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Characteristics of Equilibrium Constant

Consider the ...

Question

Consider the reaction, whose $K_{c} = 33$
$S O_{2} (g) + {N O}_{2} (g) ⇌ S O_{3} (g) + N O (g)$
If $0.1 m o l$ each of ${S O}_{2}$ and ${N O}_{2}$ are placed in $1 L$ container, what is the concentration of ${S O}_{2}$ at equilibrium?

0.003 M

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0.015 M

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0.085 M

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0.097 M

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Solution

The correct option is A $0.015 M$
Since total volume is 1 L, the number of moles is equal to molar concentration.
The initial concentrations are $[S O_{2}]_{0} = [N O_{2}]_{0} = 0.1 M$
$[S O_{3}]_{0} = [N O]_{0} = 0 M$
Let x M of $S O_{2}$ reacts with x M of $N O_{2}$ to form x M of
$S O_{3}$ and x M of $N O$
The equilibrium concentrations are $[S O_{2}]_{e q} = [N O_{2}]_{e q} = 0.1 - x M$
$[S O_{3}]_{e q} = [N O]_{e q} = x M$
$K_{c} = \frac{[S O_{3}]_{e q} [N O]_{e q}}{[S O_{2}]_{e q} [N O_{2}]_{e q}}$
$33 = \frac{x \times x}{(0.1 - x) (0.1 - x)}$
$5.74 = \frac{x}{0.1 - x}$
$0.574 - 5.74 x = x$
$6.74 x = 0.574$
$x = 0.085$
The equilibrium concentration $[S O_{2}]_{e q} = 0.1 - x = 0.1 - 0.085 = 0.015$ M.

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