Question

Under identical conditions, separate samples of 02 and an unknown gas were allowed to effuse through identical membranes simultaneously. after a certain amount of time, it was found that 6.45 ml of 02 had passed through the membrane, but only 3.25 ml of of the unknown gas had passed through. what is the molar mass of the unknown gas?

Answer 1

Graham's law was applied to the ratio of effusion rates given to calculate the molar mass of an unknown gas, which is determined to be 64 g/mol.

Step-by-step explanation:

Calculating the Molar Mass Using Graham's Law

Based on Graham's law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, this relationship is expressed as follows:

Rate of effusion of gas 1 / Rate of effusion of gas 2 = √(Molar mass of gas 2 / Molar mass of gas 1)

Given that 6.45 mL of O₂ effuses through the membrane and only 3.25 mL of the unknown gas does, we can write the equation:

6.45 mL / 3.25 mL = √(Molar mass of unknown gas / Molar mass of O₂)

Squaring both sides of the equation to isolate the molar mass of the unknown gas, and knowing that the molar mass of O₂ is 32 g/mol, we get:

Molar mass of unknown gas = (6.45 / 3.25)² × 32 g/mol = × 64 g/mol

Therefore, the molar mass of the unknown gas is 64 g/mol.