Question

The equilibrium constant for the following reactions are given at $25^{\circ} C$
$2 A \rightleftharpoons B + C , K _{1}=1.0$
$2 B \rightleftharpoons C + D , K_{2}=16$
$2 C + D \rightleftharpoons 2 P , K_{3}=25$
The equilibrium constant for the reaction $P \rightleftharpoons A+\frac{1}{2} B$ at $25^{\circ} C$ is

• A. $\frac{1}{20}$
• B. $20$
• C. $\frac{1}{42}$
• D. $21$

Answer 1

Answer: (A)

We can manipulate the given equations as follows
$\frac{1}{2} B+\frac{1}{2} C \rightleftharpoons A, K_{1}'=1 $
$\frac{1}{2} C+\frac{1}{2} D \rightleftharpoons B, K_{2}'=\frac{1}{\sqrt{16}} $
$P \rightleftharpoons C+\frac{1}{2} D, K_{3}'=\frac{1}{\sqrt{25}} $
$\therefore P \rightleftharpoons A+\frac{1}{2} B,$
$ K_{\text {final }}=1 \times \frac{1}{4} \times \frac{1}{5}=\frac{1}{20}$