alleryStart learning →An unknown gas effuses 1.66 times as fast as carbon dioxide, molar mass 44.0 g/mol. What is the molar mass of the unknown gas?
A26.5 g/mol
B16.0 g/mol
C121 g/mol
D73.0 g/mol
Answer & Solution
Correct answer: B. 16.0 g/mol
1. Write Graham's law with the unknown on top: rate of unknown over rate of carbon dioxide equals the square root of 44.0 over the square root of the unknown molar mass.
2. The left side is given as 1.66 over 1.
3. Square both sides to clear the roots: 1.66 squared equals 44.0 divided by the unknown molar mass.
4. Compute the square: 1.66 x 1.66 = 2.756.
5. Rearrange: unknown molar mass = 44.0 / 2.756 = 16.0 g/mol.
6. A faster gas must be lighter than carbon dioxide, so any answer above 44.0 g/mol is wrong before the arithmetic starts.
7. The value 16.0 g/mol points to methane, and 26.5 g/mol comes from dividing by 1.66 once instead of squaring it.
_Source: OpenStax Chemistry (CC BY 4.0), Ch 9 "Gases", section 9.4 Effusion and Diffusion of Gases_
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