Question

A large glass container $A$ is filled with 1 mole of hydrogen gas ($2g/mol$) and other container $B$ is filled with 1 mole of helium gas ($4g/mol$). If the volume and pressure of containers are equal then which of the following is true?

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

Answer 1

Answer: (E)

The rms speed of the gas molecules in Container $A$ is greater than the rms speed of the gas molecules in Container $B$.

From ideal gas law, since the pressure, volume and moles of the gases are same, the temperature of both the gases is same.

Rms speed of gas molecules is given by $\sqrt{\frac{3RT}{M_0}}$

Since $M_0$ for gas A is half of that of gas B, the rms speed of gas A is greater than that of gas B.