One percent of a measured amount of Ar(g) escapes through a tiny hole in 77.3 seconds. One percent of the same amount of an unknown gas escapes under the same conditions in 97.6 seconds. Calculate the molar mass of the unknown gas.

Calculation involves using Graham's law of effusion to determine the molar mass of an unknown gas, resulting in a molar mass value of approximately 63.882 g/mol.

Explanation:

The question pertains to the use of Graham's law of effusion to calculate the molar mass of an unknown gas. According to Graham's law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Therefore, if 1% of Ar(g) takes 77.3 seconds to effuse and the unknown gas takes 97.6 seconds for the same percentage to effuse, we can set up a ratio:

(rate of Ar / rate of unknown gas) = sqrt(molar mass of unknown gas / molar mass of Ar)
Given that the molar mass of Ar is 39.948 g/mol, we can calculate the molar mass of the unknown gas using the times given for the effusion of 1% of the gas:
(77.3 / 97.6) = sqrt(molar mass of unknown gas / 39.948)
Solving for the molar mass of the unknown gas gives us:

Molar mass of unknown gas = 39.948 * (97.6 / 77.3)²
Molar mass of unknown gas ≈ 39.948 * 1.599

≈ 63.882 g/mol
This value represents the molar mass of the unknown gas.