1. Tardigrade
  2. Question
  3. Chemistry
  4. For the pair of reaction given below, (i) N2(g)+3H2(g)leftharpoons 2NH3(g) (ii) (1/2)N2(g)+(3/2)H2(g)leftharpoons NH3(g) If at a particular temperature, textK textP text1 and textK textP text2 are the equilibrium constants for reaction (i) and (ii) respectively then,

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Q. For the pair of reaction given below,

(i) $N_{2}\left(g\right)+3H_{2}\left(g\right)\rightleftharpoons 2NH_{3}\left(g\right)$

(ii) $\frac{1}{2}N_{2}\left(g\right)+\frac{3}{2}H_{2}\left(g\right)\rightleftharpoons NH_{3}\left(g\right)$

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,

NTA AbhyasNTA Abhyas 2020Equilibrium

Solution:

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