Question

For the given gaseous phase reactions $K_1,K_2,K_3$ are equilibrium constants respectively, correlate them.
$2NO+O_2\rightleftharpoons 2N{O}_2$
$4NO+2C{l}_2\rightleftharpoons 4NOCl$
$N{O}_2+1/2C{l}_2\rightleftharpoons NOCl+1/2O_2$.

Answer 1

$2NO+O_2\rightleftharpoons 2N{O}_2$

$K_1=\frac{[N{O}_2{]}^2}{\left[NO{]}^2\right[O_2]}$ ... (ii)

$4NO+2C{l}_2\rightleftharpoons 4NOCl$

$K_2=\frac{[NOCl{]}^4}{\left[NO{]}^4\right[C{l}_2{]}^2}$ ...(ii)

$N{O}_2+\frac{1}{2}C{l}_2\rightleftharpoons NOCl+\frac{1}{2}{O}_2$

$K_3=\frac{\left[NOCl\right][O_2{]}^{1/2}}{\left[N{O}_2\right][C{l}_2{]}^{1/2}}$ .... (iii)

divide $K_2$ by square of $K_1^2$

$\frac{[NOCl{]}^4}{\left[NO{]}^4\right[C{l}_2{]}^2}\times \frac{\left[NO{]}^4\right[O_2{]}^2}{[N{O}_2{]}^4}=\frac{\left[NOCl{]}^4\right[O_2{]}^2}{\left[N{O}_2{]}^4\right[C{l}_2{]}^2}$

$K_2\times \frac{1}{K_1^2}=K_3^4\Rightarrow \frac{K_2}{K_1^2}=K_3^4$