SAT Subject Physics Practice Question 133: Answer and Explanation

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Question: 133

6. Two large glass containers of equal volume each hold 1 mole of gas. Container 1 is filled with hydrogen gas (2 g/mol), and Container 2 holds helium (4 g/mol). If the pressure of the gas in Container 1 equals the pressure of the gas in Container 2, which of the following is true?

A. The temperature of the gas in Container 1 is lower than the temperature of the gas in Container 2.
B. The temperature of the gas in Container 1 is greater than the temperature of the gas in Container 2.
C. The value of R for the gas in Container 1 is the value of R for the gas in Container 2.
D. The rms speed of the gas molecules in Container 1 is lower than the rms speed of the gas molecules in Container 2.
E. The rms speed of the gas molecules in Container 1 is greater than the rms speed of the gas molecules in Container 2.

Correct Answer: E

Explanation:

Neither A nor B can be correct. Using PV = nRT, both containers have the same V, n is the same, P is the same, and R is a universal constant. Therefore, T must be the same for both samples. C is also wrong, since R is a universal constant. The kinetic theory of gases predicts that the rms speed of the gas molecules in a sample of molar mass M and temperature T is

Hydrogen has a smaller molar mass than does helium, so vrms for hydrogen must be greater than vrms for helium (because both samples are at the same T).

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