**GASES:-** Is the branch of chemistry which deals with measurable quantities.

**PARTS OF PHYSICAL CHEMISTRY**

The physical chemistry is studied under the following sub topics. These are

1. States of matter

2. Chemical equilibrium

3. Thermochemistry/ Energetics

4. Electrochemistry

5. Chemical kinetics

**1. STATE OF MATTER**

This is the form in which matter do exist. There are three states of matter. These are

a) Gaseous state

b) Liquid state

c) Solid state

**A. GASEOUS STATE**

This is the form in which matter do exist in motion.

**PROPERTIES OF GASEOUS**

Properties of gases are governed by kinetic theory of gases (

**THE KINETIC THEORY OF GASES**

1. Kinetic theory of gases include the following points or postulates.

2. Gases contain large number of molecules which are in continuous random motion.

3. Molecules of gases are far away such that the force of attraction between individual molecules is negligible kinetic energy of the molecules is directly proportion to absolute temperature i.e the increase of temperature will causes the increases in kinetic energy of the molecules.

4. The values of individual molecules of gases is negligible compared to the volume of the container.

5. Pressure of the gas inside the container is due to the collision between molecules of the gas and the wall of the container.

6. The collision of molecules of gases are perfectly elastic that is kinetic energy is conserved (Kt before is equal to K.E after collision).

**CLASSIFICATION OF GASES**

Gases are categorized into two groups

These are

i) Ideal gases

ii) Real gases

**i. IDEAL GASES**

Ideal gases are gases which obey all assumption of kinetic theory and also they do obey the ideal gas equation

i.e PV = nRT.

Where by

P = Pressure of the gases

V = Volume of the gases

n = Number of moles of gases

R = Universal of gas constant

T = Temperature

**ii. REAL GASES**

Real gases are the gases which do not obey all the assumptions of kinetic theory of gases. Such assumptions are:

i. The volume of individual molecules of the gases is negligible compared to the volume of the container.

ii. Molecules of gases are far away such that the force of attraction between individual molecules is negligible.

From kinetic theory of gases, scientist comes up with the formula / equation that is governed by the theory the equation is

PV = Nm

Where by

P = Pressure of the gas

V = Volume of the gas

N = Number of the molecules of the gas

m = Mass of molecules of the gas

= Means square speed of the molecules

= Is given by

**DEDUCTION OF GASES LAWS FROM KINETIC THEORY OF GASES**

This is the process by which gas laws are obtained or derived from kinetic theory of gases.

**Such laws to be deduced are:**

i. Charles’s law.

ii. Boyle’s laws.

iii. Graham’s law of diffusion/ effusion.

iv. Dalton’s law of partial pressure.

v. Avogadro’s law.

**1. DEDUCTION OF CHARLES’ LAW**

It state that “ At constant pressure the volume of a fixed mass of gas is directly proportion to the absolute temperature .

i.e The ratio of volume of temperature is constant.

Thus,

From kinetic theory of gases

PV = Nm For any gas to obey charle’s law

V = k From kinetic theory of gases

= T

V = KT

=

**QUESTION**

a) Define the following terms

i) Real gases.

ii) Ideal gases.

b) State Charles’s law.

c) Deduce Charles law from kinetic theory of gases.

**2. DEDUCTION OF BOYLE’S LAW FROM KINETIC THEORY OF GASES**

It state that “ At constant thermodynamic volume of a fixed mass of gas is inversely proportional to pressure.

From kinetic of gases

PV = Nm

From gas to obey Boyle’s law

PV = K

Hence Boyle’s law deduced

**3. DEDUCTION OF GRAHAM’S LAW FROM KINETIC THEORY OF GASES**

Graham’s rate of diffusion or effusion: It states that,

“The rate of diffusion or effusion of gaseous material is inversely proportional to the square root of its density”

If rate is represented by r and density by ρ

For two gases which are G1 and G2

For Gas1

Comparison

For the ratio of their rates

In terms of their density

If the volume is constant

In terms of their masses

**4. DEDUCTION OF GRAHAM’S LAW**

From Graham’s law

From kinetic theory of gases

Pv = Nm

3PV = Nm

But Nm = m

=

=

For any gases to obey graham’s law

3P = k

constant = 1

3P = 1

Now,

=

=1/

But,

= r2

2 =

Hence grahams law deduced

**DALTON’S LAW OF PARTIAL PRESSURE**

It state that

“ The total pressure of gases which are not reacting is equal to the sum
of pressure of individual gases in a container” Consider the two gases
which are;

Gas A and Gas B

Each gas will create its own pressure.

Therefore the pressure of gases will be,

PA for gas A

PB for gas B

From Dalton’s law of partial pressure,

PT = PA + PB

Where by

PT is the total pressure of all gases in the container.

**DEDUCTION OF DALTON’S LAW OF PARTIAL PRESSURE FROM KINETIC THEORY OF GASES**

From Dalton’s law for gas A and B

PT = PA + PB

From kinetic theory of gases

PV = Nm

Since the volume is common.For gas A

PAV = NAmA A

Since the volume is common.

For gas B

PBV = NBmB B

If Pt is the total pressure

V is the common volume

Nt is the total number of molecules

M is the total mass of molecules

is the sum of of A and B

PtV= Nt m

Nt =

But Nt = NA + NB

Since K. E is conserved ( It is the same before and after )

= MA = MB PT = PA + PB, Hence Dalton law deduced

**QUESTION**

Deduced the Avogadro’s law from kinetic theory of gases

**THE IDEAL GAS EQUATION**

This is the equation which is obeyed by all ideal gases.

Formulation of ideal gas equation

The ideal gas equation is formed from the combination of two gas law . These are

i) Charles’s law

ii) Boyle’s law

i) Charle’s law

V T

ii) Boyle’s law

V

Combining

V

V =

V = kT

k represent universal gas constant which is denoted by R.

PV = RT

This is exactly for one mole of a gas.

For n moles of the gas

PV = nRT

Where

P is the pressure of the gas

V is the volume of the gas

n is the number of the moles of the gas

R is the universal constant

T is the absolute temperature

#### Units for R

R can be written as;

i) R = 0.0821 atm moles

ii) R = 8.314 -1 mol -1

Some questions need just general gas equation.

Recall

**DEVIATION OF REAL GASES FROM IDEAL BEHAVIOUR**

From kinetic theory of gases it has been observed that gases which do obey all assumption are termed as ideal gases.

For an ideal gas PV is exactly = 1

PV = nRT

For one mole of a gas.

PV = RT

The ratio of PV to RT is exactly 1.0

= 1.0

Real gases do deviate from this behaviour at high pressure and low
pressure.Therefore the variation of pressure cause the fluctuation on
the value of
and this bring about the deviation of real gases from ideal behaviour.
This deviation is graphically represent when the graph of v/s Pressure is plotted.

The graph of v/s P (Amagat curve)

**TERMS**

Critical temperature

It is the temperature above which the gas cannot be liquified without further cooling.

Critical pressure

It is the pressure at which the gas start to liquefy.

**APPLICATION OF IDEAL GAS EQUATION**

Ideal gas equation is applied in the following aspects;

1. Determination of moral mass of the gas.

From ideal gas equation

PV = nRT

But, n is the number of moles

n =

PV = RT ×

=

Mr =

Example 1

a) Define the following terms

i) Critical pressure

ii) Ideal gas

iii) Real gas

iv) Critical temperature

b) “Some gases are ideal while other are not

c) 1.27 of sample of oxide of nitrogen believed to be either NO or NO2
occupy the volume of 1.07 dm3 at 250c and pressure of 737 mmHg.
Explain what oxide is it and why? R = 0.0821 atm mol -1 k -1 L.

Solution

Mass = 1. 27g

Volume = 1.07 dm3

Temperature = 737 mmHg

R = 0.0821

Unit conversion

1 dm3 = 1.0 L

T = 273 + 25 = 298k

1 atm = 760 mmHg

= 0.97 atm

Mr =

Mr =

Mr = 29.9g/mol

Theoretical molar mass

NO2 = 14 + 32 = 46

NO = 30

∴ The gas is NO because the molar mass is 30 g/mol.

2. Determination of densities of gaseous materials

From ideal gas equation

PV = nRT

But n =

PV = RT

Mr =

MrP =

But, =

Example 1

At what temperature would the oxygen gas be if the pressure is kept
constant at 745 mmHg . If the density of the gas is 1.00g/dm3. Given
that

R is 0.0821 atm mol -1 k-1 L

Solution

From O2

Mr = .32

Pressure = 745

R = 0.0821

Density = 1.00g/dm3

T = ?

T =

= 381.9k

… The temperature required = 381.9k

Example 2

What is the volume occupied by 13.7g of chlorine gas at 45oc and 745 mmHg

R = 0.0821 atom mol-1 k-1 L

Solution

M = 13.7g

T = 45oc

P = 745mmHg

R = 0.0821

Mr = 71

Conversion of units

T = 45 + 273 = 318K

P = 1 atm = 760mmHg

T = 745

P = 0.98 atm

From

PV Mr = PV

=

V =

V =

V = 5.14 Liters

∴ The volume of chlorine gas is 5.14dm3

**EXAMPLES ON GAS LAWS**

Example1

A certain mass of an ideal gas has a volume of 3.25dm3 at 25oc and 1.01 105 NM -2 . What pressure is required to compress it to 1.88dm3 at the some temperature.

Solution

V1 = 3.25dm

T1 = 25OC

P1 = 1.01 105 NM-2

T2 = 250

P2 = ?

V2 = 1.88

So.

=

=

Note:

P2 = 1.746 105NM-2

1.01 105NM-2 = 1atm

1.01 105NM-2 = 760 mmHg

1 NM-2 = 1 Pa

Example 2.

It takes 54.4 sec. for 100cm3 of a gas to effuse through an aperture and 36 . 5 sec for 100cm3 of O2 to effuse through the same aperture

i) What is the molar mass of gas X

ii) Suggest the gas X

Solution

Rate

From Graham’s law

MrX = 70.9

MrX≈71

i) The molar mass of gas X is 71g/mol

ii) The gas X is chlorine gas

**Example 3**

a) Define the following terms

i. Effusion

ii) Critical temperature

b) State Grahm’s law of diffusion

A certain volume of hydrogen takes 2min and 10 sec to diffuse through a
porous plug and an oxide of nitrogen takes 10min 223 sec.

What is:

i) Molar mass of an oxide

ii) Give the following of an oxide

**Solution**

V be the volume of hydrogen

V be the volume of oxide

t0 = 623 sec MH = 2

tH = 130 sec

M0 = 46

i) The moles mass of the oxide is 46g/mol

ii) The formula of the oxide is NO2

iii) Effusion is the escaping of a gas through a porous without molecular collision between molecules of gas.

iv) Graham’s law of diffusion state that. At the same temperature and pressure the rate of diffusion of different is inversely proportional to the square roots their Mr mass.

v) Critical temperature is the temperature above which the gas cannot be liquefied without further cooling.

Example 4

a) State the kinetic theory of gases

b) Write down the equation of the gas which do obey all assumption in (a) above and define the terms

c) A plug of cotton wool one soaked in conc. Hcl where inserted into opposite ends of a horizontal glass tube

A disc of solid ammonium chloride formed in the tube plug is the 1m long how for from the ammonia plug is the deposited

**Solution**

Reaction

NH3 + Hcl NH4

##### 21407 429.4X + 2.147X2 = X2

2.147 X2 **Solving quadratically**

The solid deposit 59.4 cm away from N

**a) The kinetic theory of gases states that**

i) Molecules of a gas are far way such that force of attraction between the individual molecule is neglible

ii) The collision of gas molecules are perfectly elastic

iii) The pressure of a gas inside the container is due to the collision between the molecules of the gas and the wall of the container

iv) Gases container a large number of molecules which exist in continuous random motion

v) Kinetic energy of molecules is directly proportional to the absolute temperature

vi) The volume of individual molecules of the gas is negligible compared to the volume of the container.

**b) Equation of the gases that obey kinetic theory of gases is as follows:**

**PV = nRT**

Where by

P = Is the pressure of the gas

V = Is the volume of the gas

n = I s the number of molecules of the gas

R = is the universal constant

T = Is the absolute temperature

Example 5.

A) A certain volume of SO2 diffuses through a porous plug in 10.0 min and the same volume of second gas takes 15.8 min. Calculate the relative molecules mass of the second gas

B) Nicked from a carbonyl, Ni (CO) n Deduce the value of n from the fact that carbon monoxide diffuse 2.46 times faster than the carbon compound .

Solution

Let V be the volume of SO2

V be the volume of gas x (gx)

Solution

Mr of Ni (CO)n = 59 +(28)n

Mr of CO = 28

Let time takes for carbonyl to diffuse = x

Time taken for carbon monoxide to diffuse = 2.46x

From Graham’s law

28 = 9.75 + 4.62n

0.165 =

28 = 9.75 + 4.62n

=

n = 3.9 4

The volume of n in Nl (CO) is 4

**MOLE FRACTION OF A GAS**

Mole fraction of a gas is defined as the ratio of number of mass of such gas per total moles of gases present

The moles fraction is denoted by ( )

Example

If there are two gas ie. Gas A and gas B in the container. Show how can you find the mole fraction each gas

Solution

Gases present

Gas A and gas B

Let nA be number of moles of gas A

nB be number of moles of gas B

nT = nA + nB

=

= =

**Note**

When mole are expressed in % will sum up to 100%

And when expressed in decimal will not exceed 1.00

From the example above In %

In decimals

Ie

**Example**

The container was found to have 8g of oxygen and 4.4g of CO2. What is the percentage composition of O2 and CO2 in the container

**Solution**

Mass of oxygen = 8g

Mass of carbon dioxide = 4.4g

No of mole of O2 =

=

= 0.25

No of moles of CO2 =

= 0.1

Total number of moles = 0.1 + 0.25

= 0.35

% composition of m moles =

= 0.174 100

= 71.4%

% composition of CO2 = 100

= 0.285 100

= 29%

The percentage of composition of O2 and CO2 in the container are 71.4% and 29%

Critical pressure is the pressure at which the gas starts to liquify

Example

A mixture of CO and CO2 diffusion through a porous diagram in on half of the time taken for the same volume of Bromine vapour. What is the composition by volume of the mixture?

Solution

Let time taken by Br2 be t

Time taken by the mixture CO + CO2 be

Volume I is common rate of mixture = tare of Br2

but

= rate for mixture

= rate Br2

Mr Br2 = 80

= 2 =

=

4 =

M = 40

Mr of CO = 28

Mr of CO2 = 44

CO Mr CO2 Mr CO2 = 40

CO 28 + CO = 40

CO CO = 1

CO2 = 1 CO

CO 28 1

28 CO CO = 40

= 40 44

=

CO = 0.25

% Of CO = 25%

% Of CO2 = 75%

**VAN DER WAAL EQUATION**

The deviation of real gases from ideal behaviour has been stuglied by
different scientist such as Amagat who deter minal different curves in P

Later on van der wall explained the deviation and gave his equation
which tries to work / take particle volume and attraction into account

In his equation

i) He subtracted the particle volume from the volume of the
container. If the volume of container is V and that of particular be
presented as “b”

Then the total volume of the system will be

V b

This is called “Volume correction”

ii) He also added change in pressure which is caused by the existence of intermolecular forces of attraction among the gaseous molecules

This

But n = 1 for 1mole

This is correction in pressure.

From ideal gas equation

PV = nRT (n = 1)

PV = RT

For one mole of the gas

Where “a” is a van der Waal constant

**Note**

In the van der Waal equation is added to the total pressure in order to cancel the effect of intermolecular forces of attraction

Expansion of the Van der waal equation

From Van der Waal’s equation

PV

PV = RT The equation normally work under two assumption these is

If pressure is small then the volume is maximum

The terms Pb and can be neglected

PV = RT – a/V

ii) When the pressure is very low that is P is approaching O P O

So V will be infinity V is We can calculate that the three term for correction can be neglected

PV = RT

This is for one mole

General conclusion

At very low pressure the real gases normally behave as ideal gases

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