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Characteristics of Equilibrium Constant

The air pollu...

Question

The air pollutant $N O$ is produced in automobile engines from the high temperature reaction $N_{2} (g) + O_{2} (g) ⇌ 2 N O (g); K_{2} = 16$ at $2300 K$ .If the initial concentrations of $N_{2}$ and $O_{2}$ at $2300 K$ are both $1.5 M$ , what are the concentrations of $N O, N_{2}$ and $O_{2}$ when the reaction mixture reaches equilibrium ?

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Solution

$N_{2} (g) + O_{2} (g) ⇌ 2 N O (g)$
Given, $k_{2} = 16 T = 2300 k$
initial conc. of $N_{2} = O_{2} = 1.5 M$
To find :- Initial conc of $N O = ?, N_{2} = ?, O_{2} = ?$
Let as consider that at equation $N O_{2} = 2 x$
$N_{2} = O_{2} = 1.5 - x$
$∴ k_{2} = \frac{[N O_{2}]^{2}}{[N_{2}] [O_{2}]} = \frac{[2 x]^{2}}{[1.5 - x]^{2}}$
$16 = \frac{[2 x]^{2}}{[1.5 - x]^{2}}$
Taking sq. root on both the side
$4 = \frac{2 x}{1.5 - x} \Rightarrow 2 x = 4 (1.5 - x)$
$2 x = 6 - 4 x \Rightarrow 2 x + 4 x = 6 \Rightarrow 6 x = 6$
$x = 1$
Therefore No $= 2 x = 2 \times 1 = 2 M$
$N_{2} = 1.5 - x = 1.5 - 1 = 0.5 M$
$O_{2} = 1.5 - x = 1.5 - 1 = 0.5 M$

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