Question

Statement: For the given gaseous phase reactions $K_1,K_2,K_3$ are equilibrium constants respectively

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

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

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

Correlation between them is $K_3^2=\sqrt{K_2/K_1}$.

If the given statement is true enter 1, else enter 0.

Answer 1

For the given gaseous phase reactions $K_1,K_2,K_3$ are equilibrium constants respectively

$2NO+O_2\rightleftharpoons 2N{O}_2$ .....(1)

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

$N{O}_2+\frac{1}{2}C{l}_2\rightleftharpoons NOCl+\frac{1}{2}{O}_2$ ...... (3)

For reaction (1) $K_1=\frac{[N{O}_2{]}^2}{\left[NO{]}^2\right[O_2]}$

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

For reaction (3) $K_3=\frac{\left[NOCl\right][O_2{]}^{1/2}}{\left[N{O}_2\right][C{l}_2{]}^{1/2}}=\sqrt{\frac{\left[NOCl{]}^2\right[O_2]}{\left[N{O}_2{]}^2\right[C{l}_2]}}=\sqrt{\frac{\frac{[NOCl{]}^4}{\left[NO{]}^4\right[C{l}_2{]}^2}}{\frac{[N{O}_2{]}^2}{\left[NO{]}^2\right[O_2]}}}$

Thus, the correlation between them is $K_3=\sqrt{K_2/K_1}$.

Hence, the given statement is $false$