A sample of an unknown gas effuses in 11.1 min. An equal volume of H2 in the same apparatus at the same temperature and pressure effuses in 2.02 min. What is the molar mass of the unknown gas?
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To determine the molar mass of the unknown gas, we can use Graham's law of effusion. Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Let's denote the molar mass of the unknown gas as M, and the molar mass of H2 as M(H2). The rate of effusion of the unknown gas can be represented as M unknown / t unknown, and the rate of effusion of H2 is M(H2) / t(H2), where t represents the respective effusion times.
According to Graham's law, these rates of effusion are inversely proportional:
M unknown / t unknown = (M(H2) / t(H2))^0.5
Now, let's plug in the given values:
t unknown = 11.1 min
t(H2) = 2.02 min
M(H2) = 2 g/mol (molar mass of H2)
M unknown / 11.1 min = (2 g/mol / 2.02 min)^0.5
To solve for M unknown, we can rearrange the equation:
M unknown = (2 g/mol / 2.02 min)^0.5 * 11.1 min
Now, let's calculate the molar mass of the unknown gas:
M unknown = (2 / 2.02)^0.5 * 11.1
≈ 1.039 * 11.1
≈ 11.5 g/mol
Therefore, the molar mass of the unknown gas is approximately 11.5 g/mol.