The equilibrium constant for the following reactions are $K_{1}$ and $K_{2}$ , respectively.
$2 P (g) + 3 {C l}_{2} (g) ⇌ 2 P {C l}_{3} (g)$
$P {C l}_{3} (g) + {C l}_{2} (g) ⇌ P {C l}_{5} (g)$
Then the equilibrium constant for the reaction
$2 P (g) + 5 {C l}_{2} (g) ⇌ 2 P {C l}_{5} (g)$ is:

K_{1} K_{2}

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K_{1} K_{2}^{2}

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K_{1}^{2} K_{2}^{2}

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K_{1}^{2} K_{2}

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Solution

The correct option is B $K_{1} K_{2}^{2}$
Given that,
$2 P (g) + 3 {C l}_{2} (g) ⇌ 2 P {C l}_{3} (g)$ ---- 1

$K_{1} =$ equilibrium constant

$P {C l}_{3} (g) + {C l}_{2} (g) ⇌ P {C l}_{5} (g)$ -------- 2

$K_{2} =$ equilibrium constant
Now, Eqn. $1 + 2 \times$ Eqn. 2 gives the resultant equation

$2 P (g) + 5 {C l}_{2} (g) ⇌ 2 P {C l}_{5} (g)$ .

The equilibrium constant of the final reaction reaction will be given as:

$K = K_{1} . K_{2}^{2}$ as the final reaction is the addition of (reaction 1 + 2 $\times$ reaction 2)

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Similar questions

C O (g) + \frac{1}{2} O_{2} (g) ⇌ C O_{2} (g)

2 C O (g) + O_{2} (g) ⇌ 2 C O_{2} (g)

Equilibrium constants $K_{1}$ and $K_{2}$ for the following equilibria are

$N O (g) + 0.5 O_{2} (g) \to K_{1} N O_{2} (g)$ and
$2 N O_{2} (g) \to K_{2} 2 N O (g) + O_{2} (g)$

For the two gaseous reactions (i) and (ii), at $25^{\circ} C$

(i) $N O (g) + \frac{1}{2} O_{2} (g) ⇌ N O_{2} (g)$

(ii) $2 N O_{2} (g) ⇌ 2 N O (g) + O_{2} (g)$ ,

The equilibrium constants are $K_{1}$ and $K_{2}$ respectively are related as:

For the two gaseous reactions (i) and (ii), at $25^{0} C$

$(i) N O (g) + \frac{1}{2} O_{2} (g) ⟵ N O_{2} (g)$

$(i i) 2 N O_{2} (g) ⟵ 2 N O (g) + O_{2} (g)$ ,

The equilibrium constants are $K_{1}$ and $K_{2}$ respectively. these two constants are related as:

S O_{2} + \frac{1}{2} O_{2} ⇌ S O_{2}

2 S O_{2} + O_{2} ⇌ 2 S O_{3}

K_{1}

K_{2}

K_{1}

K_{2}

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