Question

Two flasks $A$ and $B$ have equal mass and volume. $A$ contains $H_2$ gas, $B$ contains $C{H}_4$ gas maintained at 300 $K$ and $B$ at 600 $K$ respectively. Identify the flask in which molecules are moving faster.

[Assuming ideal behaviors for both the gases]

• A. $A$
• B. $B$
• C. Both $A$ and $B$
• D. None

Answer 1

The correct option is A $A$

The average velocity as given by Maxwell will be :

$({\mu }_{av}{)}_A=\sqrt{\frac{8R{T}_A}{\pi M_A}}$

$({\mu }_{av}{)}_B=\sqrt{\frac{8R{T}_B}{\pi M_B}}$
Hence,
$\frac{({\mu }_{av}{)}_A}{({\mu }_{av}{)}_B}=\sqrt{\frac{T_A}{M_A}}\times \sqrt{\frac{M_B}{T_B}}$

$=\sqrt{\frac{300\times 16}{2\times 600}}$

$\frac{({\mu }_{a}v{)}_A}{({\mu }_{a}v{)}_B}=2$

$\therefore ({\mu }_{av}{)}_A>({\mu }_{av}{)}_B$

Hence, option $\left(A\right)$ is correct.