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Characteristics of Equilibrium Constant

What should b...

Question

What should be the value of $K_{c}$ for the reaction $2 S O_{2 (g)} + O_{2 (g)} ⇌ 2 S O_{3 (g)}$ , if the amount are $S O_{3} = 48 g, S O_{2} = 12.8 g$ and $O_{2} = 9.6 g$ at equilibrium and the volume of the container is one litre?

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Solution

The correct option is C 30
$2 {S O}_{2 (g)} + O_{2 (g)} ⇌ 2 {S O}_{3 (g)}$

We know, $K_{C} = \frac{{[{S O}_{3}]}^{2}}{{[{S O}_{2}]}^{2} [O_{2}]}$

Given, ${S O}_{3} = 48 g, {S O}_{2} = 12.8 g, O_{2} = 9.6 g$ at equilibrium concentration $= \frac{m o l e s}{V (i n l i t)}$ ,
Given volume $= 1$ lit

moles of ${S O}_{3} = \frac{w e i g h t}{m o l e c u l e s w e i g h t} = \frac{48}{80} = 0.6$

moles of ${S O}_{2} = \frac{12.8}{64} = 0.2$

moles of $O_{2} = \frac{9.6}{32} = 0.3$

moles $=$ concentration ( $∵$ volume 1 lit)

$K_{C} = \frac{{(0.6)}^{2}}{(0.3) {(0.2)}^{2}} = 30$

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