Q17 / 120 · VITEEE 2017 · Chemistry

Standard entropies of $\mathrm{X}_{2}, \mathrm{Y}_{2}$ and $\mathrm{XY}_{3}$ are 60 , 30 and $50 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ respectively. For the reaction $\frac{1}{2} \mathrm{X}_{2}+\frac{3}{2} \mathrm{Y}_{2} \rightleftharpoons \mathrm{XY}_{3}, \Delta H=-30 \mathrm{~kJ}$ to be at equilibrium, the temperature should be:

  • Correct answer
    A
    $750 \mathrm{~K}$
  • B
    $1000 \mathrm{~K}$
  • C
    $1250 \mathrm{~K}$
  • D
    $500 \mathrm{~K}$

Solution

$\Delta S$ for the reaction $\frac{1}{2} \mathrm{X}_{2}+\frac{3}{2} \mathrm{Y}_{2} \rightleftharpoons \mathrm{XY}_{3}$ $\Delta S=50-(30+60)=-40 \mathrm{~J}$ For equilibrium $\Delta G=0=\Delta H-T \Delta S$ $T=\frac{\Delta H}{\Delta S}=\frac{-30000}{-40}=750 \mathrm{~K}$

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

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