressure are
1. Millimeter of Hg
2. Atmosphere
3. Torr
4. Newton / m(2)
Factors for Vapour Pressure
1. Nature of Liquid
Vapour pressure of a liquid depends upon the nature of the liquid. Low
boiling liquid exert more vapour pressure at a given temperature.
2. Temperature
Vapour pressure of a liquid also depends upon temperature. The vapour
pressure of the liquid increases with the increase of temperature due
to the increase of average of kinetic energy.
3. Intermolecular Forces
Those liquids in which the intermolecular forces are weak shows high
vapour pressure.
Explanation of Evaporation on the Basis of Kinetic Theory
According to this theory the molecules of a liquid collide with each
other during their motion. Due to these collisions some of the
molecules acquire greater energy than Van der Walls forces which binds
the molecules of the liquid together so these molecules of higher
energy escapes from the surface into the air in the form of vapours.
Evaporation is a Cooling Process
In liquids, due to collision between molecules some molecules acquire
higher energy and escapes from the surface of the liquid in the form
of vapours. The kinetic energy of the remaining molecules decreases
due to which the temperature of the liquid also decreases and hence we
can say that evaporation is a cooling process.
Boiling Point
Definition
The temperature at which the vapour pressure of a liquid becomes equal
to the atmospheric pressure is called boiling point.
When a liquid is heated the rate of evaporation of the molecules also
increases with the increase in temperature. When the pressure of the
vapours becomes equal to the atmospheric pressure the liquid starts
boiling and this temperature is known as boiling point.
If the external pressure on a liquid is changed the boiling point of
the liquid also change. The increase in external pressure on a liquid
increases the boiling point while the decreases of external pressure
decrease the boiling point.
Solid State
It is a state of matter which posses both definite shape and definite
volume. In solids the particles are very close to each and tightly
packed with a greater force of attraction.
Properties of Solids
1. Diffusibility
Diffusion also occurs in solids but its rate is very slow. If a
polished piece of zinc is clamped with a piece of copper for a long
time. After few years we will see that some particles of zinc are
penetrated into copper and some particles of copper are penetrated
into zinc. It shows that the diffusion in solids is possible but it
occurs with a slow rate.
2. Compressibility
In solids the molecules are close to each other so it is not easy to
compress a solid. In other words we can say that the effect of
pressure on solids is negligible.
3. Sublimation
It is a property of some solids that on heating these solids are
directly converted into vapours without liquification. This property
of solids is known as sublimation.
4. Melting
When solids are heated, they are changed into liquids and the property
is called melting of the solids.
5. Deformity
Solids may be deformed by high pressure. When a high pressure is
applied on solids due to which some particles are dislocated the force
of attraction is so strong that the rearranged atoms are held equally
well with their new neighbours and hence the solid is deformed.
Classification of Solids
Solids are classified into two main classes.
1. Crystalline
2. Amorphous
1. Crystalline Solids
In a solid if the atoms are attached with each other with a definite
arrangement and it also possesses a definite geometrical shape. This
type of solid is called crystalline solid.
e.g. NaCl, NiSO4 are crystalline solids.
2. Amorphous Solids
In these solids there is no definite arrangement of the particles so
they do not have a definite shape. The particles of such solids have a
random three dimensional arrangement. Examples of amorphous solids are
glass, rubber, plastic etc.
The properties of crystalline and amorphous solids are quite different
from each other. These differences in properties are given below.
Difference of Geometry
1. Crystalline Solids
In crystalline solids particles are arranged in a definite order due
to which it possesses a definite structure.
2. Amorphous Solids
In amorphous solids particles are present without any definite
arrangement so they do not have definite shape.
Difference of Melting Point
1. Crystalline Solids
Crystalline solids have sharp melting point due to uniform arrangement.
2. Amorphous Solids
Amorphous solids melts over a wide range of temperature.
Cleavage and Cleavage Plane
1. Crystalline Solids
When a big crystal is broken down into smaller pieces the shape of the
smaller crystals is identical with the bigger crystal. This property
of crystalline solids is called cleavage and the plane from where a
big crystal is broken is called cleavage plane.
2. Amorphous Solids
Amorphous solids do not break up into smaller pieces with an identical shape.
Anisotropy & Isotropy
1. Crystalline Solids
It is a property of crystalline solid that they show different
physical properties in different direction. For example graphite can
conduct electric current only through the plane which is parallel to
its layers. This property is called anisotropy.
2. In amorphous solids the physical properties are same in all
directions. This property of solids is called isotropy.
Symmetry in Structure
1. Crystalline solids are symmetric in their structure when they are
rotated about an axis, their appearance remains same so they are
symmetric in structure.
2. Amorphous Solids
Amorphous solids are not symmetric.
Types of Crystals
There are four types of crystals.
1. Atomic crystals
2. Ionic crystals
3. Covalent crystals
4. Molecular crystal
1. Atomic Crystals
Metals are composed of atoms. These atoms are combined with each other
by metallic bond and the valency electrons in metals can move freely
throughout the crystal lattice. This type of solid is called atomic
crystal.
The properties of atomic crystals are
1. High melting point.
2. Electrical and thermal conductivity.
3. These are converted into sheets so these are malleable.
4. These are used as wire so these are ductile.
2. Ionic Crystals
Those solids which consists of negativity and positively charged ions
held together by strong electrostatic force of attraction are called
ionic crystals. Ionic crystalline solids possesses the following
properties.
1. The melting and boiling point of ionic crystals is high.
2. They conduct electricity in molten state.
3. Ionic crystals are very hard.
4. Indefinite growth of crystals is also a property of ionic crystals.
3. Covalent Crystals
In covalent solids, the atoms or molecules are attached with each
other by sharing of electrons. Such type of solids are called covalent
solids e.g. diamond is a covalent solid in which carbon atoms are
attached with each other by covalent bond. The other examples of
covalent crystals are sulphur, graphite etc.
Covalent crystals possesses the following properties.
1. High melting point.
2. High refractive index.
3. Low density.
4. Molecular Crystals
Those solid in which molecules are held together due to intermolecular
forces to form a crystal lattice are called molecular crystals e.g.
iodine and solid CO2 are molecular crystals. The general properties of
molecular crystals are as follows.
1. Low melting and boiling point.
2. Non - conductor of heat and electricity.
Isomorphism
When two different substance have same crystalline structure, they are
said to be isomorphous and the phenomenon is called isomorphism.
e.g. ZnSO4 and NiSO4 are two different substances but both are
orthorhombic similarly the structure of CaCO3 and NaNO3 is frigonal.
Polymorphism
If a substance exist in more than one crystalline form it is called
polymorphous and the phenomenon is known as polymorphism. E.g. sulphur
exist in rhombic and monoclinic form similarly CaCO3 exist in trigonal
and orthorhombic form.
Unit Cell
The basic structural unit of a crystalline solid which when repeated
in three dimensions generates the crystal structure is called a unit
cell.
A unit cell of any crystalline solid has a definite geometric shape
and distinguish from other crystals on the basis of length of the
edges and angle between the edges.
Crystal Lattice
In crystalline solids atoms, ions or molecules are arranged in a
definite order and form a three dimensional array of particles which
is known as crystal lattice.
ATOMIC STRUCTURE.
Atomic Structure
Introduction
About the structure of atom a theory was put on by John Dalton in
1808. According to this theory matter was made from small indivisible
particles called atoms.
But after several experiments many particles have been discovered with
in the atom which are electrons, protons, neutrons, positrons etc. For
the discovery of these fundamental particles the experiments are as
follows.
1. Faraday's experiment indicates the existence of electron.
2. Crook's tube experiment explains the discovery of electron and proton.
3. Radioactivity also confirms the presence of electrons and protons.
4. Chadwick's experiment shows the presence of neutrons.
The details of these experiments are given below.
Faraday's Experiment
Passage of Electricity Through Solution
In this experiment Faraday passed the electricity through an
electrolytic solution. He observed that when two metal plates called
electrodes are placed in an electrolytic solution and electricity is
passed through his solution the ions present in the solution are moves
towards their respective electrodes. In other words these ions are
moves towards the oppositely charge electrodes to give up their charge
and liberated as a neutral particles.
Faraday also determined the charges of different ions and the amount
of elements liberated from the electrolytic solution. Due to this
experiment presence of charge particles in the structure of atoms is
discovered. The basic unit of electric charge was later named as
electron by Stoney in 1891.
Crook's Tube Or Discharge Tube Experiment
Passage of Electricity Through Gases Under Low Pressure
Introduction
The first of the subatomic particles to be discovered was electron.
The knowledge about the electron was derived as a result of the study
of the electric discharge in the discharge tube by J.J. Thomson in
1896. This work was later extended by W. Crooke
Working of Discharge Tube
When a very high voltage about 10,000 volts is applied between the two
electrodes, no electric discharge occurs until the part of the air has
been pumped out of the tube. When the pressure of the gas inside the
tube is less than 1 mm, a dark space appears near the cathode and
thread like lines are observed in the rest of 0.01 mm Hg it fills the
whole tube. The electric discharge passes between the electrodes and
the residual gas in the tube begins to glow. These rays which proceed
from the cathode and move away from it at right angle in straight
lines are called cathode rays.
Properties of Cathode Rays
1. They travel in straight lines away from the cathode and produce
shadow of the object placed in their path.
2. The rays carry a negative charge.
3. These rays can also be easily deflected by an electrostatic field.
4. The rays can exert mechanical pressure showing that these consist
of material particle which are moving with kinetic energy.
5. The produce fluorescence when they strike the glass wall of the
discharge tube.
6. Cathode rays produce x-rays when they strike a metallic plate.
7. These rays consists of material particle whose e/m resembles with electron.
8. These rays emerge normally from the cathode and can be focused by
using a concave cathode.
Positive Rays
In 1890 Goldstein used a discharge tube with a hole in the cathode. He
observed that while cathode rays were emitting away from the cathode,
there were coloured rays produced simultaneously which passed through
the perforated cathode and caused a glow on the wall opposite to the
anode. Thomson studied these rays and showed that they consisted of
particles carrying a positive charge. He called them positive rays.
Properties of Positive Rays
1. These rays travel in a straight line in a direction opposite to the cathode.
2. These are deflected by electric as well as magnetic field in the
way indicating that they are positively charged.
3. The charge to mass ratio (e/m) of positive particles varies with
the nature of the gas placed in the discharge tube.
4. Positive rays are produced from the ionization of gas and not from
anode electrode.
5. Positive rays are deflected in electric field. This deflection
shows that these are positively charged so these are named as
protons.
The Information Obtained From Discharge Tube Experiment
The negatively charge particles electrons and the positively charge
particles protons are the fundamental particle of every atom.
Radioactivity
In 1895, Henry Becqueral observed that uranium and its compounds
spontaneously emitted certain type of radiation which affected a
photographic plate in the dark and were able to penetrate solid
matter. He called these rays as radioactivity rays and a substance
which possessed the property of emitting these radioactivity rays was
said to be radioactivity element and the phenomenon was called
radioactivity.
On further investigation by Maric Curic, it was found that the
radiation emitted from the element uranium as well as its salts is
independent of temperature and the source of the mineral but depend
upon the mineral but depend upon the quantity of uranium present e.g.
Pitchblende U3O8 was found to be about four times more radioactive
than uranium.
Radioactive Rays
Soon after the discovery of radium it was suspected that the rays
given out by radium and other radioactive substance were not of one
kind. Rutherford in 1902 devised an ingenious method for separating
these rays from each other by passing them between two oppositely
charged plate. It was observed that the radioactive rays were of three
kinds, the one bending towards the negative plate obviously carrying
positive charge were called a-rays and those deflected to the positive
plate and carrying -ve charge were named as ß-rays. The third type
gamma rays, pass unaffected and carry no charge.
Properties of alpha - RAYS
1. These rays consists of positively charged particles.
2. These particles are fast moving helium nuclei.
3. The velocity of a-particles is approximately equal to 1/10th of the
velocity of light.
4. Being relatively large in size, the penetrating power of a-rays is very low.
5. They ionize air and their ionization power is high.
Properties of beta - RAYS
1. These rays consists of negatively charged particles.
2. These particles are fast moving electron.
3. The velocity of ß-particles is approximately equal to the velocity of light.
4. The penetrating power of ß-rays is much greater than a-rays.
5. These rays ionizes gases to lesser extent.
Properties of Y - RAYS
1. Gamma rays do not consist of particles. These are electromagnetic radiations.
2. They carry no charge so they are not deflected by electric or magnetic field.
3. Their speed is equal to that of light.
4. These are weak ionizer of gases.
5. Due to high speed and non-material nature they have great power of
penetration.
Chadwick Experiment (Discovery of Neutron)
When a light element is bombarded by a-particles, these a-particles
leaves the nucleus in an unstable disturbed state which on settling
down to stable condition sends out radioactivity rays. The phenomenon
is known as "Artificial Radioactivity".
In 1933, Chadwick identified a new particle obtained from the
bombardment of beryllium by a-particles. It had a unit mass and
carried no charge. It was named "Neutron".
Spectroscopic Experiment
After the discovery of fundamental particles which are electrons,
protons & neutron, the next question concerned with electronic
structure of atom.
The electronic structure of the atom was explained by the
spectroscopic studies. In this connection Plank's Quantum theory has
great impact on the development of the theory of structure of atom.
Planck's Quantum Theory
In 1900, Max Planck studied the spectral lines obtained from hot body
radiations at different temperatures. According to him,
When atoms or molecules absorb or emit radiant energy, they do so in
separate units of waves called Quanta or Photons.
Thus light radiations obtained from excited atoms consists of a stream
of photons and not continuous waves.
The energy E of a quantum or photon is given by the relation
E = h v
Where v is the frequency of the emitted radiation and h the Planck's
constant. The value of h = 6.62 x 10(-27) erg. sec.
The main point of this theory is that the amount of energy gained or
lost is quantized which means that energy change occurs in small
packets or multiple of those packets, hv, 2 hv, 3 hv and so on.
Spectra
A spectrum is an energy of waves or particles spread out according to
the increasing or decreasing of some property. E.g. when a beam of
light is allowed to pass through a prism it splits into seven colours.
This phenomenon is called dispersion and the band of colours is called
spectrum. This spectrum is also known as emission spectrum. Emission
spectra are of two types.
1. Continuous Spectrum
2. Line Spectrum
1. Continuous Spectrum
When a beam of white light is passed through a prism, different wave
lengths are refracted through different angles. When received on a
screen these form a continuous series of colours bands: violet,
indigo, blue, green, yellow and red (VIBGYOR). The colours of this
spectrum are so mixed up that there is no line of demarcation between
different colours. This series of bands that form a continuous rainbow
of colours is called continuous spectrum.
2. Line Spectrum
When light emitted from a gas source passes through a prism a
different kind of spectrum may be obtained.
If the emitted from the discharge tube is allowed to pass through a
prism some discrete sharp lines on a completely dark back ground are
obtained. Such spectrum is known as line spectrum. In this spectrum
each line corresponds to a definite wave length.
Identification of Element By Spectrum
Each element produces a characteristics set of lines, so line spectra
came to serve as "finger prints" for the identification of element. It
is possible because same element always emit the same wave length of
radiation. Under normal condition only certain wave lengths are
emitted by an element.
Rutherford's Atomic Model
Evidence for Nucleus and Arrangement of Particles
Having known that atom contain electrons and a positive ion,
Rutherford and Marsden performed their historic "Alpha particle
scattering experiment" in 1909 to know how and where these fundamental
particles were located in the structure of atom.
Rutherford took a thin of gold with thickness 0.0004 cm and bombarded
in with a-particles. He observed that most of the a-particles passed
straight through the gold foil and thus produced a flash on the screen
behind it. This indicated that old atoms had a structure with plenty
of empty space but some flashes were also seen on portion of the
screen. This showed that gold atoms deflected or scattered a-particles
through large angles so much so that some of these bounced back to the
source.
Based on these observations Rutherford proposed a model of the atom
which is known as Rutherford's atomic model.
Assumption Drawn From the Model
1. Atom has a tiny dense central core or the nucleus which contains
practically the entire mass of the atom leaving the rest of the
atom almost empty.
2. The entire positive charge of the atom is located on the nucleus.
While electrons were distributed in vacant space around it.
3. The electrons were moving in orbits or closed circular paths around
the nucleus like planets around the sun.
4. The greater part of the atomic volume comprises of empty space in
which electrons revolve and spin.
Weakness of Rutherford Atomic Model
According to the classical electromagnetic theory if a charged
particle accelerate around an oppositely charge particle it will
radiate energy. If an electron radiates energy, its speed will
decrease and it will go into spiral motion finally falling into the
nucleus. Similarly if an electron moving through orbitals of ever
decreasing radii would give rise to radiations of all possible
frequencies. In other words it would given rise to a continuous
spectrum. In actual practise, atom gives discontinuous spectrum.
X-Rays and Atomic Number
In 1895, W.Roentgen discovered that when high energy electrons from
cathode collide with the anode in the Crook's tube, very penetrating
rays are produced. These rays were named as X-rays.
Explanation
When an electron coming from the cathode strike with the anode in the
crook's tube, it can remove an electron from the inner shell of the
atom. Due to removal of t his electron the electronic configuration of
this ion is unstable and an electron from an orbital of higher energy
drops into the inner orbital by emitting energy in form of a photon.
This photon corresponds to electromagnetic radiations in the x-rays
region.
Relationship Between Wave Length and Nuclear Charge
In 1911, Mosley stablished a relationship between the wave length and
nuclear charge. He found that when cathode rays struck elements used
as anode targets in the discharge tube, characteristic x-rays were
emitted. The wave length of the x-rays emitted decreases regularly
with the increase of atomic mass. On careful examination of his data
Mosely found that the number of positive charges on the nucleus
increases from atom to atom by single electronic unit. He called the
number of positive charges as the atomic number.
Diagram Coming Soon
Bohr's Theory
Rutherford's model of atom fails to explain the stability of atom and
appearance of the line spectra. Bohr in 1913 was the first to present
a simple model of the atom which explained the appearance of line
spectra.
Some of the postulates of Bohr's theory are given below.
1. An atom has a number of stable orbits or stationary states in which
an electron can reside without emission or absorption of energy.
2. An electron may pass from one of these non-radiating states to
another of lower energy with the emission of radiations whose
energy equals the energy difference between the initial and final
states.
3. In any of these states the electrons move in a circular path about
the nucleus.
4. The motion of the electron in these states is governed by the
ordinary laws of mechanics and electrostatic provided its angular
momentum is an integral multiple of h/2p
It can be written as
mvr = nh / 2p
Here mvr becomes the angular momentum of the electron. Thus Bohr's
first condition defining the stationary states could be stated as
"Only those orbits were possible in which the angular momentum of the
electrons would be an integral multiple of h/2p". These stationary
states correspond to energy levels in the atom.
Calculation of Radius of Orbits
Consider an electrons of charge e revolving.
Atomic number and e the charge on a proton.
Let m be the mass of the electro, r the radius of the orbit and v the
tangential velocity of the revolving electron.
The electrostatic force of attraction between the nucleus and the
electron according to Coulomb's law
= Z e x e / r2
Diagram Coming Soon
The centrifugal force acting on the electron.
= mv2 / r
Bohr assumed that these two opposing forces must be balanced each
other exactly to keep the electron in an orbit.
Therefore
Ze2 / r2 = m v2 / r
Multiply both sides by r
r x Ze2 / r2 = r x m v2 / r
Ze2 / r = m v2
OR
r = Ze2 / m v2 .................. (1)
The Bohr's postulate states that only those orbits are possible in which
mvr = nh / 2p
Therefore,
V = nh / 2pmr
Substituting the value of V in eq (1)
r = Ze2 / m(nh/2pmr)2
or
r = Ze2 x 4p2 mr2/n2h2
or
1/r = 4p2mZe2/n2h2
cr
r = n2h2 / 4p2mZe2 ............... (2)
This equation gives the radii of all the possible stationary states.
The values of constants present in this equation are as follows.
H = 6.625 x 10(-27) ergs sec OR 6.625 x 10(-37) J.s
Me = 9.11 x 10(-28) gm OR 9.11 x 10(-31) kg
E = 4.802 x 10(-10) e.s.u OR 1.601 x 10(-19) C
By substituting these values we get for first shell of H atom
r = 0.529 x 10(-8) m OR 0.529
The above equation may also be written as
r = n2 (h2 / 4p2mZe2) x n2 a0 .................... (3)
For the first orbit n = 1 and r = 0.529. This is the value of the
terms in the brackets sometimes written as a0 called Bohr's Radius.
For the second shell n = 2 and for 3rd orbit n = 3 and so on.
Hydrogen Atom Spectrum
Balmer Series
The simplest element is hydrogen which contain only one electron in
its valence shell.
Balmer in 1885 studied the spectrum of hydrogen. For this purpose he
used hydrogen gas in the discharge tube. Balmer observed that hydrogen
atom spectrum consisted of a series of lines called Balmer Series.
Balmer determined the wave number of each of the lines in the series
and found that the series could be derived by a simple formula.
Lyman Series
Lyman series is obtained when the electron returns to the ground state
i.e. n = 1 from higher energy level n(2) = 2, 3, 4, 5, etc. This
series of lines belongs to the ultraviolet region of spectrum.
Paschen Series
Paschen series is obtained when the electron returns to the 3rd shell
i.e. n = 3 from the higher energy levels n2 = 4, 5, 6 etc. This series
belongs to infrared region.
Bracket Series
This series is obtained when an electron jumps from higher energy
levels to 4th energy level.
Heisenberg Uncertainty Principle
According to Bohr's theory an electron was considered to be a particle
but electron also behaves as a wave according to be Broglie.
Due to this dual nature of electron in 1925 Heisenberg gave a
principle known as Heisenberg Uncertainty Principle which is stated
as,
It is impossible to calculate the position and momentum of a moving
electron simultaneously.
It means that if one was known exactly it would be impossible to known
the other exactly. Therefore if the uncertainty in the determination
of momentum is ?px and the uncertainty in position is ?x then
according to this principle the product of these two uncertainties may
written as
?px . ?x ˜ h
So if one of these uncertainties is known exactly then the uncertainty
in its determination is zero and the other uncertainty will become
infinite which is according to the principle.
Energy Levels and Sub-Levels
According to Bohr's atomic theory, electrons are revolving around the
nucleus in circular orbits which are present at definite distance from
the nucleus. These orbits are associated with definite energy of the
electron increasing outwards from the nucleus, so these orbits are
referred as Energy Levels or Shells.
These shells or energy levels are designated as 1, 2, 3, 4 etc K, L, M, N etc.
The spectral lines which correspond to the transition of an electron
from one energy level to another consists of several separate close
lying lines as doublets, triplets and so on. It indicates that some of
the electrons of the given energy level have different energies or the
electrons belonging to same energy level may differ in their energy.
So the energy levels are accordingly divided into sub energy levels
which are denoted by letters s, p, f (sharp, principle, diffuse &
fundamental).
The number of sub levels in a given energy level or shell is equal to
its value of n.
e.g. in third shell where n = 3 three sub levels s, p, d are possible.
Quantum Numbers
There are four quantum numbers which describe the electron in an atom.
1. Principle Quantum Number
It is represented by "n" which describe the size of orbital or energy level.
The energy level K, L, M, N, O etc correspond to n = 1, 2, 3, 4, 5 etc.
If
n = 1 the electron is in K shell
n = 2 the electron is in L shell
n = 3 the electron is in M shell
2. Azimuthal Quantum Number
This quantum number is represented by "l" which describes the shape of
the orbit. The value of Azimuthal Quantum number may be calculated by
a relation.
l = 0 ----> n - 1
So for different shell the value of l are as
n = 1 K Shell l = 0
n = 2 L Shell l = 0, 1
n = 3 M Shell l = 0, 1, 2
n = 4 N Shell l = 0, 1, 2, 3
when l = 0 the orbit is s
when l = 1 the orbit is p
when l = 2 the orbit is d
when l = 3 the orbit is f
3. Magnetic Quantum Number
It is represented by "m" and explains the magnetic properties of an
electron. The value of m depends upon the value of l. It is given by
m = + l ----> 0 ----> l
when l = 1, m has three values (+1, 0, -1) which corresponds to p
orbital. Similarly when l = 2, m has five values which corresponds to
d orbital.
4. Spin Quantum Number
It is represented by "s" which represents spin of a moving electron.
This spin may be either clockwise or anticlockwise so the values for s
may be +1/2 or -1/2.
Pauli's Exclusion Principle
According to this principle
No two electrons in the same atom can have the same four quantum number.
Consider an electron is present in 1s orbital. For this electron n =
1, l = 0, m = 0. Suppose the spin of this electron is s = +1/2 which
will be indicated by an upward arrow ?. Now if another electron is put
in the same orbital (1s) for that electron n = 1, l = 0, m = 0. It can
occupy this orbital only if the direction of its spin is opposite to
that of the first electron so s = -1/2 which is symbolized by downward
arrow ?. From this example, we can observe the application of Pauli's
exclusion principle on the electronic structure of atom.
Electronic Configuration
The distribution of electrons in the available orbitals is proceeded
according to these rules.
1. Pauli Exclusion Principle
2. Aufbau Principle
3. (n + l) Rule
4. Hund's Rule
The detail of these rules and principles is given below.
1. Aufbau Principle
It is states as
The orbitals are filled up with electrons in the increasing order of
their energy.
It means that the orbitals are fulled with the electrons according to
their energy level. The orbitals of minimum energy are filled up first
and after it the orbitals of higher energy are filled.
2. Hund's Rule
If orbitals of equal energy are provided to electron then electron
will go to different orbitals and having their parallel spin.
In other words we can say that electrons are distributed among the
orbitals of a sub shell in such a way as to give the maximum number of
unpaired electrons and have the same direction of spin.
3. (n + l) Rule
According to this rule
The orbital with the lowest value of (n + l) fills first but when the
two orbitals have the same value of (n + l) the orbital with the lower
value of n fills first.
For the electronic configuration the order of the orbital is as follows.
1s, 2s, 2p, 3s, 4s, 3d, 4p, 5s, 4d, 5p, 6s etc.
Atomic Radius
For homonuclear diatomic molecules the atomic radius may be defined as
The half of the distance between the two nuclei present in a
homonuclear diatomic molecules is called atomic radius.
It may be shown as
In case of hetronuclear molecular like AB, the bond length is
calculated which is (rA + rB) and if radii of any one is known the
other can be calculated.
For the elements present in periodic table the atomic radius decreases
from left to right due to the more attraction on the valence shell but
it increases down the group with the increase of number of shells.
Ionic Radius
Ionic radius is defined as
The distance between nucleus of an ion and the point up to which
nucleus has influence of its electron cloud.
When an electron is removed from a neutral atom the atom is left with
an excess of positive charge called a cation e.g
Na ----> Na+ + c-
But when an electron is added in a neutral atom a negative ion or
anion is formed.
Cl + e- ----> Cl-
As the atomic radius, the ionic radii are known from x-ray analysis.
The value of ionic radius depends upon the ions that surround it.
Ionic radii of cations have smaller radii than the neutral atom
because when an electron is removed. The effective charge on the
nucleus increases and pulls the remaining electrons with a greater
force.
Ionic radii of anions have a large radii than the neutral atom because
an excess of negative charge results in greater electron repulsion.
Radius of Na atom = 1.57
Radius of Na+ atom = 0.95 (smaller than neutral atom)
Radius of Cl atom = 0.99
Radius of Cl- atom = 1.81 (larger than neutral atom)
Ionization Potential
Definition
The amount of energy required to remove most loosely bounded electron
from the outermost shell of an atom in its gaseous state is called is
called ionization potential energy.
It is represented as
M(gas) ----> M+(gas) + e- ................... ?E = I.P
The energy required to remove first electron is called first I.P. The
energy required to remove 2nd or 3rd electron is called 2nd I.P or 3rd
I.P
M(gas) ----> M+(gas) + e- ................... ?E = 1st I.P
M+(gas) ----> M++(gas) + e- ................?E = 2nd I.P
M++(gas) ----> M+++(gas) + e- ............ ?E = 3rd I.P
The units of I.P is kilo-Joule per mole.
Factors on which I.P Depends
1. Size of the Atom
If the size of an atom is bigger the I.P of the atom is low, but if
the size of the atom is small then the I.P will be high, due to fact
if we move down the group in the periodic table. The I.P value
decreases down the group.
2. Magnitude of Nuclear Charge
If the nuclear charge of atom is greater than the force of attraction
on the valence electron is also greater so the I.P value for the atom
is high therefore as we move from left to right in the periodic table
the I.P is increased.
3. Screening Effect
The shell present between the nucleus and valence electrons also
decreases the force of attraction due to which I.P will be low for
such elements.
Electron Affinity
Definition
The amount of energy liberated by an atom when an electron is added in
it is called electron affinity.
It shows that this process is an exothermic change which is represented as
Cl + e- ----> Cl- ............ ?H = -348 kJ / mole
Factors on which Electron Affinity Depends
1. Size of the Atom
If the size of atom is small, the force of attraction from the nucleus
on the valence electron will be high and hence the E.A for the element
will also be high but if the size of the atoms is larger the E.A for
these atoms will be low.
2. Magnitude of the Nuclear Charge
Due to greater nuclear charge the force of attraction on the added
electron is greater so the E.A of the atom is also high.
3. Electronic Configuration
The atoms with the stable configuration has no tendency to gain an
electron so the E.A of such elements is zero. The stable configuration
may exist in the following cases.
1. Inert gas configuration
2. Fully filled orbital
3. Half filled orbital
Electronegativity
Definition
The force of attraction by which an atom attract a shared pair of
electrons is called electronegativity.
Application of Electronegativity
1. Nature of Chemical Bond
If the difference of electronegativity between the two combining atoms
is more than 1.7 eV, the nature of the bond between these atoms is
ionic but if the difference of electronegativity is less than 1.7 eV
then the bond will be covalent.
2. Metallic Character
If an element possesses high electronegativity value then this element
is a non-metal but if an element exist with less electronegativity, it
will be a metal.
Factors for Electronegativity
1. Size of the Atom
If the size of the atom is greater the electronegativity of the atom
is low due to the large distance between the nucleus and valence
electron.
2. Number of Valence Electrons
If the electrons present in the valence shell are greater in number,
the electronegativity of the element is high.
CHEMICAL BOND.
Chemical Bond
Introduction
Atoms of all the elements except noble gases have incomplete outermost
orbits and tends to complete them by chemical combination with the
other atoms.
In 1916, W Kossel described the ionic bond which is formed by the
transfer of electron from one atom to another and also in 1916 G.N
Lewis described about the formation of covalent bond which is formed
by the mutual sharing of electrons between two atoms.
Both these scientists based their ideas on the fact that atoms
greatest stability when they acquire an inert gas electronic
configuration.
Definition
When two or more than two atoms are combined with each other in order
to complete their octet a link between them is produced which is known
as chemical bond.
OR
The force of attraction which holds atoms together in the molecule of
a compound is called chemical bond.
Types of Chemical Bond
There are three main types of chemical bond.
1. Ionic bond or electrovalent bond
2. Covalent bond
3. Co-ordinate covalent bond or Dative covalent bond
Ionic Bond OR Electrovalent Bond
Definition
A chemical bond which is formed by the complete shifting of electron
between two atoms is called ionic bond or electrovalent bond.
OR
The electrostatic attraction between positive and negative ions is
called ionic bond.
Conditions for the Ionic Bond Formation
1. Electronegativity
Ionic bond is formed between the element having a difference of
electronegativity more than 1.7 or equal to 1.7 eV.
Therefore ionic bond is generally formed between metals (low
electronegative) and non-metal (high electronegative) elements.
2. Ionization Potential
We know that ionic bond is formed by the transference of electron from
one atom to another, so in the formation of ionic bond an element is
required which can lose its electrons from the outer most shell. It is
possible to remove electron from the outermost shell of metals because
of their low ionization potential values.
3. Electron Affinity
In the formation of ionic bond an element is also required which can
gain an element is also required which can gain electron, since
non-metals can attract electrons with a greater force due to high
electronegativity. So a non-metal is also involved in the formation of
ionic bond due to high electron affinity.
Example of Ionic Bond
In order to understand ionic bond consider the example of NaCl. During
the formation of Ionic bond between Na and Cl2, Sodium loses one
electron to form Na+ ion while chlorine atom gains this electron to
form Cl- ion. When Na+ ion and Cl- ion attract to each other NaCl is
formed. The stability of NaCl is due to the decrease in the energy.
These energy change which are involved in the formation of ionic bond
between Na and Cl are as follows.
i. Sodium has one valence electron. In order to complete its octet Na
loses its valence electron. The loss of the valence electron required
495 kJ/mole.
Na ----> Na+ + e- ....................... ?H = 495 kJ/mole
ii. Chlorine atom has seven electrons in its valence shell. It require
only one electron to complete its octet, so chlorine gains this
electron of sodium and release 348 kJ/mole energy.
Cl + e- ----> Cl- ...................... ?H = -348 kJ/mole
Here the energy difference is 147 kJ/mole (495 - 348 = 147). This loss
of energy is balanced when oppositely charged ions are associated to
form a crystal lattice.
iii. In third step, positively charged Na+ ion and negatively charged
Cl- ion attract to each other and a crystal lattice is formed with a
definite pattern.
Na+(g) + Cl-(g) ----> Na+Cl- ........... ?H = - 788 kJ/mole
This energy which is released when one mole of gaseous ions arrange
themselves in definite pattern to form lattice is called lattice
energy.
From this example, we can conclude that it is essential for the
formation of ionic bond that the sum of energies released in the
second and third steps must be greater than the energy required for
the first step.
Characteristics of Ionic Compounds
1. An ionic compounds, the oppositely charged ions are tightly packed
with each other, so these compounds exist in solid state.
2. Due to strong attractive forces between ions a larger amount of
energy is required to melt or to boil the compound and hence the
melting and boiling point of the ionic compound are generally high.
3. Ionic compounds are soluble in water but insoluble in organic
solvents like benzene, CCl4. etc.
4. In the aqueous solution, the ionic compounds are good electrolytes,
because in water the interionic forces are so weakened that the
ions are separated and free to move under the influence of electric
current. Due to this free movement of ions, the ionic compounds
conduct electricity in their solutions.
Covalent Bond
Definition
A link which is formed by the mutual sharing of electrons between two
atoms is called covalent bond.
Explanation
In the formation of covalent bond, mutual sharing of electron takes
place. This mutual sharing is possible in non-metals, therefore
covalent bond is generally formed between the atoms of non-metals. For
example
In Cl2 molecule, two atoms of chlorine are combined with each other to
form Cl2 molecule. Each atom of chlorine having seven electrons in its
valencies shell. These atoms are united with each other by sharing one
of its valence electron as shown.
Cl Cl: ----> :Cl :Cl OR Cl - Cl
In this molecule, one shared pair of electrons forms a single covalent
bond between two chlorine the atoms. With the formation of a covalent
bond the energy of the system is also decreased.
Cl + Cl ----> Cl - Cl .............. ?H = - 242 kJ / mole
This released energy lowered the energy of the molecule and the
stability of the compound is also increased.
Types of Covalent Bond
There are three main types of covalent bond.
1. Single Covalent Bond
When a covalent bond is formed by sharing of one electron from each
atom, that it is called single covalent bond and denoted by (-) single
line between the two bonded atoms e.g.
Cl - Cl, H - H, H - Br etc.
2. Double Covalent Bond
In a covalent bond, if two electrons are shared from each of the
bonded atom then this covalent bond is called double covalent bond and
denoted by (=) two lines e.g.
O = O, O : : O
3. Triple Covalent Bond
When a covalent bond is formed by sharing of three electrons from each
atom then this type of covalent bond is called triple covalent bond,
and denoted by (=) three lines between the two bonded atoms e.g.
N : : N :, N = N
The bond distance of multiple bonds are shorter and the bond energies
are higher.
Characteristics of Covalent Compounds
The main characteristics properties of covalent compounds are as follows
1. The covalent compounds exist as separate covalent molecules,
because the particles are electrically neutral so they passes
solid, liquid or gaseous state. This intermolecular force of
attraction among the molecules.
2. Since the covalent compound exist in all the three states of matter
so their melting points and boiling point may be high or low.
3. Covalent compounds are non-electrolytes so they do not conduct
electricity from their aqueous solution.
4. Covalent compounds are generally insoluble in water and similar
polar solvent but soluble in the organic solvents.
Co-Ordinate OR Dative Covalent Bond
Definition
It is a type of covalent bond in which both the shared electrons are
donated only be one atom, this type is called co-ordinate covalent
bond.
The 8 ordinate covalent bond between two atoms is denoted by an arrow
(?). The atom which donates an electron pair is called as a donor of
electron and the other atom involved in this bond is called acceptor.
E.g.
A + B ----> A : B OR A ? B
Dipole Moment
Definition
The product of the charge and the distance present in a polar
molecules is called dipole moment and represented by µ.
OR
The extent of tendency of a molecule to be oriented under the
influence of an electric field is called dipole moment.
Mathematical Representation of Dipole Moment
Suppose the charge present on a polar molecule is denoted by e and the
separation between the two oppositely charged poles of the molecules
is d, then the product of these two may be written as
e x d = µ
Where µ is dipole moment.
Dipole Moment in Diatomic Molecules
The diatomic molecules which are made up of similar atoms will be
non-polar and their dipole moment is zero but the diatomic molecules
made up of two different atoms e.g. HCl or Hl are polar and have some
dipole moment. The value of the dipole moment depends upon the
difference of electronegativities of the two bonded atom. If the
difference of electronegativity between the atoms is greater, the
polarity and also the dipole moment of the molecule is greater e.g.
The dipole moment of HCl = 1. debye
Whereas dipole moment of HF = 1.90 debye
Dipole Moment of Poly Atomic Molecules
In poly atomic molecules, the dipole moment of molecules depends upon
the polarity of the bond as well as the geometry of the molecule.
Ionic Character of Covalent Bond
In homonuclear diatomic molecules like Cl2, O2, l2, H2 both the atoms
are identical so the shared electrons are equally attracted due to
identical electronegativities and hence the molecules are non-polar.
When two dissimilar atoms are linked by a covalent bond the shared
electrons are not attracted equally by the two bonded atoms. Due to
unsymmetrical distribution of electrons one end of the molecules
acquire partial positive charge and the other end acquire a partial
negative charge. This character of a covalent bond is called Ionic
character of a covalent bond.
The ionic character of a covalent bond depends upon the difference of
electronegativity of the two dissimilar atoms joined with each other
in a covalent bond. E.g., the H-F bond is 43% ionic whereas the H-Cl
bond is 17% ionic. The ionic character greatly affects the properties
of a molecules e.g., melting point, boiling point of polar molecules
are high and they are soluble in polar solvent like H2O. Similarly the
presence of partial polar character shortens the covalent bond and
increases the bond energies.
Bond Energy
Definition
The amount of energy required to break a bond between two atoms in a
diatomic molecule is known as Bond Energy.
OR
The energy released in forming a bond from the free atoms is also
known as Bond Energy.
It is expressed in kilo Joules per mole or kCal/mole.
Examples
i. The bond energy for hydrogen molecule is
H - H(g) ----> 2 H(g) .......................... ?H = 435 kJ/mole
OR
H(g) + H(g) ----> H - H ....................... ?H = 435 kJ/mole
It can be observed from this example that the breaking of bond is
endothermic whereas the formation of the bond is exothermic.
ii. The bond energy for oxygen molecule is
O = O(g) ----> 2 O(g) ........................ ?H = 498 kJ/mole
OR
O(g) + O(g) ----> O = O .................... ?H = -498 kJ/mole
Bond energy of a molecule also measure the strength of the bond.
Generally bond energies of polar bond are greater than pure covalent
bond.
E.g.
Cl - Cl ----> 2 Cl ........................ ?H = 244 kJ/mole
H - Cl ----> H+ + Cl- ................... ?H = 431 kJ/mole
The value of bond energy e.g., triple bonds are usually shorter than
the double bond therefore the bond energy for triple bond is greater
than double bond.
Sigma & PI Bond
Sigma Bond Definition
When the two orbitals which are involved in a covalent bond are
symmetric about an axis, then the bond formed between these orbitals
is called Sigma Bond.
OR
A bond which is formed by head to head overlap of atomic orbitals is
called Sigma Bond.
Explanation
In the formation of a sigma bond the atomic orbital lies on the same
axis and the overlapping of these orbital is maximum therefore, all
such bonds, in which regions of highest density around the bond axis
are termed as sigma bond.
Types of Overlapping in Sigma Bond
There are three types of overlapping in the formation of sigma bond.
1. s-s orbitals overlapping
2. s-p orbitals overlapping
3. p-p orbitals overlapping
In all the three types, when the two atomic orbitals are overlapped
with each other two molecular orbitals are formed. In these two
molecular orbitals the energy of one orbital is greater than the the
atomic orbitals which is known as sigma antibonding orbital while the
energy of the other orbital is less than the atomic orbital this
orbital of lower energy is called sigma bonding orbital and the shared
electron are always present in the sigma bonding orbitals.
1. s-s Orbitals Overlapping
In order to explain s-s overlapping consider the example of H2
molecule. In this molecule is orbital of one hydrogen overlaps with is
orbital of other hydrogen to form sigma bonding orbitals. Due to this
bonding a single covalent bond is formed between the two hydrogen
atoms.
Diagram Coming Soon
2. s-p Orbitals Overlapping
This type of overlapping takes place in H-Cl molecule. 1s orbital of
hydrogen overlaps with 1p orbital of chlorine to form a single
covalent bond. In this overlapping two molecular orbitals are formed,
one of the lower energy while the other orbital is of higher energy.
The shapes of these orbitals are as follows.
Diagram Coming Soon
3. p-p Orbitals Overlapping
This type of overlapping takes place in fluorine molecule. In this
mole 1p orbital of a fluorine atom is overlapped with 1p orbital of
the other fluorine atom. The molecular orbitals formed in this
overlapping are given in figure
Diagram Coming Soon
PI Bond
When the two atomic orbital involved in a covalent bond are parallel
to each other then the bond formed between them is called pi bond.
In this overlapping, two molecular orbitals are also formed. The lower
energy molecular orbitals is called p bonding orbital while the higher
energy molecular orbital is called p antibonding orbital. The shape of
these molecular orbitals are as follows.
Diagram Coming Soon
Hybridization
Definition
The process in which atomic orbitals of different energy and shape are
mixed together to form new set of equivalent orbitals of the same
energy and same shape.
There are many different types of orbital hybridization but we will
discuss here only three main types.
1. sp3 Hybridization
The mixing of one s and three p orbitals to form four equivalent sp3
hybrid orbitals is called sp3 hybridization. These sp3 orbitals are
directed from the center of a regular tetrahedron to its four corners.
The angles between tetrahedrally arranged orbitals are 109.5º.
It has two partially filled 2p orbitals which indicate that it is
divalent, but carbon behaves as tetravalent in most of its compounds.
It is only possible if one electron from 2s orbital is promoted to an
empty 2pz orbital to get four equivalent sp3 hybridized orbitals.
Diagram Coming Soon
The four sp3 hybrid orbitals of the carbon atom overlap with 1s
orbitals of four hydrogen atoms to form a methane CH4 molecule.
The methane molecule contains four sigma bonds and each H-C-H bond
angle is 109.5º.
2. sp2 Hybridization
The mixing of one s and two p orbitals to form three orbitals of equal
energy is called sp2 or 3sp2 hybridization. Each sp2 orbital consists
of s and p in the ratio of 1:2. These three orbitals are co-planar and
at 120º angle as shown
Diagram Coming Soon
A typical example of this type of hybridization is of ethane molecule.
In ethylene, two sp2 hybrid orbitals of each carbon atom share and
overlap with 1s orbitals of two hydrogen atoms to form two s bonds.
While the remaining sp2 orbital on each carbon atom overlaps to form a
s bond. The remaining two unhybridized p orbitals (one of each) are
parallel and perpendicular to the axis joining the two carbon nuclei.
These generates a parallel overlap and results in the formation of 2 p
orbitals. Thus a molecule of ethylene contain five s bonds and one p
bond.
Diagram Coming Soon
3. sp Hybridization
When one s and one p orbitals combine to give two hybrid orbitals the
process is called sp hybridization. The sp hybrid orbitals has two
lobes, one with greater extension in shape than the other and the
lobes are at an angle of 180º from each other. It means that the axis
of the two orbitals form a single straight line as shown.
Now consider the formation of acetylene molecule HC = CH. The two C-H
s bonds are formed due to sp-s overlap and a triple bond between two
carbon atoms consist of a s bond and two p bond. The sigma bond is due
to sp-sp overlap whereas p bonds are formed as a result of parallel
overlap between the unhybridized four 2p orbitals of the two carbon.
Diagram Coming Soon
Valence Shell Electron Pair Repulsion Theory
The covalent bonds are directed in space to give definite shapes to
the molecules. The electrons pairs forming the bonds are distributed
in space around the central atom along definite directions. The shared
electron pairs as well as the lone pair of electrons are responsible
for the shape of molecules.
Sidwick and Powell in 1940 pointed out that the shapes of the
molecules could be explained on the basis of electron pairs present in
the outermost shell of the central atom. Pairs of electrons around the
central atom are arranged in space in such a way so that the distances
between them are maximum and coulombie repulsion of electronic cloud
are minimized.
The known geometries of many molecules based upon measurement of bond
angles shows that lone pairs of electrons occupy more space than
bonding pairs. The repulsion between electronic pairs in valence
shell, decreases in the following order.
Lone Pair - Lone Pair > Lone Pair - Bond Pair > Bond Pair - Bond Pair
When we apply this theory we can see the variation of angle in the
molecular structures.
Consider the molecular structures of NH3, OH & H2O.
Diagram Coming Soon
Variation from ideal bond angles are caused by multiple covalent bonds
and lone electron pairs both of which require more space than single
covalent bonds and therefore cause compression of surrounding bond
angles.
Thus the number of pairs of electrons in the valency shell determine
the overall molecular shape.
Structure of BeCl2
The two bond pairs of electrons in BeCl2 arrange themselves as far
apart as possible in order to minimize the repulsion between them.
Structure of BF3 OR BCl3
In this molecule three bond pair are present around boron to arrange
themselves as far apart as possible a trigonal structure is formed.
Hydrogen Bond
When hydrogen is bonded with a highly electronegative element such as
nitrogen oxygen, fluorine, the molecule will be polarized and a dipole
is produced. The slightly positive hydrogen atom is attracted by the
slightly negatively charged electronegative atom. An electrostatic
attraction between the neighbouring molecules is set up when the
positive pole of one molecule attracts the negative pole of the
neighbouring molecule. This type of attractive force which involves
hydrogen is known as hydrogen bonding.
ENERGETICS OF CHEMICAL REACTION.
Energetics Of Chemical Reaction
Thermodynamics
Definition
It is branch of chemistry which deals with the heat energy change
during a chemical reaction.
Types of Thermochemical Reactions
Thermo-chemical reactions are of two types.
1. Exothermic Reactions
2. Endothermic Reactions
1. Exothermic Reaction
A chemical reaction in which heat energy is evolved with the formation
of product is known as Exothermic Reaction.
An exothermic process is generally represented as
Reactants ----> Products + Heat
2. Endothermic Reaction
A chemical reaction in which heat energy is absorbed during the
formation of product is known as endothermic reaction.
Endothermic reaction is generally represented as
Reactants + Heat ----> Products
Thermodynamic Terms
1. System
Any real or imaginary portion of the universe which is under
consideration is called system.
2. Surroundings
All the remaining portion of the universe which is present around a
system is called surroundings.
3. State
The state of a system is described by the properties such as
temperature, pressure and volume when a system undergoes a change of
state, it means that the final description of the system is different
from the initial description of temperature, pressure or volume.
Properties of System
The properties of a system may be divided into two main types.
1. Intensive Properties
Those properties which are independent of the quantity of matter are
called intensive properties.
e.g. melting point, boiling point, density, viscosity, surface,
tension, refractive index etc.
2. Extensive Properties
Those properties which depends upon the quantity of matter are called
extensive properties.
e.g. mass, volume, enthalpy, entropy etc.
First Law of Thermodynamics
This law was given by Helmheltz in 1847. According to this law
Energy can neither be created nor destroyed but it can be changed from
one form to another.
In other words the total energy of a system and surroundings must
remain constant.
Mathematical Derivation of First Law of Thermodynamics
Consider a gas is present in a cylinder which contain a frictionless
piston as shown.
Diagram Coming Soon
Let a quantity of heat q is provided to the system from the
surrounding. Suppose the internal energy of the system is E1 and after
absorption of q amount of heat it changes to E2. Due to the increase
of this internal energy the collisions offered by the molecules also
increases or in other words the internal pressure of the system is
increased after the addition of q amount of heat. With the increase of
internal pressure the piston of the cylinder moves in the upward
direction to maintain the pressure constant so a work is also done by
the system.
Therefore if we apply first law of thermodynamics on this system we can write
q = E2 - E1 + W
OR
q = ΔE + W
OR
ΔE = q - W
This is the mathematical representation of first law of thermodynamics.
Pressure - Volume Work
Consider a cylinder of a gas which contain a frictionless and
weightless piston, as shown above. Let the area of cross-section of
the piston = a
Pressure on the piston = P
The initial volume of the gases = V1
And the final volume of the gases = V2
The distance through which piston moves = 1
So the change in volume = ΔV = V2 - V1
OR ΔV = a x 1
The word done by the system W = force x distance
W = Pressure x area x distance
W = P x a x 1
W = P Δ V
By substituting the value of work the first law of thermodynamics may
be written as
q = ΔE + P Δ V
The absorption or evolution of heat during chemical reaction may take
place in two ways.
1. Process at Constant Volume
Let qv be the amount of heat absorbed at constant volume.
According to first law qv = ΔE + P ΔV
But for constant volume ΔV = O
Therefore,
P ΔV = P x O = O
So,
qv = ΔE + 0
Or
qv = ΔE
Thus in the process carried at constant volume the heat absorbed or
evolved is equal to the energy ?E.
2. Process at Constant Pressure
Let qp is the amount of heat energy provided to a system at constant
pressure. Due to this addition of heat the internal energy of the gas
is increased from E1 to E2 and volume is changed from V1 to V2, so
according to first law.
qp = E2 - E1 + P(V2 - V1)
Or
qp = E2 - E1 + PV2 - PV1
Or
qp = E2 + PV2- E1 - PV1
Or
qp = (E2 + PV2) - (E1 - PV1)
But we known that
H = E + PV
So
E1 + PV1 = H1
And
E2 + PV2 = H2
Therefore the above equation may be written as
qp = H2 - H1
Or
qp = ΔH
This relation indicates that the amount of heat absorbed at constant
pressure is used in the enthalpy change.
Sign of ΔH
ΔH represent the change of enthalpy. It is a characteristic property
of a system which depends upon the initial and final state of the
system.
For all exothermic processes ?H is negative and for all endothermic
reactions ?H is positive.
Thermochemistry
It is a branch of chemistry which deals with the measurement of heat
evolved or absorbed during a chemical reaction.
The unit of heat energy which are generally used are Calorie and kilo
Calorie or Joules and kilo Joules.
1 Cal = 4.184 J
OR
1 Joule = 0.239 Cal
Hess's Law of Constant Heat Summation
Statement
If a chemical reaction is completed in a single step or in several
steps the total enthalpy change for the reaction is always constant.
OR
The amount of heat absorbed or evolved during a chemical reaction must
be independent of the particular manner in which the reaction takes
place.
Explanation
Suppose in a chemical reactant A changes to the product D in a single
step with the enthalpy change ΔH
Diagram Coming Soon
This reaction may proceed through different intermediate stages i.e.,
A first changes to B with enthalpy change ΔH1 then B changes to C with
enthalpy change ΔH2 and finally C changes to D with enthalpy ΔH3.
According to Hess's law
ΔH = ΔH1 + ΔH2 + ΔH3
Verification of Hess's Law
When CO2 reacts with excess of NaOH sodium carbonate is formed with
the enthalpy change of 90 kJ/mole. This reaction may take place in two
steps via sodium bicarbonate.
In the first step for the formation of NaHCO3 the enthalpy change is
-49 kJ/mole and in the second step the enthalpy change is -41 kJ/mole.
According to Hess's Law
ΔH = ΔH1 + ΔH2
ΔH = -41 -49 = -90 kJ/mole
The total enthalpy change when the reaction is completed in a single
step is -90 kJ/mole which is equal to the enthalpy change when the
reaction is completed into two steps. Thus the Hess's law is verified
from this example.
CHEMICAL EQUILIBRIUM.
Chemical Equilibrium
Reversible Reactions
Those chemical reactions which take place in both the directions and
never proceed to completion are called Reversible reaction.
For these type of reaction both the forward and reverse reaction occur
at the same time so these reaction are generally represented as
Reactant ≅Product
The double arrow ≅indicates that the reaction is reversible and that
both the forward and reverse reaction can occur simultaneously.
Some examples of reversible reactions are given below
1. 2Hl ≅H2 + l2
2. N2 + 2 H2 ≅2 NH3
Irreversible Reactions
Those reactions in which reactants are completely converted into
product are called Irreversible reaction.
These reaction proceed only in one direction. Examples of such type of
reaction are given below
1. NaCl + AgNO3 ----> AgCl + NaNO3
2. Cu + H2SO4 ----> CuSO4 + H2
Equilibrium State
The state at which the rate of forward reaction becomes equal to the
rate of reverse reaction is called Equilibrium state.
Explanation
Consider the following reaction
A + B ≅C + D
It is a reversible reaction. In this reaction both the changes (i.e.
forward & backward) occur simultaneously. At initial stage reactant A
& B are separated from each other therefore the concentration of C and
D is zero.
When the reaction is started and the molecules of A and B react with
each other the concentration of reactant is decreased while the
concentration of product is increased. With the formation of product,
the rate of forward reaction decreased with time but the rate of
reverse reaction is increased with the formation of product C & D.
Ultimately a stage reaches when the number of reacting molecules in
the forward reaction equalizes the number of reacting molecules in the
reverse direction, so this state at which the rate of forward reaction
becomes equal to the rate of reverse reaction is called equilibrium
state.
Law of Mass Action
Statement
The rate at which a substance reacts is proportional to its active
mass and the rate of a chemical reaction is proportional to the
product of the active masses of the reactant.
The term "active mass" means the concentration in terms of moles/dm3
.Derivation of Equilibrium Constant Expression
Consider in a reversible reaction "m" mole of A and "n" moles of B
reacts to give "x" moles of C and "y" moles of D as shown in equation.
mA + nB ≅xC + yD
In this process
The rate of forward reaction 8 [A]m n
Or
The rate of forward reactin = Kf [A]m n
&
The rate of reverse reaction 8 [C]x [D]y
Or
The rate of reverse reaction = Kf [C]x [D]y
But at equilibrium state
Rate of forward reaction = Rate of reverse reaction
Therefore,
Kf [A]m n = Kf [C]x [D]y
Or
Kf / Kr = [C]x [D]y / [A]m n
Or
Ke = [C]x [D]y / [A]m n
This is the expression for equilibrium constant which is denoted by Ke
and defined as
The ratio of multiplication of active masses of the products to the
product of active masses of reactant is called equilibrium constant.
Equilibrium Constant for a Gaseous System
Consider in a reversible process, the reactants and product are gases as shown
A(g) + B(g) ? C(g) + D(g)
When the reactants and products are in gaseous state, their partial
pressures are used instead of their concentration, so according to law
of mass action.
Determination of Equilibrium Constant
The value of equilibrium constant K(C) does not depend upon the
initial concentration of reactants. In order to find out the value of
K(C) we have to find out the equilibrium concentration of reactant and
product.
1. Ethyl Acetate Equilibrium
Acetic acid reacts with ethyl alcohol to form ethyl acetate and water as shown
CH3COOH + C2H5OH ≅CH3COOC2H5 + H2O
Suppose 'a' moles of acetic acid and 'b' moles of alcohol are mixed in
this reaction. After some time when the state of equilibrium is
established suppose 'x' moles of H2O and 'x' moles of ethyl acetate
are formed while the number of moles of acetic acid and alcohol are
a-x and b-x respectively at equilibrium.
According to law of mass action
K(C) = [CH3COOC2H5] [H2O] / [CH3COOH] [C2H5OH]
K(C) = [x/V] [x/V] / [a-x/V] [b-x/V]
K(C) = (x) (x) / (a-x) (b-x)
K(C) = x2 / (a-x) (b-x)
2. Hydrogen Iodide Equilibrium
For the reaction between hydrogen and iodine suppose a mole of
hydrogen and 'b' moles of iodine are mixed in a scaled bulb at 444ºC
in the boiling sulphur for some time. The equilibrium mixture is then
cooled and the bulbs are opened in the solution of NaOH. Let the
amount of hydrogen consumed at equilibrium be 'x' moles which means
that the amount of hydrogen left at equilibrium is a-x moles. Since 1
mole of hydrogen reacts with 1 mole of iodine 'o' form two moles of
hydrogen iodide hence the amount of iodine used is also x moles so its
moles at equilibrium are b-x and the moles of hydrogen iodide at
equilibrium are 2x.
According to law of mass action
K(C) = [Hl]2 / [H2] [l2]
K(C) = [2x/V]2 / [a-x/V] [b-x/V]
K(C) = 4x2 / (a-x) (b-x)
Applications of Law of Mass Action
There are two important applications of equilibrium constant.
1. It is used to predict the direction of reaction.
2. K(C) is also used to predict the extent of reaction.
To Predict the Direction of Reaction
The value of equilibrium constant K(C) is used to predict the
direction of reaction. For a reversible process.
Reactant ≅Product
With respect to the ratio of initial concentration of the reagent.
There are three possibilities for the value of K
1. It is greater than K(C)
2. It is less than K(C)
3. It is equal to K(C)
Case I
If [Reactant]initial / [Product]initial > K(C) the reaction will shift
towards the reverse direction.
Case II
If [Reactant]initial / [Product]initial > K(C) the reaction will shift
towards the forward direction.
Case III
If [Reactant]initial / [Product]initial > K(C) this is equilibrium
state for the reaction.
To Predict the Extent of Reaction
From the value of K(C) we can predict the extent of the reaction.
If the value of K(C) is very large e.g.
For 2 O3 ≅3 O2 ........... K(C) = 10(55)
From this large value of K(C) it is predicted that the forward
reaction is almost complete.
When the value of K(C) is very low e.g.,
2 HF ≅H2 + F2 ........... K(C) = 10(-13)
From this value it is predicted that the forward reaction proceeds
with negligible speed.
But if the value of K(C) is moderate, the reaction occurs in both the
direction and equilibrium will be attained after certain period of
time e.g., K(C) for
N2 + 3 H2 ≅2 NH3 ............. is 10
So the reaction occurs in both the direction.
Le Chatelier's Principle
Statement
When a stress is applied to a system at equilibrium the equilibrium
position changes so as to minimize the effect of applied stress.
The equilibrium state of a chemical reaction is altered by changing
concentration pressure or temperature. The effect of these changes is
explained by Le Chatelier.
Effect of Concentration
By changing the concentration of any substance present in the
equilibrium mixture, the balance of chemical equilibrium is disturbed.
For the reaction,
A + B ? C + D
K(C) = [C][D] / [A]
If the concentration of a reactant A or B is increased the equilibrium
state shifts tc right and yield of products increases.
But if the concentration of C or D is increased then the reaction
proceed in the backward direction with a greater rate and more A & B
are formed.
Effect of Temperature
The effect of temperature is different for different type of reaction.
For an exothermic reaction the value of K(C) decreased with the
increase of temperature so the concentration of products decreases.
For a endothermic reaction heat is absorbed for the conversion of
reactant into product so if temperature during the reaction is
increased then the reaction will proceed with a greater rate in
forward direction.
ENDOTHERMIC REACTION
Temperature increase ----> More products are formed
Temperature decrease ----> More reactants are formed
EXOTHERMIC REACTION
Temperature increase ----> More reactants are formed
Temperature decrease ----> More products are formed
Effect of Pressure
The state of equilibrium of gaseous reaction is distributed by the
change of pressure. There are three types of reactions which show the
effect of pressure change.
1. When the Number of Moles of Product are Greater
In a reaction such as
PCl5 <----> PCl3 + Cl2
The increase of pressure shifts the equilibrium towards reactant side.
2. When the Number of Moles of Reactant are Greater
In a reaction such as
N2 + 3H2 <----> 2NH3
The increase of pressure shifts the equilibrium towards product side
because the no. of moles of product are less than the no. of moles of
reactant.
3. When Number of Moles of Reactants and Products are Equal
In these reactions where the number of moles of reactant are equal to
the number of moles of product the change of pressure does not change
the equilibrium state e.g.,
H2 + l2 ≅2 Hl
Since the number of moles of reactants and products are equal in this
reaction so the increase of pressure does not affect the yield of Hl.
Important Industrial Application of Le Chatelier's Principle
Haber's Process
This process is used for the production of NH3 by the reaction of
nitrogen and hydrogen. In this process 1 volume of nitrogen is mixed
with three volumes of hydrogen at 500ºC and 200 to 1000 atm pressure
in presence of a catalyst
N2 + 3 H2 ≅2 NH3 ............... ΔH = -46.2 kJ/mole
1. Effect of Concentration
The value of K(C) for this reaction is
K(C) = [NH3]2 / [N2] [H2]3
Increase in concentration of reactants which are nitrogen and hydrogen
the equilibrium of the process shifts towards the right so as to keep
the value of K(C) constant. Hence the formation of NH3 increases with
the increase of the concentration of N2 or hydrogen.
2. Effect of Temperature
It is an exothermic process, so heat is liberated with the formation
of product. Therefore, according to Le Chatelier's principle at low
temperature the equilibrium shifts towards right to balance the
equilibrium state so low temperature favours the formation of NH3
3. Effect of Pressure
The formation of NH3 proceeds with the decrease in volume, therefore,
the reaction is carried out under high pressure or in other words high
pressure is favourable for the production of NH3.
Contact Process
The process is used to manufacture H2SO4 on large scale. In this
process the most important step is the oxidation of SO2 to SO3 in
presence of a catalyst vanadium pentoxide.
2 SO2 + O2 ≅2 SO3 ................... ΔH = - 395 kJ/mole
1. Effect of Concentration
The value of K(C) for this reaction is
K(C) = [SO3]2 / [SO2]2 [O2]
Increase in concentration of SO2 or O2 shifts the equilibrium towards
the right and more SO3 is formed.
2. Effect of Temperature
Since the process is exothermic, so low temperature will favour the
formation of SO3. The optimum temperature for this reaction is 400 to
450ºC.
3. Effect of Pressure
In this reaction decrease in volume takes place so high pressure is
favourable for the formation of SO3.
Common Ion Effect
Statement
The process in which precipitation of an electrolyte is caused by
lowering the degree of ionization of a weak electrolyte when a common
ion is added is known as common ion effect.
Explanation
In the solution of an electrolyte in water, there exist an equilibrium
between the ions and the undissociated molecules to which the law of
mass action can be applied.
Considering the dissociation of an electrolyte AB we have
AB ℘A+ + B-
And
[A+][B-] / [AB] = K (dissociation constant)
If now another electrolyte yielding A+ or B- ions be added to the
above solution, it will result in the increase of concentration of the
ions A+ or B- and in order that K may remain the same, the
concentration AB must evidently increase. In other words the degree of
dissociation of an electrolyte is suppressed by the addition of
another electrolyte containing a common ion. This phenomenon is known
as common ion effect.
Application of Common Ion Effect in Salt Analysis
An electrolyte is precipitated from its solution only when the
concentration of its ions exceed from the solubility product. The
precipitates are obtained when the concentration of any one ion is
increased. Thus by adding the common ion, the solubility product can
be exceeded.
In this solution Ou(OH)2 is a weak base while H2SO3 is a strong acid
so the pH of the solution is changed towards acidic medium.
When Na2CO3 is dissolved in water, it reacts with water such as
Na2CO3 + 2 H2O ℘2 NaOH + H2CO3
In this solution H2CO3 which is weak acid an NaOH which is a strong
base are formed. Due to presence of strong base the medium is changed
towards basic nature.
Solubility Product
When a slightly soluble ionic solid such as silver chloride is
dissolved in water, it decompose into its ions
AgCl ℘Ag+ + Cl-
These Ag+ and Cl- ions from solid phase pass into solution till the
solution becomes saturated. Now there exists an equilibrium between
the ions present in the saturated solution and the ions present in the
solid phase, thus
AgCl ℘Ag+ + Cl-
Applying the law of mass action
K(C) = [Ag+][Cl-] / [AgCl]
Since the concentration of solid AgCl in the solid phase is fixed, no
matter how much solid is present in contact with solution, so we can
write.
K(C) = [Ag+][Cl-] / K
Or
K(C) x K = [Ag+][Cl-]
Or
K(S.P) = [Ag+][Cl-]
Where K(S.P) is known as solubility product and defined as
The product of the concentration of ions in the saturated solution of
a sparingly soluble salt is called solubility product.
the value of solubility product is constant for a given temperature.
Calculation of Solubility Product From Solubility
The mass of a solute present in a saturated solution with a fixed
volume of solvent is called solubility, which is generally represented
in the unit of gm/dm3. With the help of solubility we can calculate
the solubility product of a substance e.g., the solubility of Mg(OH)2
at 25ºC is 0.00764 gm/dm3. To calculate the K(S.P) of Mg(OH)2, first
of all we will calculate the concentration of Mg(OH)2 present in the
solution.
Mass of Mg(OH)2 = 0.00764 gm/dm3
Moles of Mg(OH)2 = 0.00764 / 58 moles / dm3
= 1.31 x 10(-4) moles/dm3
The ionization of Mg(OH)2 in the solution is as follows.
Mg(OH)2 ℘Mg(+2) + 2 OH-
And the solubility product for Mg(OH)2 may be written as,
K(S.P) = [Mg(+2)] [OH-]2
Since in one mole of Mg(OH2) solution one mole of Mg++ ions are
present while two moles of OH- ions are present, therefore in 1.31 x
10(-4) mole/dm3 solution of Mg(OH)2, the concentration of Mg(+2) is
1.31 x 10(-4) moles/dm3 while the concentration of OH- is 2. 62 x
10(-8) moles/dm3. By substituting these values
K(S.P) = [Mg(+2)][OH-]2
= [1.31 x 10(-4)] [2.62 x 10(-4)]2
= 9.0 x 10(-12) mole3 / dm9
So in this way the solubility product of a substance may be calculated
with the help of solubility.
Calculation of Solubility from Solubility Product
If we know the value of solubility product, we can calculate the
solubility of the salt.
For example, the solubility of PbCrO4at 25ºC is 2.8 x 10(-13) moles/dm3.
m = n2 / w1 in kg
m = (w2 / m2) / (w1 / 1000)
m = w2 / m2) x (1000 / w1)
Hydration
Addition of water or association of water molecules with a substance
without dissociation is called Hydration.
Water is a good solvent and its polar nature plays very important part
in dissolving substances. It dissolves ionic compounds readily.
When an ionic compound is dissolved in water, the partial negatively
charged oxygen of water molecule is attracted towards the cation ion
similarly the partial positively charged hydrogen of water molecule is
attracted towards the anions so hydrated ions are formed.
In solution, the number of water molecules which surround the ions is
indefinite, but when an aqueous solution of a salt is evaporated the
salt crystallizes with a definite number of water molecules which is
called as water of crystallization E.g., when CuSO4 recrystallized
from its solution the crystallized salt has the composition CuSO4.
5H2O. Similarly when magnesium chloride is recrystallized from the
solution, it has the composition MgCl2.6H2O. This composition
indicates that each magnesium ion in the crystal is surrounded by six
molecules. This type of salts is called hydrated salts.
It is observed experimentally that the oxygen atom of water molecule
is attached with the cation of salt through co-ordinate covalent bond
so it is more better to write the molecular formulas of the hydrated
salts as given below.
[Cu(H2O)5]SO4 ................. [Mg(H2O)6]Cl2
It is also observed that these compound exist with a definite
geometrical structure e.g., the structure of [Mg(H2O)6]Cl2 is
octahedral and [Cu(H2O)4]+2 is a square planar.
Factors for Hydration
The ability of hydration of an ion depend upon its charge density.
For example the charge density of Na+ is greater than K+ because of
its smaller size, so the ability of hydration for Na+ is greater than
K+ ion. Similarly small positive ions with multiple charges such as
Cu(+2), Al(+3), Cr(+3) posses great attraction for water molecules.
Hydrolysis
Addition of water with a substance with dissociation into ions is
called Hydrolysis.
OR
The reaction of cation or anion with water so as to change its pH is
known as Hydrolysis.
Theoritically it is expected that the solution of salts like CuSO4 or
Na2CO3 are neutral because these solutions contain neither H+ ion nor
OH-, but it is experimentally observed that the solution of CuSO4 is
acidic while the solution of Na2CO3 is basic. This acidic or basic
nature of solution indicate but H+ ions or OH- ions are present in
their solutions which can be produced only by the dissociation of
water molecules.
Theory of Ionization
1n 1880, a Swedish chemist Svante August Arrhenius put forward a
theory known as theory of ionization, in order to account for the
conductivity of electrolytes, electrolysis and certain properties of
electrolytic solutions. According to this theory.
1. Acids, Bases and Salts when dissolved in water yield two kinds of
ions, one carry positive charge and the other carry negative charge.
The positively charged ions are called cations which are derived from
metals or it may be H+ ion but the negatively charged ions which are
known as anions are derived from non-metals
NaCl ----> Na+ + Cl-
H2SO4 ----> 2 H+ + SO4(-2)
KOH ----> K+ + OH-
2. Ions in the solution also recombine with each other to form neutral
molecules and this process continues till an equilibrium state
between an ionized and unionized solid is attained.
CHEMICAL KINETICS.
Chemical Kinetics
Introduction
The branch of physical chemistry which deals with the speed or rate at
which a reaction occurs is called chemical kinetics.
The study of chemical kinetics, therefore includes the rate of a
chemical reaction and also the rate of chemical reaction and also the
factors which influence its rate.
Slow and Fast Reaction
Those reactions for which short time is required to convert a reactant
into product are called fast reaction but if more time is required for
the formation of a product then the reactions are called slow
reactions.
Usually ionic reactions which involve oppositely charged ions in
aqueous medium are very fast. For example, reaction between aqueous
solution of NaCl and AgNO3 gives white precipitates of AgCl
instantaneously.
AgNO3 + NaCl ----> AgCl + NaNO3
Such reactions are very fast and these are completed in fractions of seconds.
But those reactions which involve covalent molecules take place very
slowly. For example, conversion of SO2 into SO3
2 SO2 + O2 ----> 2 SO3
It is a slow reaction and required more time for the formation of a product.
Rate Or Velocity of a Reaction
Definition
It is the change in concentration of a reactant or product per unit time.
Mathematically it is represented as
Rate of reaction = Change in concentration of reactant or product /
Time taken for the change
The determination of the rate of a reaction is not so simple because
the rate of a given reaction is never uniform. It falls off gradually
with time as the reactants are used up. Hence we can not get the
velocity or rate of reaction simply by dividing the amount of
substance transformed by the time taken for such transformation. For
this reason we take a very small interval of time "dt" during which it
is assumed that velocity of reaction remains constant. If "dx" is the
amount of substance transformed during that small interval of time
"dt" then the velocity of reaction is expressed as
Velocity of a reaction = dx / dt
Thus with the velocity of a chemical reaction we mean the velocity at
the given moment or given instant.
The Rate Constant
Definition
The proportionality constant present in the rate equation is called
rate constant.
According to law of mass action we know that the rate of chemical
reaction is directly proportional to the molar concentration of the
reactants. For example
R ----> P
The rate of reaction 8 [R]
Or
dx / dt = K [R]
Where K is known as rate constant.
Specific Rate Constant
When the concentration and temperature both are specified, the rate
constant is known as specific rate constant.
When the concentration of each reactant is 1 mole per dm3 at given
temperature, the specific rate constant numerically equals to the
velocity of the reaction.
dx / dt = V = K [R]
Or
K = V / [R]
When R = 1 mole/dm3
K = V
But when different reactant are reacting with different number of
moles then the value of K may be calculated as
2 SO2 + O2 ----> 2 SO3
= dx / dt = K [SO2]2 [O2]
Or
K = V / [SO2]2 [O2]
Determination of Rate of Reaction
There are two method for the determination of rate of a chemical reaction.
1. Physical Method
When the rate of a chemical reaction is determined by using physical
properties such as colour change, volume change, state change the
method known as physical method.
2. Chemical Method
In the method the change in concentration of reactant or product is
noted and with the help of this change rate of reaction is determined
e.g.,
For the reaction R ----> P
Velocity of reaction = - d[R] / dt = + d[P] / dt
The negative sign indicates a decrease in concentration of the
reactant while positive sign indicates an increase in the
concentration of product.
Ionization is thus a reversible process. To this process, the law of
mass action can be applied as
K(C) = [Na+] [Cl-] / [NaCl]
3. The number of positive and negative charges on the ions must be
equal so that the solution as a whole remains neutral.
4. The degree of ionization of an electrolyte depends upon (a) the
nature of electrolyte, (b) dilution of the solution (c) the
temperature
5. When an electric current passes through the solution of an
electrolyte the positive ions i.e., the cations move towards the
cathode and the anions move towards the anode. This movement of ions
is responsible for the conductance of electric current through
the solution.
6. The electrical conductivity of the solution of an electrolyte
depends upon the number of ions present in the solution. On
reaching the electrodes, the ions lose their charge and change into
neutral atoms or molecules by the gain or loss of electrons.
Applications of Arrhenius Theory
This theory explain many peculiarities in the behaviour of
electrolytic solutions.
For example, the elevation in boiling point of 1 molal solution of
glucose is 0.52ºC while this elevation in 1 molal solution of NaCl is
1.04ºC. This difference in elevation of boiling point can be explained
on the basis of Arrhenius theory.
In one molal solution of glucose the number of (molecules) particles
are 6.02 x 10(23) per dm3 of solution while in 1 molal solution of
NaCl 6.02 x 10(23) ions of Na+ and 6.02 x 10(23) ions of Cl- are
present because NaCl is an ionic compound. Since the number of
particle are double in NaCl solution, therefore the elevation in
boiling point is also double than the solution of glucose.
Similarly the other collegative properties such as lowering in vapour
pressure, depression in freezing point and osmosis are explained on
the basis of this theory.
Note
Collegative properties are those properties which depends upon the
number of particles.
Conductance of Electric Current Through Solutions
The ability of a solution to conduct electric current depends upon the
ions present in the solution. The conductance of a solution is
increased when
1. The solution is diluted
2. The degree of dissociation of the electrolyte is high
3. The temperature of the solution is high
4. The velocity of the ions is high
But in a concentrated solution, the number of ions per unit volume of
solution increases and the distance between ions decreases causing
strong interionic attraction. As a result, migration of ions becomes
more difficult and the conductance decreases with increase in
concentration. As the conductance is related with the movement of
ions, so conductance increase with the increase of absolute velocity
of ions in the solution.
The conductance of an electrolyte also depends upon the degree of
ionization. The degree of ionization is denoted by a and calculated as
a = No. of dissociated molecules / Total molecules dissovled
Electrolysis
Electrolyte
A chemical substance which can conduct electric current in molten form
or in its aqueous solution with a chemical change is called
electrolyte.
Electrolysis
The movement of anions and cations towards their respective electrodes
with all accompanying chemical changes in an electrolytic solution
under the influence of electric current is known as electrolysis.
Explanation
To explain the phenomenon of electrolysis consider the example of
CuCl2 solution. the ionization of CuCl2 in the solution may be
represented as
CuCl2 <----> Cu+2 + 2 Cl-
When electric current is passed through this solution, the movement of
these ions begins to take place Cu+2 ions migrate towards cathode and
Cl- ions towards anode. At cathode Cu+2 ions are discharged as copper
atoms by the gain of electrons (reduction)
Cu+2 + 2 e- ----> Cu(M) ........ Reduction at Cathode
At anode Cl- ions are discharged as Cl2 by the loss of electrons (oxidation)
2 Cl- - 2 e- ----> Cl2(g0 ...... Oxidation at Anode
The overall reaction of the electrolysis may be written as
Cu+2 + 2 e- ----> Cu(M)
2 Cl- - 2 e- ----> Cl2(g)
Cu+2 + 2 Cl- ----> Cu(M) + Cl2(g)
OR
CuCl2 ----> Cu(M) + Cl2(g)
When all the ions present in the solution have been changed to neutral
particles, the flow of current is stopped….
THE END
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