Question

The equilibrium constant values, under the same conditions of temperature and pressure, for the equilibria $ A_{2} + 3 B_{2} \rightleftharpoons 2AB_{3} $ and $ AB_{3} \rightleftharpoons \frac{1}{2}A_{2}+\frac{3}{2}B_{2} $ are respectively, $ x\, mol^{-2} \, L^{2} $ and $ y \, mol\, L^{-1} $ . The correct relation between $ x $ and $ y $ is

• A. $ x = 2y $
• B. $ y=2x $
• C. $ x=y^{1/2} $
• D. $ y=x^{-1/2} $

Answer 1

Answer: (D)

$A_{2}+3B_{2} \rightleftharpoons 2AB_{3}; $
$K_{1}=x\,mol^{-2}\,L^{2} \dots(i)$
$AB_{3} \rightleftharpoons \frac{1}{2} A_{2}+\frac{3}{2}B_{2}$,
$K_{2}=y\,mol\,L^{-1} \dots (ii)$
Equation $(ii)$ is obtained by reversing equation $(i)$ and then dividing by $2$,
$\therefore K_{2}=\frac{1}{\sqrt{K_{1}}}$
$\Rightarrow y=\frac{1}{\sqrt{x}}$
$=x^{-1 /2}$