Question

A gas of unknown identity diffuses at a rate of 83.3 mL/s in a diffusion apparatus. If carbon dioxide diffuses at the rate of 102 mL/s, what is the ratio of the diffusion rates of the unknown gas to carbon dioxide?

a) 1.23
b) 0.816
c) 1.22
d) 0.823

Answer 1

To calculate the molecular mass of the unknown gas, use Graham's law of diffusion, which relates the diffusion rates and molar masses of gases. The molar mass of the unknown gas is approximately 53 g/mol.

Step-by-step explanation:

In order to calculate the molecular mass of the unknown gas, we can use Graham's law of diffusion, which states that the ratio of the diffusion rates of two gases is equal to the square root of the ratio of their molar masses.

Given that carbon dioxide (CO₂) diffuses at a rate of 102 mL/s and the unknown gas diffuses at a rate of 83.3 mL/s, we can set up the following equation:

(Rate of unknown gas) / (Rate of CO₂) = √(Molar mass of CO₂) / (Molar mass of unknown gas)

Substituting the given values, we get:

83.3 / 102 = √44 / Molar mass of unknown gas

Solving for the molar mass of the unknown gas:

Molar mass of unknown gas = (√44 * 102) / 83.3

Calculating this expression gives us a molar mass of approximately 53 g/mol for the unknown gas.