Q68 / 180 · NEET 2025 · Chemistry

For the reaction $\mathrm{A}(\mathrm{g}) \rightleftharpoons 2 \mathrm{~B}(\mathrm{~g})$, the backward reaction rate constant is higher than the forward reaction rate constant by a factor of 2500 , at 1000 K . [Given : $\mathrm{R}=0.0831 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ ] $\mathrm{K}_{\mathrm{p}}$ for the reaction at 1000 K is

  • A
    83.1
  • B
    $2.077 \times 10^5$
  • Correct answer
    C
    0.033
  • D
    0.021

Solution

$\begin{aligned} \mathrm{K}_{\mathrm{C}} & =\frac{\mathrm{K}_{\mathrm{f}}}{\mathrm{K}_{\mathrm{b}}} \\ & =\frac{\mathrm{K}_{\mathrm{f}}}{2500 \mathrm{~K}_{\mathrm{f}}} \\ & =\frac{1}{2500} \\ \mathrm{~K}_{\mathrm{p}} & =\mathrm{K}_{\mathrm{C}}(\mathrm{RT})^{\Delta \mathrm{n}_{\mathrm{g}}} \\ = & \frac{1}{2500}(0.0831 \times 1000)^1 \\ \mathrm{~K}_{\mathrm{p}} & =0.033\end{aligned}$

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

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