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An unknown gas effuses at a rate of 31.2 mL/min. Under the same conditions, methane effuses at 45.6 mL/min. What is the molar mass of the unknown gas?

A. 27.0 g/mol
B. 39.6 g/mol
C. 69.3 g/mol
D. 100.8 g/mol

Answer :

Final answer:

Using Graham's Law of effusion, the molar mass of the unknown gas is found to be 39.6 g/mol by comparing its rate of effusion to methane, making (b) 39.6 g/mol the correct answer.

Explanation:

The question requires the use of Graham's Law of effusion to determine the molar mass of an unknown gas. Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. We can express this as the formula:

Rate of effusion of Gas 1 / Rate of effusion of Gas 2 = sqrt(Molar mass of Gas 2 / Molar mass of Gas 1)

For this problem, we compare the unknown gas to methane (CH4), which has a known molar mass of 16.04 g/mol. We plug in the rates of effusion into Graham's Law to find:

31.2 ml/min / 45.6 ml/min = sqrt(16.04 g/mol / Molar mass of unknown gas)

Upon calculating, we derive that the molar mass of the unknown gas is 39.6 g/mol, which corresponds to answer choice (b). Therefore, (b) 39.6 g/mol is the correct option.

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