Question

K1 and K2 are equilibrium constant for reaction (1) & (2)
${\mathrm{N}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{NO}\left(\mathrm{g}\right)$ …(1)

$NO\left(g\right)\rightleftharpoons \frac{1}{2}{N}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)$ …(2)
Then,

• A. $K_1=\frac{1}{K_2^2}$
• B. $K_1=K_2^2$
• C. $K_1=\frac{1}{K_2}$
• D. $K_1={\left(K_2\right)}^o$

Answer 1

The correct option is A

$K_1=\frac{1}{K_2^2}$

Step 1: Applying the law of mass action,

The equilibrium constant of concentration (denoted by ${\mathrm{K}}_{\mathrm{c}}$) of a chemical reaction at equilibrium can be defined as the ratio of the concentration of products to the concentration of the reactants, each raised to their respective stoichiometric coefficients.

${\mathrm{N}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{NO}\left(\mathrm{g}\right)$

$K_1=\frac{{\left[NO\right]}^2}{\left[N_2\right]\left[O_2\right]}$

Step 2: $NO\left(g\right)\rightleftharpoons \frac{1}{2}{N}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)$

$K_2=\frac{{\left[N_2\right]}^{{\displaystyle \frac{1}{2}}}{\left[O_2\right]}^{{\displaystyle \frac{1}{2}}}}{\left[NO\right]}$

Step 3: Relation between K₁ and K₂

$K_1=\frac{1}{K_2^2}$

Final Answer: (a) $K_1=\frac{1}{K_2^2}$