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# A mixture of 1.57 mol of N_2, 1.92 mol of H_2 and 8.13 mol of NH_3 is introduced into a 20 L reaction vessel at 500 K. At this temperature, the equilibrium constant, K_c for the reaction

7.12     A mixture of 1.57 mol of N2, 1.92 mol of H2 and 8.13 mol of NH3 is introduced into a 20 L reaction vessel at 500 K. At this temperature, the equilibrium constant, Kc for the reaction $N_{2}_{(g)}+3H_{2}_{(g)}\rightleftharpoons 2NH_{3}_{(g)}$  is 1.7 × 102. Is the reaction mixture at equilibrium? If not, what is the direction of the net reaction?

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We have,
$N_{2}_{(g)}+3H_{2}_{(g)}\rightleftharpoons 2NH_{3}_{(g)}$

$K_c = 1.7 \times 10^{2}$

The concentration of species are-
$[N_2] = 1.57/20 mol L^{-1}\\ {[H_2]}=1.92/20mol L^{-1}\\ {[NH_3]}=8.13/20mol L^{-1}$

We know the formula of

$Q_c = \frac{[NH_3]^2}{[N_2][H_2]^3}$
$\\=\frac{(8.13/20)^2}{(1.57/20)(1.92/20)^3}\\ =2.4\times 10^{-3}$
The reaction is not in equilibrium. Since $Qc>K_c$, the equilibrium proceeds in reverse direction.

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