Multiple Choice
Which gas will have a faster rate of effusion according to Graham's law?
7. Gases
Effusion
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If H2 has an effusion rate that is 3.72 times faster than a gas, what is the identity of the unknown gas?
A
Cl2
B
CO2
C
N2O4
D
N2
E
O2
Verified step by step guidance1
Understand that the problem involves effusion rates, which can be analyzed using Graham's Law of Effusion. This law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Express Graham's Law mathematically: \( \frac{\text{Rate of effusion of } H_2}{\text{Rate of effusion of unknown gas}} = \sqrt{\frac{M_{\text{unknown gas}}}{M_{H_2}}} \), where \( M \) represents molar mass.
Given that the effusion rate of \( H_2 \) is 3.72 times faster than the unknown gas, set up the equation: \( 3.72 = \sqrt{\frac{M_{\text{unknown gas}}}{M_{H_2}}} \).
Square both sides of the equation to eliminate the square root: \( (3.72)^2 = \frac{M_{\text{unknown gas}}}{M_{H_2}} \).
Solve for \( M_{\text{unknown gas}} \) by multiplying both sides by \( M_{H_2} \). Use the known molar mass of \( H_2 \) (approximately 2.02 g/mol) to find the molar mass of the unknown gas, and compare it to the given options to identify the gas.
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