Question

The density of a gas at SATP is 2.50g/L. Determine the molecular mass of the gas

Answer 1

According to the ideal gas law, the equation of state is:

$pV=nRT$ ,

where $p$ is the pressure, $V$ is the volume, $n$ is the number of the moles, $R$ is the ideal gas constant (8.314 J mol^-1 K^-1) and $T$ is the temperature.

The mass of the gas $m$ is the product of the number of the moles and the molar mass $M$:

$m = n·M$ .

Joining the two equations above:

$pV = \frac{m}{M}RT$

The density $d$ of a gas is the ratio of the mass to the volume:

$d =\frac{m}{V} = \frac{pM}{RT}$ .

Therefore, the molar mass of the gas is:

$M = \frac{d}{p}RT$ .

Standard conditions for temperature and pressure (SATP) are 10⁵ Pa and 273.15 K. Finally:

$M= \frac{2.50·10^3(\text{g/m}^3)}{10^5(\text{Pa})}·8.314(\text{J/(mol K)})·273.15(\text{K})$

$M = 56.8 \text{ g/mol}$ .

Answer: the molar mass of the gas is 56.8 g/mol