Q48 / 150 · MHT CET 2023 (10 May Shift 1) · Chemistry

Calculate the final volume when 2 moles of an ideal gas expand from $3 \mathrm{dm}^3$ at constant external pressure 1.6 bar and the work done in the process is $800 \mathrm{~J}$.

  • A
    $2.66 \mathrm{dm}^3$
  • B
    $4.8 \mathrm{dm}^3$
  • C
    $5.0 \mathrm{dm}^3$
  • Correct answer
    D
    $8.0 \mathrm{dm}^3$

Solution

$\begin{aligned} & \mathrm{W}=-\mathrm{P}_{\text {ext }} \Delta \mathrm{V}=-\mathrm{P}_{\text {ext }}\left(\mathrm{V}_2-\mathrm{V}_1\right) \\ & \mathrm{V}_1=3 \mathrm{dm}^3 \\ & \mathrm{~V}_2=? \\ & \mathrm{P}_{\text {ext }}=1.6 \text { bar } \\ & \mathrm{W}=-800 \mathrm{~J}=8 \mathrm{dm}^3 \text { bar }\left(\because 100 \mathrm{~J}=1 \mathrm{dm}^3 \text { bar }\right) \\ & -8=-1.6\left(\mathrm{~V}_2-3\right) \\ & \mathrm{V}_2-3=5 \\ & \mathrm{~V}_2=8 \mathrm{dm}^3\end{aligned}$

Hence, the correct answer is option: 'D'.

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