Two large glass containers of equal volume each hold 1 mole of gas. Container 1 is filled with hydrogen gas (2g/mol), and container 2 holds helium (4g/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?

Options

A. The temperature of the gas is container 1 is lower than the temperature of the gas is 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 `1/2` the value of R for the gas is container 2.
D. The rms speed of the gas molecules in container 1 is greater than the rms speed of the gas molecules in container 2.

Answer

D

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. Choice (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 is T is
`v_(rms)=sqrt((3RT)/(M))`.
Hydrogen has a smaller molar mass than does helium, so `v_(rms)` for hydrogen must be greater than `v_(rms)` for helium (because both samples are at the same T).