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Molar Volume

According to the kinetic gas theory, gases are composed of molecules. These molecules are in constant random motion in a straight line. The gas molecules are rigid spheres which exert pressure on the wall of the container due to collision with each other and with a wall of container. These collisions are completely elastic in nature and there will be no loss of energy during collisions.

Pressure, volume and temperature are major factors which are used to determine the other properties of any gas. The volume of gas can be measured with the help of a gas syringe or an upturned measuring cylinder. The molar volume helps to understand the mole concept of gas. It represents the volume of one mole of gas at STP conditions. You must be aware of the ideal gas equation of gases that is

PV = nRT
.

The volume of one mole of gas is called the molar gas volume. The volume of gas produced in a chemical reaction can be measured by collecting it over water. Let’s discuss the determination of the molar volume of gas and its applications.

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Molar Volume of a Gas

One mole of any gas at a given temperature and pressure has same fixed volume and is better known as its Molar gas volume.
In order to compare the molar volume of gases, chemists use a fixed reference of temperature and pressure. This is called as "Standard temperature and pressure (abbreviated as S.T.P)".

The standard temperature used is 273 Kelvin or 0o C and the standard pressure is 1 atmospheres (760 mm Hg). At STP we find experimentally that one mole of any gas occupies a volume of 22.4 liters. The equation can be written as:

1 mole of a gas at STP = 22.4 liters of a gas

According to the ideal gas law, and the three simple gas laws:

1. Boyle's Law : V $\propto$$\frac{1}{P}$ (T, n constant)
2. Charle's Law : V $\propto$ T (n, P constant)
3. Avogadro's Law : V $\propto$ n ( P, T constant)

These three laws can be combined into a single more general law:

V $\propto$ n $\frac{T}{ P}$

This is called as Universal Gas Law. It is also called Ideal Gas Law as it applies to all gases which exhibit ideal behavior, i.e, obey the gas laws perfectly. The ideal gas law may be stated as:

"The volume of a given amount of gas is directly proportional to the number of moles of gas, directly proportional to the temperature and inversely proportional to the pressure."

Introducing the proportionality constant R in the expression (1), we can write:

V = R n $\frac{T}{P}$

P V = n R T

Determining the Molar Volume of a Gas

Molar volume is considered to be the volume occupied by one mole of any gas at a given pressure and temperature.
This is denoted by Vm.
The Molar volume unit is found to be litre per mole or milliliter per mole. The Molar volume determination of any substance is invariably depending on temperature and pressure.
As per the Avogadro law, "at constant temperature and pressure, equal volumes of any gas would contain equal number of molecules." This leads to the assumption that equal number of molecules of any gas, should occupy the same volume, provided, there is constant temperature and pressure.

Example of oxygen

Mass of 1 liter of oxygen at STP = 1.59 g

Mass of 1 mole of oxygen = 32 g

Volume : Mass

1 liter : 1. 59 g

x : 32 g

'x' = (32 / 1.59) litres = 20.126 litres

Molar Volume at STP

The table given below provides the relationship existing between Gram Molecular Weight (GMW), moles, the molar volume and the number of particles of gases at standard temperature pressure.

Gas Molecular Formula
GMW
(in g)
No.of Moles
Molar Volume
dm3 or l
No.of moles in 1 mole
Hydrogen H2 2 1 22.4 6.023x 1023
Oxygen O2 32 1 22.4 6.023x 1023
Nitrogen N2 28 1 22.4 6.023x 1023
Chlorine Cl2 71 1 22.4 6.023x 1023
Carbon dioxide CO2 44 1 22.4 6.023x 1023
Nitrogen dioxide NO2 46 1 22.4 6.023x 1023
Ammonia NH3 17 1 22.4 6.023x 1023
Methane CH4 16 1 22.4 6.023x 1023
Sulphur dioxide SO2 64 1 22.4 6.023x 1023

Standard Molar Volume

Standard molar volume of a gas is the volume occupied by 1 mole of any gas at 273 K and 1 atmospheric pressure (STP). It is equal to 22.4 liters of 22,400 ml. It is the same for all gases.

S.T.P. = Standard Temperature and Pressure

Standard Temperature = 0oC or 273 K

Standard Pressure = 1 atm or 760 mm of mercury

Partial Molar Volume

When a liquid is present in a mixture, the volume of one component depends upon the molecules that are surrounding that particular liquid. Partial molar volume is the volume contributed by any particular component in the mixture. So, if A and B are present in a mixture, the partial molar volume will be given both with respect to A and with respect to B.

Thus, Partial molar volume of A would be: Change in volume of the mixture, per mole of A added to it. This can be best represented with the help of one solvent, say water, added to another solvent, like benzene or ether.
Partial molar volume of B would be: Change in the volume of the mixture per mole of B added to it.

Molar Volume of Water

We know that volume occupied by one mole of a gas is its molar volume. This applies to a liquid and a solid too. So, molar volume of water, a liquid is the volume occupied by one mole of water, in any form. So, 1 mole of water occupies 18 grams. Since density of water is almost equal to 1, we take the grams of water as volume of water. So, Molar volume, or the volume occupied by one mole of water would be 18 milliliters.

Now, what would be the partial volume of water in a mixture?
To give an example for partial molar volume, let us take two solvents
• Water
• Ethanol
When we add one mole of water to 100 liters of water already present in a vessel, the volume of the liquid will increase by 18 ml. So, this shows that water has a partial molar volume of 18ml/mol in that mixture.

When we add the same one mole of water to 1000ml of Ethanol, instead of 18 ml increase, the volume of the mixture is raised only by 14 ml. So, the partial molar volume depends upon the degree of solvation or the number of moles of surrounding water particles per one mole of water particle.

Molar Volume Problems

Solved examples on calculating molar volume are given below-

Solved Examples

Question 1: Find out the volume contained by 6.8 g of ammonia at STP. (N=14, H=1)
Solution:
Gram molecular mass of NH3 =  [N = 1 x 14)] + [H = (3 + 1)] = 14 + 3 = 17 g

The mass of 1 mole of NH3 = 17g

Molar volume = 22.4 liters

Volume of 6.8 g of ammonia at STP = ?

The ratio between mass and volume is as follows:

17 g : 22.4 liters

6.8 g : x

x = (6.8 x 22.4) / 17 = 8.96 Liters

Volume occupied by 6.8 g of ammonia at STP = 8.96 liters

Question 2: 112 ml of CO2 has a mass at 0.22 g at standard conditions. What would be the molar mass of CO2.
Solution:
Mass of 112 ml of CO2 at STP = 0.22 g

Mass of 22400 ml of CO2 = ?

The ratio of mass to volume is as follows

0.22 g : 112 ml

x g : 22400 ml

'x' g = (0.22 x 22400) / 112 = 44 g

The mass of 22400 ml of CO2 at STP = 44 g

The molar mass of CO2 = 44 g per mole

Question 3: One gram of pure SO2 has a volume of 450 ml at STP. What would be the Relative Molecular Mass of SO2.
Solution:
Volume of sulfur dioxide gas = 450 ml at STP

Mass of sulfur dioxide gas = 1 g

Mass of one mole of sulfur dioxide = x g/mole

Volume of 1 mole of sulfur dioxide = 22400 ml at STP

Mass : Volume

1 : 450 ml

x : 22400 ml

x = (22400 x 1) / 450 = 49.78

Mass of 1 mole of SO2 = 49.78 g/mole

Relative molecular mass of sulfur dioxide = 49.78

Question 4: Find the mass of 1 mole of CO, if 150 ml of CO contains a mass of 0.225 g at standard conditions.
Solution:
The CO volume = 150 ml

The mass of CO = 0.225 g

The molar volume = 22400 ml

Mass of 1 mole of CO = ?

The ratio between mass and volume is as follows

150 ml : 0.225 g

22400 ml : x g

'x' = (22400 x 0.225) / 150 = 33.6 g

Mass of one mole of CO = 33.6 g/mole

Relative molecular mass of CO = 33.6

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