Chapter 21, Problem 66AP

The balance between ${\text{SO}}_{\text{2}}{\text{ and SO}}_{\text{3}}$ is important in understanding acid rain formation in the troposphere. From the following information at $\text{25°C}$:

$\begin{array}{l}\text{S(}s{\text{) + O}}_{\text{2}}\text{(}g\text{) }\rightleftarrows {\text{ SO}}_{\text{2}}\text{(}g\text{) }{K}_{\text{1}}\text{ = 4}\text{.2 }\times {\text{ 10}}^{\text{52}}\\ 2\text{S}(s){\text{ + 3O}}_{\text{2}}\text{(}g\text{) }\rightleftarrows {\text{ 2SO}}_{\text{3}}\text{(}g\text{) }{K}_{\text{2}}\text{ = 9}\text{.8 }\times {\text{ 10}}^{\text{128}}\end{array}$

calculate the equilibrium constant for the reaction:

$2{\text{SO}}_{\text{2}}(g){\text{ + O}}_{\text{2}}\text{(}g\text{) }\rightleftarrows {\text{ 2SO}}_{\text{3}}\text{(}g\text{)}$