Question

Consider the following gaseous equilibria with equilibrium constants $K_1$ and $K_2$ respectively. $SO_{2(g)} + \frac{1}{2} O_{2(g)} \leftrightharpoons SO_{3(g)}$ $2SO_{3(g)} \leftrightharpoons 2SO_{2(g)} + O_{2(g)}$ The equilibrium constants are related as

• A. $2 \, K_1 = K^2_2$
• B. $K^2_1 = \frac{1}{K_2}$
• C. $K^2_2 = \frac{1}{K_1}$
• D. $K_2 = \frac{2}{K^2_1}$

Answer 1

Answer: (B)

$K^2_1 = \frac{1}{K_2}$

Answer 2

$SO _{2}(g)+\frac{1}{2} O _{2}(g) \rightleftharpoons SO _{3}(g)$...(i) $K_{1}$

Equation (i) is reversed and multiplied by 2

$2 SO _{3}(g) \rightleftharpoons 2 SO _{2}(g)+ O _{2}(g)$...(i) $\frac{1}{K_{1}^{2}}$
$2 SO _{3}(g) \rightleftharpoons 2 SO _{2}(g)+ O _{2}(g)$(ii) $K_{2}$
$\therefore K_{2} =\frac{1}{K_{1}^{2}}$
$K_{1}^{2} =\frac{1}{K_{2}}$