Question

$CO{Cl}_2\left(g\right)\rightleftharpoons CO\left(g\right)+{Cl}_2\left(g\right);K_1=0.329$
$2CO\left(g\right)+O_2\left(g\right)\rightleftharpoons 2C{O}_2\left(g\right);K_2=2.24\times {10}^{22}$
Calculate the equilibrium constant for the reaction given below from the data given above at $1000K$:
$2CO{Cl}_2\left(g\right)+O_2\left(g\right)\rightleftharpoons 2C{O}_2\left(g\right)+{Cl}_2\left(g\right)$

Answer 1

The given reaction is :-

$\left(I\right)$ $Co{Cl}_2\left(g\right)\rightleftharpoons Co\left(g\right)+{Cl}_2\left(g\right)$

$\Rightarrow K_1=\frac{\left[Co\right]\left[{Cl}_2\right]}{\left[Co{Cl}_2\right]}=0.329\to \left(I\right)$

$\left(II\right)$ $2CO\left(g\right)+O_2\left(g\right)\rightleftharpoons 2{CO}_2\left(g\right)$

$\Rightarrow K_2=\frac{{\left[{CO}_2\right]}^2}{{\left[CO\right]}^2\left[O_2\right]}=2.24\times {10}^{22}\to \left(II\right)$

So, for $2CO{Cl}_2\left(g\right)+O_2\left(g\right)\rightleftharpoons 2{CO}_2\left(g\right)+{Cl}_2\left(g\right)$

$\Rightarrow K=\frac{{\left[{CO}_2\right]}^2\left[{Cl}_2\right]}{{\left[{COCl}_2\right]}^2\left[O_2\right]}=K_1\times K_2=2.24\times {10}^{22}\times 0.329$

$=73.696\times {10}^{20}$