Chapter 20, Problem 20.86QP

The balance between SO₂ and SO₃ is important in understanding acid rain formation in the troposphere. From the following information at 25°C

$\begin{array}{l}\text{S}(s)+{\text{O}}_2(g)\rightleftharpoons {\text{SO}}_2(g)K_1=4.2\times {10}^{52}\\ 2\text{S}(s)+3{\text{O}}_2(g)\rightleftharpoons 2{\text{SO}}_3(g)K_2=9.8\times {10}^{128}\end{array}$

calculate the equilibrium constant for the reaction

$2{\text{SO}}_2(g)+{\text{O}}_2(g)\rightleftharpoons 2{\text{SO}}_3(g)$