Helium effuses through a small opening at a rate of 1´10^-⁹ mol s^-¹. An unknown gas at the same temperature and pressure is found to effuse through the same opening at a rate of 3.78´10^-¹⁰ mol s^-¹. What is the molecular mass of the unknown gas?

Question

Quizplus · Accepted Answer

The rate of effusion of a gas is inversely proportional to the square root of its molar mass (Graham's law). Given the rate of effusion of helium (4 g/mol) and the unknown gas, we can set up the equation: $ \sqrt{M_{He}} / \sqrt{M_{X}} = rate_{X} / rate_{He} $. Plugging in the given values, $ \sqrt{4} / \sqrt{M_{X}} = 3.78 / 1 $. Solving for $M_{X}$, we find that the molar mass of the unknown gas is approximately 28 g/mol.

Helium Effuses Through a Small Opening at a Rate of 1´10-9

Helium Effuses Through a Small Opening at a Rate of 1´10^-⁹