Question

At 400 K, This Reaction Has Kp 8.2 X 104 What Is Kp At 400 K For The Following Reaction

Answer 1

The given question is incomplete, here is a complete question.

At 400 K, this Reaction has $K_p=8.2\times 10^{-4}$

$SO_3(g)\rightleftharpoons SO_2(g)+\frac{1}{2}O_2(g)$

What Is $K_p$ at 400 K for the following reaction?

$2SO_3(g)\rightleftharpoons 2SO_2(g)+O_2(g)$

(A) 8.2 x 10⁻⁴

(B) 2.9 x 10⁻²

(C) 6.7 x 10⁻⁷

(D) 1.6 x 10⁻⁷

Answer : The correct option is, (C) $6.7\times 10^{-7}$

Explanation :

The given chemical equation follows:

$SO_3(g)\rightleftharpoons SO_2(g)+\frac{1}{2}O_2(g)$

The equilibrium constant for the above equation, $K_p=8.2\times 10^{-4}$.

We need to calculate the equilibrium constant for the following equation of above chemical equation, which is:

$2SO_3(g)\rightleftharpoons 2SO_2(g)+O_2(g)$,   $K_p'$

The equilibrium constant for the doubled reaction will be the square of the initial reaction.

Or, we can say that

If the equation is multiplied by a factor of '2', the equilibrium constant will be the square of the equilibrium constant of initial reaction.

The value of equilibrium constant for the following reaction is:

$K_{p}'=(K_p)^2$

$K_{p}'=(8.2\times 10^{-4})^2$

$K_{p}'=6.7\times 10^{-7}$

Hence, the value of equilibrium constant for the following reaction is, $6.7\times 10^{-7}$