The equilibrium constants of the following are The equilibrium constant (K) of the reaction: will be [2017, 2007, 2003]

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Q.
The equilibrium constants of the following are

$N_{2} + 3 H_{2}$ $⇌ 2 {NH}_{3}; K_{1}$

$N_{2} + O_{2} ⇌ 2 NO; K_{2}$

$H_{2} + \frac{1}{2} O_{2} ⇌ H_{2} O; K_{3}$

The equilibrium constant (K) of the reaction:

$2 {NH}_{3} + \frac{5}{2} O_{2} \overset{k}{⇌} 2 NO + 3 H_{2} O$ will be [2017, 2007, 2003]

1 $\frac{K_{2} K_{3}^{3}}{K_{1}}$

2 $\frac{K_{2} K_{3}}{K_{1}}$

3 $\frac{K_{2}^{3} K_{3}}{K_{1}}$

4 $\frac{K_{1} K_{3}^{3}}{K_{2}}$

Ans.
(1)

From the given equations,

$2 {NH}_{3} ⇌ N_{2} + 3 H_{2}; \frac{1}{K_{1}}$ ...(i)

$N_{2} + O_{2} ⇌ 2 NO; K_{2}$ ...(ii)

$3 H_{2} + \frac{3}{2} O_{2} ⇌ 3 H_{2} O; K_{3}^{3}$ ...(iii)

By adding equations (i), (ii) and (iii), we get

$2 {NH}_{3} + \frac{5}{2} O_{2} \overset{k}{⇌} 2 NO + 3 H_{2} O, K = \frac{K_{2} K_{3}^{3}}{K_{1}}$

Solution

1 $\frac{K_{2} K_{3}^{3}}{K_{1}}$

2 $\frac{K_{2} K_{3}}{K_{1}}$

3 $\frac{K_{2}^{3} K_{3}}{K_{1}}$

4 $\frac{K_{1} K_{3}^{3}}{K_{2}}$

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Solution

Q. The equilibrium constants of the following are N2+3H2⇌2NH3;K1 N2+O2⇌2NO;K2 H2+12O2⇌H2O;K3 The equilibrium constant (K) of the reaction: 2NH3+52O2⇌k2NO+3H2O will be [2017, 2007, 2003]

1 K2K33K1

2 K2K3K1

3 K23K3K1

4 K1K33K2

Ans. (1) From the given equations, 2NH3⇌N2+3H2; 1K1 ...(i) N2+O2⇌2NO; K2 ...(ii) 3H2+32O2⇌3H2O; K33 ...(iii) By adding equations (i), (ii) and (iii), we get 2NH3+52O2⇌k2NO+3H2O, K=K2K33K1

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1 $\frac{K_{2} K_{3}^{3}}{K_{1}}$

2 $\frac{K_{2} K_{3}}{K_{1}}$

3 $\frac{K_{2}^{3} K_{3}}{K_{1}}$

4 $\frac{K_{1} K_{3}^{3}}{K_{2}}$