Derive a relation between density and molar mass of the gas with the help of ideal gas equation.

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Solution

The relationships between molar mass and density for a monoatomic gas can be easy.
The Ideal Gas Law, PV = nRT can be arranged so that n moles equals the mass/molar mass of the gas to become,
PV = $\frac{m R T}{M}$
where m is the mass and M is the molar mass.
M = $\frac{m R T}{P V}$ , if you hold the temperature of the gas constant the equation reduces to the Boyle's law or $\frac{m}{P V}$
The mass will be constant assuming the container is closed and so the gas cannot be escaped so, PV will be constant.
D = $\frac{m}{V}$ and M = $\frac{m R T}{P V}$
M = $\frac{D R T}{P}$
The higher the density of the gas the higher the molar mass and vice versa.

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