Q7 / 160 · TS EAMCET 2024 (11 May Shift 1) · Chemistry
At what temperature will the RMS velocity of sulphur dioxide molecules at 400 K be the same as the most probable velocity of oxygen molecules?
- A600 K
- B200 K
- C400 K
- Correct answerD300 K
Solution
RMS velocity $\left(v_{\mathrm{rms}}\right)=\sqrt{\frac{3 R T}{M}}$ ...(i)
Most probable velocity $=\sqrt{\frac{2 \mathrm{RT}}{\mathrm{M}}}$ ...(ii)
given,
$\begin{aligned}
& \mathrm{T}_1=400 \\
& \mathrm{M}_1\left(\mathrm{SO}_2\right)=64 \\
& \mathrm{~T}_2=? \\
& \mathrm{M}_2\left(\mathrm{O}_2\right)=32
\end{aligned}$
Comparing equation (i) and (ii) $\begin{aligned} & \sqrt{\frac{3 \mathrm{R} \times 400}{64}}=\sqrt{\frac{2 \mathrm{RT}_2}{32}} \\ & \frac{1200}{64}=\frac{2 \mathrm{~T}_2}{32} \\ \therefore \quad & \mathrm{~T}_2=300 \mathrm{~K} \end{aligned}$
Comparing equation (i) and (ii) $\begin{aligned} & \sqrt{\frac{3 \mathrm{R} \times 400}{64}}=\sqrt{\frac{2 \mathrm{RT}_2}{32}} \\ & \frac{1200}{64}=\frac{2 \mathrm{~T}_2}{32} \\ \therefore \quad & \mathrm{~T}_2=300 \mathrm{~K} \end{aligned}$
Hence, the correct answer is option: 'D'.