Question

6. The equilibrium constant Kc for the reaction: 2SO2 (g) + O2 (g) → 2SO3 (g) is 800 at 527oC. Calculate the equilibrium constant for the reaction SO3 (g) → SO2 (g) + ½O2. (4 marks)

Answer 1

Answer : The value of $K'_c$ for the reaction is, 0.0353

Explanation :

The balanced equilibrium reactions are:

(1) $2SO_2(g)+O_2(g)\rightleftharpoons 2SO_3(g)$         $K_c=800$

(2) $SO_3(g)\rightleftharpoons SO_2+\frac{1}{2}O_2$       $K'_c=?$

The expression of equilibrium constant for the reaction (1) will be:

$K_c=\frac{[SO_3]^2}{[SO_2]^2[O_2]}$

$[O_2]=\frac{1}{K_c}\times (\frac{[SO_3]}{[SO_2]})^2$     .......(1)

The expression of equilibrium constant for the reaction (2) will be:

$K'_c=\frac{[SO_2][O_2]^{1/2}}{[SO_3]}$    ......(2)

Now put equation 1 in equation 2, we get:

$K'_c=\frac{[SO_2][\frac{1}{K_c}\times (\frac{[SO_3]}{[SO_2]})^2]^{1/2}}{[SO_3]}$

$K'_c=(\frac{1}{K_c})^{1/2}$        ..........(3)

Now put the value of $K_c$ in the equation 3, we get:

$K'_c=(\frac{1}{800})^{1/2}$

$K'_c=0.0353$

Therefore, the value of $K'_c$ for the reaction is, 0.0353