1. Tardigrade
  2. Question
  3. Chemistry
  4. For the reaction, N2(g) + O2(g) leftharpoons 2NO(g), equilibrium constant K1. 2NO(g) + O2(g) leftharpoons 2NO2(g), equilibrium constant K2 What is K for the reaction, NO2(g) leftharpoons (1/2) N2(g) + O2(g)

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Q. For the reaction,
$N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)},$ equilibrium constant $K_1.$
$2NO_{(g)} + O_{2(g)} \rightleftharpoons 2NO_{2(g)}$, equilibrium constant $K_2$
What is K for the reaction,
$NO_{2(g)} \rightleftharpoons \frac {1}{2} N_{2(g)} + O_{2(g)} $

Equilibrium

Solution:

$ \mathrm{N}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO} ; K_{1}$
$2 \mathrm{NO}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}_{2} ; K_{2}$
$\mathrm{NO}_{2} \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2}+\mathrm{O}_{2} ; K$
$K_{1}=\frac{[\mathrm{NO}]^{2}}{\left[\mathrm{~N}_{2}\right]\left[\mathrm{O}_{2}\right]} ; K_{2}=\frac{\left[\mathrm{NO}_{2}\right]^{2}}{[\mathrm{NO}]^{2}\left[\mathrm{O}_{2}\right]} $
$K=\frac{\left[\mathrm{N}_{2}\right]^{1 / 2}\left[\mathrm{O}_{2}\right]}{\left[\mathrm{NO}_{2}\right]}=\sqrt{\frac{\left[\mathrm{N}_{2}\right]\left[\mathrm{O}_{2}\right] \times[\mathrm{NO}]^{2}\left[\mathrm{O}_{2}\right]}{[\mathrm{NO}]^{2} \times\left[\mathrm{NO}_{2}\right]^{2}}} $
$K=\sqrt{\frac{1}{K_{1} K_{2}}}$