Molar Volume Formula
Vm = M/ρ
where,
Vm 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,
Vm = 22.4 n
where,
Vm 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,
Vm = 22.4 n
= 22.4 (0.166)
= 3.73 L
Sample Problems based on Molar Volume Formula
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
Vm = 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
Vm = 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
Vm = M/D
=> D = M/Vm
=> 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,
Vm = 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,
Vm = 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,
Vm = 22.4 n
=> n = Vm/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,
Vm = 22.4 n
= 22.4 (0.125)
= 2.80 L
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