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Sufficient Condition for an Extrema

Which reactio...

Question

Which reaction has the smallest equilibrium constant ( $K_{p}$ )?

N_{2} (g) + {3 H}_{2} (g) ⇌ 2 {N H}_{3} (g)

When:

N_{2} = 1 a t m

H_{2} = 2 a t m

{N H}_{3} = 4 a t m

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I_{2} (g) + H_{2} (g) ⇌ 2 H I (g)

When:

I_{2} = 2 a t m

H_{2} = 2 a t m

H I = 2 a t m

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

When:

P {C l}_{3} = 3 a t m

{C l}_{2} = 4 a t m

P {C l}_{5} = 1 a t m

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2 {S O}_{2} + O_{2} ⇌ 2 {S O}_{3}

When:

{S O}_{2} = 2 a t m

O_{2} = 2 a t m

{S O}_{3} = 3 a t m

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Solution

The correct option is D ${P C l}_{3} (g) + {C l}_{2} (g) ⇌ {P C l}_{5} (g)$
When: $P {C l}_{3} = 3 a t m$ , ${C l}_{2} = 4 a t m$ , $P {C l}_{5} = 1 a t m$
$(I)$ $N_{2} (g) + 3 H_{2} (g) ⇌ 2 {N H}_{3} (g)$

$K_{P} = \frac{{(p {N H}_{3})}^{2}}{{p N}_{2} . {(p H_{2})}^{3}} = \frac{4 \times 4}{1 \times 2^{3}} = \frac{16}{8} = 2$

$(I I)$ $I_{2} (g) + H_{2} (g) ⇌ 2 H I (g)$

$K_{P} = \frac{{(p H I)}^{2}}{{p I}_{2} . {p H}_{2}} = \frac{2 \times 2}{2 \times 2} = 1$

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

$K_{P} = \frac{{p P C l}_{5}}{{p P C l}_{3} . {p C l}_{2}} = \frac{1}{4 \times 3} = \frac{1}{12}$

$(I V)$ $2 {S O}_{2} + O_{2} ⇌ 2 {S O}_{3}$

$K_{P} = \frac{{(p {S O}_{3})}^{2}}{{(p {S O}_{2})}^{2} . {p O}_{2}} = \frac{3 \times 3}{2 \times 2 \times 2} = \frac{9}{8}$

So, the correct option is $C$

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Which reaction has the smallest equilibrium constant (Kp)?

Which reaction has the smallest equilibrium constant ( $K_{p}$ )?