Question

At a certain temperature, the following reactions have the equilibrium constant as show below:
$S\left(s\right)+O_2\left(g\right)\rightleftharpoons S{O}_2\left(g\right);K_c=5\times {10}^{52}$
$2S\left(s\right)+3O_2\left(g\right)\rightleftharpoons 2S{O}_3\left(g\right);K_c={10}^{29}$
What is the equilibrium constant $K_c$ for the reaction at the same temperature?

Answer 1

For the chemical equilibrium,the equilibrium constants can be defined as the ratios of concentrations of products and reactants raise to the power of their coefficients.

By the below eqilibrium equation,

$2{SO}_{2\left(g\right)}+O_{2\left(g\right)}\leftrightharpoons 2{SO}_{3\left(g\right)}$

Equilibrium constants can be written to this equation as,

$K_c=\frac{{\left[S{O}_3\right]}^2}{{\left[{SO}_2\right]}^2\left[O_2\right]}$

Then for the another given equation

$2{SO}_{3\left(g\right)}\rightleftharpoons 2{SO}_{2\left(g\right)}+O_{2\left(g\right)}$

The equilibrium constants takes the form,

$K_C^{{}^{\prime }}=\frac{{\left[{SO}_2\right]}^2\left[O_2\right]}{{\left[{SO}_3\right]}^2}=K_C^{{}^{\prime }}=\frac{1}{K_C}$