Question

A gas of unknown identity diffuses at a rate of 83.3 mL/s in a diffusion apparatus in which carbon dioxide diffuses at the rate of 102 mL/s. Calculate the molecular mass of the unknown gas. Give your answers in units of g/mol to three significant figures.

Answer 1

The rate of diffusion increases as the concentration difference increases. It related to the molar mass of a substance by KMT and the Graham's law of diffusion which is as follows:

Rate1 / Rate2 = (√MM2 / √MM1)
83.3 / 102 = √44.01 / MM1
MM1 = 65.99 g / mol

Answer 2

Answer: 65.7 g/mol

Explanation:

To calculate the rate of diffusion of gas, we use Graham's Law.

This 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:

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

$\frac{Rate_{X}}{Rate_{CO_2}}=\sqrt{\frac{M_{CO_2}}{M_{X}}}$

$\frac{83.3}{102}=\sqrt{\frac{44}{M_{X}}$

Squaring both sides and solving for $M_{X}$

$M_{X}=65.7g/mol$

Hence, the molar mas of unknown gas is 65.7 g/mol.