Question

The root mean square speed at $NTP$ for the gases $C{H}_4$, $H_2$, $He$ and $F_2$ are in the order:

• A. $C{H}_4$<$H_2$<$He$<$F_2$
• B. $H_2$<$He$<$C{H}_4$<$F_2$
• C. $H_2$<$He$<$F_2$<$C{H}_4$
• D. $F_2$<$C{H}_4$<$H_2$<$He$

Answer 1

Answer: (D)

$F_2$<$C{H}_4$<$H_2$<$He$

$V_{rms}=\sqrt{\frac{3RT}{M}}$

Under same conditions,

$V_{rms}\propto \frac{1}{\sqrt{M}}$

Since, $M_{He}<M_{H_2}<M_{C{H}_4}<M_{F_2}$

Hence, $V_{He}>V_{H_2}>V_{C{H}_4}>V_{F_2}$