Question

It takes 192 seconds for an unknown gas to diffuse through a porous wall and 84 seconds for N2 gas to effuse at the same temperature and pressure . What is the molar mass of the unknown gas?​

Answer 1

Step 1 of 3

Graham’s law of diffusion states that under the same conditions of temperature and pressure, rates of diffusion for gases are inversely proportional to the square rots of their molar masses.

Answer 2

Answer:

146.29 g/mol is the molar mass of the unknown gas.

Explanation:

Let the volume of the gases effusing out be V.

Effusion rate of the unknown gas = $R=\frac{V}{192 s}$

Effusion rate of the nitrogen gas = $r=\frac{V}{84 s}$

Molar mass of unknown gas = m

Mass of nitrogen gas = 28 g/mol

Graham's law states that the rate of effusion or diffusion of gas is inversely proportional to the square root of the molar mass of the gas. The equation given by this law follows the equation:

$\text{Rate of diffusion}\propto \frac{1}{\sqrt{\text{Molar mass of the gas}}}$

$\frac{R}{r}=\sqrt{\frac{28 g/mol}{M}}$

$\frac{\frac{V}{192 s}}{\frac{V}{84 s}}=\sqrt{\frac{28 g/mol}{M}}$

$\frac{84}{192}=\sqrt{\frac{28 g/mol}{M}}$

$M=\frac{28 g/mol\times 192 \times 192}{84\times 84}=146.29 g/mol$

146.29 g/mol is the molar mass of the unknown gas.