Question

For the pair of reaction given below,

(i) $N_2\left(g\right)+3H_2\left(g\right)\rightleftharpoons 2N{H}_3\left(g\right)$

(ii) $\frac{1}{2}{N}_2\left(g\right)+\frac{3}{2}{H}_2\left(g\right)\rightleftharpoons N{H}_3\left(g\right)$

If at a particular temperature, ${\text{K}}_{{\text{P}}_{\text{1}}}$ and ${\text{K}}_{{\text{P}}_{\text{2}}}$ are the equilibrium constants for reaction (i) and (ii) respectively then,

• A. ${\text{K}}_{{\text{P}}_{\text{1}}}\text{=}{\text{2K}}_{{\text{P}}_{\text{2}}}$
• B. ${\text{K}}_{{\text{P}}_{\text{1}}}\text{=}{\text{K}}_{{\text{P}}_{\text{2}}}^{\text{2}}$
• C. ${\text{2K}}_{{\text{P}}_{\text{1}}}\text{=}{\text{K}}_{{\text{P}}_{\text{2}}}$
• D. ${\text{K}}_{{\text{P}}_{\text{1}}}^{\text{2}}\text{=}{\text{K}}_{{\text{P}}_{\text{2}}}$

Answer 1

Answer: (B)

${\text{K}}_{{\text{P}}_{\text{1}}}\text{=}\frac{{\text{p}}_{{\text{NH}}_{\text{3}}}^{\text{2}}}{{\text{p}}_{{\text{N}}_{\text{2}}}{\text{.p}}_{{\text{H}}_{\text{2}}}^{\text{3}}}$ ...(i)

${\text{K}}_{{\text{P}}_{\text{2}}}\text{=}\frac{{\text{P}}_{{\text{NH}}_{\text{3}}}}{{\text{p}}_{{\text{N}}_{\text{2}}}^{\frac{\text{1}}{\text{2}}}{\text{.p}}_{{\text{H}}_{\text{2}}}^{\frac{\text{3}}{\text{2}}}}$

${\text{K}}_{{\text{P}}_{\text{2}}}^{\text{2}}\text{=}\frac{{\text{p}}_{{\text{NH}}_{\text{3}}}^{\text{2}}}{{\text{p}}_{{\text{N}}_{\text{2}}}{\text{.p}}_{{\text{H}}_{\text{2}}}^{\text{3}}}$ ...(ii)

Dividing equation (ii) by equation (i)

$\frac{{\text{K}}_{{\text{P}}_{\text{1}}}}{{\text{K}}_{{\text{P}}_{\text{2}}^{\text{2}}}}\text{=1}$

or ${\text{K}}_{{\text{P}}_{\text{1}}}\text{=}{\text{K}}_{{\text{P}}_{\text{2}}}^{\text{2}}$