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AIIMS 201925 May
Exam
AIIMS
Year
2019
Date
25 May
Subject
Chemistry
Chapter
Thermodynamics (C)

AIIMS 2019 · 25 May · Chemistry · Thermodynamics (C)

Reaction, A leftharpoons B+3 C at 25^ C is in equilibrium. If...

Reaction, A⇌B+3CA \rightleftharpoons B+3 C at 25∘C25^{\circ} \mathrm{C} is in equilibrium. If equilibrium constant and Gibbs' free energy for this reaction are yy and xx respectively, then the Gibbs' free energy for reaction, 12A⇌12B+32C\frac{1}{2} A \rightleftharpoons \frac{1}{2} B+\frac{3}{2} C is

Options

  1. Ax2\sqrt{x}^2
  2. Bx2x^2
  3. Cx2/3x^{2 / 3}
  4. Dx/2x / 2

Correct answer

D. x/2x / 2

Step-by-step solution

A⇌B+3CK=[B][C]3[A]ΔG∘=−RTln⁡K=x\begin{aligned} & \mathbf{} A \rightleftharpoons B+3 C \\ & K=\frac{[B][C]^3}{[A]} \\ & \Delta G^{\circ}=-R T \ln K=x\end{aligned} For the reaction, 12A⇌12B+32C\frac{1}{2} A \rightleftharpoons \frac{1}{2} B+\frac{3}{2} CK′=[B]1/2[C]3/2[A]1/2 or (K′)2=[B][C]3[A]=KΔG2∘=−RTln⁡K′=−RTln⁡K=−12RTln⁡K=x2\begin{aligned} & K^{\prime}=\frac{[B]^{1 / 2}[C]^{3 / 2}}{[A]^{1 / 2}} \quad \text{ or } \quad\left(K^{\prime}\right)^2=\frac{[B][C]^3}{[A]}=K \\ & \Delta G_2^{\circ}=-R T \ln K^{\prime}=-R T \ln \sqrt{K} \\ & =-\frac{1}{2} R T \ln K=\frac{x}{2}\end{aligned}$$
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