How does the density of a gas depend on the molar mass of the gas?

The density of the ideal gas is directly proportional to its molar mass.

Explanation:

Density is a scalar quantity that is denoted by the symbol ρ (rho). It is defined as the ratio of the mass (m) of the given sample and the total volume (V) of the sample.

                         ......equation (1)

According to the ideal gas law for ideal gas:

                                      ......equation (2)

Here, V is the volume of gas, P is the pressure of gas, T is the absolute temperature, R is Gas constant and n is the number of moles of gas

As we know,

The number of moles:

where m is the given mass of gas and M is the molar mass of the gas

So equation (2) can be written as:

⇒

⇒             ......equation (3)

Now from equation (1) and (3), we get

⇒ Density of an ideal gas:  

⇒ Density of an ideal gas: ρ ∝ molar mass of gas: M

Therefore, the density of the ideal gas is directly proportional to its molar mass.

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