Which of the following would effuse at a rate equal to 31.5% of the rate of H2?
Question
Which of the following would effuse at a rate equal to 31.5% of the rate of H2?
Solution
The question is asking for a gas that effuses at a rate of 31.5% of the rate of Hydrogen gas (H2).
The rate of effusion of a gas is inversely proportional to the square root of its molar mass. This is according to Graham's law of effusion.
Mathematically, this can be represented as:
Rate1/Rate2 = sqrt(M2/M1)
Where: Rate1 and Rate2 are the rates of effusion of the two gases, M1 and M2 are their respective molar masses.
Given that the rate of effusion of the unknown gas is 31.5% of that of Hydrogen, we can set up the equation as follows:
0.315 = sqrt(M2/2)
Solving for M2 gives:
M2 = (0.315)^2 * 2 M2 = 0.099225 * 2 M2 = 0.19845 g/mol
This is the molar mass of the gas that would effuse at a rate equal to 31.5% of the rate of Hydrogen.
However, there are no common gases with this exact molar mass. The closest common gas is Helium (He) with a molar mass of approximately 4 g/mol. But it would effuse faster than Hydrogen, not slower.
Therefore, without additional options provided in the question, it's not possible to identify a specific gas that would effuse at exactly 31.5% of the rate of Hydrogen.
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