Question

How is the relative vapor density of a gas related to the relative molecular mass of the gas?

Answer 1

Avogadro's law

It states that the equal volume of any gas under the same pressure and temperature contains the same number of molecules.

Relative vapor density

At the same pressure and temperature, the mass of a given volume of gas in comparison to the mass of a given volume of hydrogen is known as the relative vapor density of a gas or vapor.

Relationship between relative vapor density and relative molecular mass of the gas

Avogadro's law establishes a relationship between relative molecular mass and relative vapor density of a gas.

Let $V$ be the volume of a gas, then the formula for relative vapor density of a gas is as follows:

$\text{Relative vapor density=}\frac{\text{Mass of volume}V\text{of the gas}}{\text{Mass of volume}V\text{of hydrogen}}$

Now apply Avogadro's law as follows:-

$\text{Relative vapor density=}\frac{\text{Mass of 1 molecule of the gas}}{\text{Mass of}1\mathrm{molecule}\text{of hydrogen}}$

One molecule of hydrogen contains $2\text{atoms}$. So, the above equation can be written as follows:-

$\text{Relative vapor density}=\frac{\text{Mass of 1 molecule of the gas}}{\text{Mass of 2 atoms of hydrogen}}$

In the above equation, multiply by $2$ on both sides as follows:

$\text{2×Relative vapor density}=\frac{\text{Mass of 1 molecule of the gas}}{\text{Mass of 1 atom of hydrogen}}$

$\text{2×Relative vapor density}=\text{Relative molecular mass of gas}$

Hence, the relative molecular mass of gas is two times the relative vapor density.