Question

How can the molar volume be used to find the density of a gas?

Answer 1

Hint: To solve this we must know that molar volume is the volume occupied by one mole of a chemical element at standard temperature and pressure is known as molar volume. Molar volume of a gas is one mole of any gas at a specific temperature and pressure has a fixed volume.

Complete solution:
We know that molar volume is the volume occupied by one mole of a chemical element at standard temperature and pressure is known as molar volume. Molar volume of a gas is one mole of any gas at a specific temperature and pressure has a fixed volume.
The standard temperature and pressure means the temperature is $273{\text{ K}}$ or ${0^ \circ }{\text{C}}$ and the pressure is $1{\text{ atm}}$or $760{\text{ mm Hg}}$.
The molar volume of any gas is directly proportional to the molar mass of the gas and inversely proportional to the density of the gas. The formula for the molar volume of the gas is as follows:
${V_m} = \dfrac{M}{\rho }$
Where ${V_m}$ is the molar volume of the gas,
$M$ is the molar mass of the gas,
$\rho $ is the density of the gas.
We know that one mole of any gas at standard temperature and pressure occupies a volume of $22.4{\text{ L}}$. Thus, the molar volume of gas is $22.4{\text{ L}}$.
Now, we know that density is the ratio of mass to the molar volume. The formula for density is as follows:
$\rho = \dfrac{M}{{{V_m}}}$
Where ${V_m}$ is the molar volume of the gas,
$M$ is the molar mass of the gas,
$\rho $ is the density of the gas.
Substitute $22.4{\text{ L}}$ for the molar volume of the gas. Thus,
$\rho = \dfrac{M}{{22.4{\text{ L}}}}$
Thus, molar volume can be used to calculate the density of the gas.

Note:For example consider the nitrogen i.e. ${{\text{N}}_{\text{2}}}$ gas. The molar mass of nitrogen gas is $28{\text{ g}}$, the molar volume of gas is $22.4{\text{ L}}$. Thus, the density of nitrogen gas will be,
${\rho _{{{\text{N}}_{\text{2}}}}} = \dfrac{{28{\text{ g}}}}{{22.4{\text{ L}}}} = 1.25{\text{ g/L}}$
Thus, the density of nitrogen gas is $1.25{\text{ g/L}}$. The unit of density is ${\text{g/L}}$.