Q13 / 180 · KCET 2011 · Chemistry
The rms velocity of hydrogen is $\sqrt{7}$ times the rms velocity of nitrogen. If $T$ is the temperature of the gas, which of the following is true?
- A$T_{\mathrm{H}_{2}}=\sqrt{7} T_{\mathrm{N}_{2}}$
- B$T_{\mathrm{N}_{2}}=T_{\mathrm{H}_{2}}$
- C$T_{\mathrm{N}_{2}}=\sqrt{7} T_{\mathrm{H}_{2}}$
- Correct answerD$T_{\mathrm{N}_{2}}=2 T_{\mathrm{H}_{2}}$
Solution
$$
\begin{aligned}
\frac{C_{\mathrm{H}_{2}}}{C_{\mathrm{N}_{2}}}=\sqrt{7} &=\sqrt{\frac{T_{\mathrm{H}_{2}} \times 28}{2 \times T_{\mathrm{N}_{2}}}} \\
7 &=\frac{14 T_{\mathrm{H}_{2}}}{T_{\mathrm{N}_{2}}} \\
T_{\mathrm{N}_{2}} &=2 T_{\mathrm{H}_{2}}
\end{aligned}
$$
Hence, the correct answer is option: 'D'.