The r.m.s. velocity of gas molecules kept at temperature $27^{\circ} \mathrm{C}$ in a vessel is $61…

The r.m.s. velocity of gas molecules kept at temperature $27^{\circ} \mathrm{C}$ in a vessel is $61 \mathrm{~m} / \mathrm{s}$. Molecular weight of gas is nearly $\left[\mathrm{R}=8.31 \frac{\mathrm{~J}}{\mathrm{~mol} \mathrm{~K}}\right]$
  1. 2
  2. 28
  3. 4
  4. 32

Solution

Given, $\begin{array}{ll} & T=27^{\circ} \mathrm{C}+273=300 \mathrm{~K} \\ & \text { Also, } v_{\mathrm{rms}}=61 \mathrm{~m} / \mathrm{s} \\ & \mathrm{~V}_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}} \\ \therefore \quad & M=\frac{3 R T}{\mathrm{v}_{\mathrm{ms}}^2}=\frac{3 \times 8.31 \times 300}{61 \times 61}=2 \end{array}$

Asked in: MHT CET 2024 (03 May Shift 2)

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