Molar Volume Formula

Molar volume is defined as the volume of one mole of an element or compound at standard temperature and pressure. In other words, it is the ratio of molar mass and density. It is directly proportional to the mass of the substance but changes inversely with the density of the substance. The molar volume of ideal gases follows the perfect gas equation. If the sample is a mixture of two or more components, the density of the mixture is used to approximate the molar volume by adding the molar volumes of the individual components.

Formula

V_m = M/ρ

where,

V_m is the molar volume,

M is the molar mass of gas,

ρ is the density of gas.

It is known that 1 mole of a gas has a volume of 22.4 L at STP. In terms of the number of moles, the formula is expressed as,

V_m = 22.4 n

where,

V_m is the molar volume,

n is the number of moles of gas.

For example,

Carbon dioxide is formed when carbon reacts with air.

C (s) + O₂ (g) → CO₂ (g)

Suppose we have to find the molar volume of carbon dioxide gas formed when 2 g of carbon reacts with air.

From the reaction it is clear that 1 mole of carbon gives 1 mole of carbon dioxide.

Number of moles of 2 g of carbon = 2/12 = 0.166 mol

So, number of moles of carbon dioxide (n) = 0.166 mol

Using the formula we get,

V_m = 22.4 n

= 22.4 (0.166)

= 3.73 L

Sample Problems

Problem 1. Calculate the molar volume for oxygen if the density of the gas is 1.4291 g/L?

Solution:

We have,

M = 32

D = 1.4291

V_m = M/D

= 32/1.4291

= 22.39 L

Problem 2. Calculate the molar volume for sulphur dioxide if the density of the gas is 2.6288 g/L?

Solution:

We have,

M = 32 + 2 (16) = 64

D = 2.6288

V_m = M/D

= 64/2.6288

= 24.34 L

Problem 3. Calculate the density of a gas if its molar volume is 22.40 L and molar mass is 28 g.

Solution:

We have,

Vm = 22.40

M = 28

V_m = M/D

=> D = M/V_m

=> D = 28/22.40

=> D = 1.25 g/L

Problem 4. Calculate the molar volume of 3 moles of a gas.

Solution:

We have,

n = 3

Using the formula we have,

V_m = 22.4 n

= 22.4 (3)

= 67.2 L

Problem 5. Calculate the molar volume of 10 moles of a gas.

Solution:

We have,

n = 10

Using the formula we have,

V_m = 22.4 n

= 22.4 (10)

= 224 L

Problem 6. Calculate the number of moles of a gas if its molar volume is 336 L.

Solution:

We have,

Vm = 336

Using the formula we have,

V_m = 22.4 n

=> n = V_m/22.4

=> n = 336/22.4

=> n = 15

Problem 7. Consider the chemical reaction given below:

N (s) + NO (g) → N₂ (g) + O

Calculate the molar volume of nitrogen gas formed if 1.5 g of nitrogen reacts with nitric oxide.

Solution:

From the reaction, it is clear that 1 mole of nitrogen gives 1 mole of nitrogen gas.

Number of moles of 1.5 g of nitrogen = 1.5/14 = 0.125 mol

So, number of moles of nitrogen (n) = 0.125 mol

Using the formula we get,

V_m = 22.4 n

= 22.4 (0.125)

= 2.80 L

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