Deduction of molar volume of gases

Molar volume is the volume occupied by one mole of any gas at a definite pressure and temperature. It is denoted by V_m. Molar volume of the substance depends on temperature and pressure. The unit of molar volume is litre per mol or millilitre per mol.

As per Avogadro's law, equal volumes of all gases contain equal number of molecules, at a constant temperature and pressure. Therefore, equal number of molecules of any gas, must occupy the same volume, at constant temperature and pressure.

Standard Molar Volume

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

Remember

S.T.P. = Standard Temperature and Pressure

Standard Temperature = 0^oC or 273 K

Standard Pressure = 1 atm or 760 mm of mercury

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Calculation of Molar Volume

Example of oxygen

Mass of 1 litre of oxygen at STP = 1.429 g

Mass of 1 mol of oxygen = 32 g

Volume : Mass

1 litre : 1. 429 g

x : 32 g

The following table gives the relation between the Gram Molecular Weight (GMW), Number of moles, Molar Volume and the Number of particles for gases at STP.

Relationship between Various Parameters of Gases, at STP

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

Problems Based on Molar Volume

Example:

Calculate the volume occupied by 3.4 g of ammonia at STP. (N=14, H=1)

Solution

Gram molecular mass of ammonia (NH₃) = (1 x 14) + (3 + 1) = 14 + 3 = 17 g

Mass of 1 mol of ammonia = 17g

Molar volume = 22.4 litres

Volume of 3.4 g of ammonia at STP = ?

Mass : Volume

17 g : 22.4 litre

3.4 g : x

Volume occupied by 3.4 g of ammonia at STP =4.48 litres

Example:

56 ml of carbon dioxide has a mass at 0.11 g at STP. What is the molar mass of the carbon dioxide?

Solution:

Mass of 56 ml of carbon dioxide at STP = 0.11 g

Mass of 22400 ml of carbon dioxide = ?

Mass : Volume

0.11 g : 56 ml

x g : 22400 ml

Mass of 22400 ml of carbon dioxide at STP = 44 g

Molar Mass of carbon dioxide = 44 g/mole.

Example:

One gram of pure sulphur dioxide has a volume of 350 ml at STP. What is the Relative Molecular Mass of sulphur dioxide?

Solution:

Volume of sulphur dioxide gas = 350 ml at STP

Mass of sulphur dioxide gas = 1 g

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

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

Mass : Volume

1 : 350 ml

x : 22400 ml

Mass of 1 mole of SO₂ = 64 g/mole

\ Relative molecular mass of sulphur dioxide = 64.

Example:

100 ml of carbon monoxide, has a mass of 0.125 g at STP. Calculate the mass of 1 mole of carbon monoxide.

Solution:

Volume of carbon monoxide = 100 ml

Mass of carbon monoxide = 0.125 g

Molar volume = 22400 ml

Mass of 1 mole of carbon monoxide =?

Volume : Mass

100 ml : 0.125 g

22400 ml : x g

Mass of one mole of carbon monoxide = 28 g/mole

\ Relative molecular mass of carbon monoxide = 28.