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NEET 2007
Exam
NEET
Year
2007
Subject
Chemistry
Chapter
Chemical Equilibrium

NEET 2007 · Chemistry · Chemical Equilibrium

The following equilibrium constant are given: aligned N_2+3 H_2 &...

The following equilibrium constant are given: N2+3H2⇌2NH3;K1 N2+O2⇌2NO;K2H2+1/2O2⇌H2O;K3\begin{aligned} \mathrm{N}_2+3 \mathrm{H}_2 & \rightleftharpoons 2 \mathrm{NH}_3 ; \mathrm{K}_1 \\ \mathrm{~N}_2+\mathrm{O}_2 & \rightleftharpoons 2 \mathrm{NO} ; \mathrm{K}_2 \\ \mathrm{H}_2+1 / 2 \mathrm{O}_2 & \rightleftharpoons \mathrm{H}_2 \mathrm{O} ; \mathrm{K}_3 \end{aligned} The equilibrium constant for the oxidation of NH3\mathrm{NH}_3 by oxygen to give NO\mathrm{NO} is:

Options

  1. AK2 K32 K1\frac{\mathrm{K}_2 \mathrm{~K}_3^2}{\mathrm{~K}_1}
  2. BK22 K3 K1\frac{\mathrm{K}_2^2 \mathrm{~K}_3}{\mathrm{~K}_1}
  3. CK1 K2 K3\frac{\mathrm{K}_1 \mathrm{~K}_2}{\mathrm{~K}_3}
  4. DK2K33K1\frac{K_2 K_3^3}{K_1}

Correct answer

D. K2K33K1\frac{K_2 K_3^3}{K_1}

Step-by-step solution

Given, N2+3H2⇌2NH3;K1N2+O2⇌2NO;K2H2+12O2⇌H2O;K3\begin{aligned} & \mathrm{N}_2+3 \mathrm{H}_2 \rightleftharpoons 2 \mathrm{NH}_3 ; \mathrm{K}_1 \\ & \mathrm{ N}_2+\mathrm{O}_2 \rightleftharpoons 2 \mathrm{NO} ; \mathrm{K}_2 \\ & \mathrm{H}_2+\frac{1}{2} \mathrm{O}_2 \rightleftharpoons \mathrm{H}_2 \mathrm{O} ; \mathrm{K}_3 \end{aligned} We have to calculate 4NH3+5O2⟶4NO+6H2O;K= ?  or 2NH3+52O2⟶2NO+3H2O\begin{aligned} & 4 \mathrm{NH}_3+5 \mathrm{O}_2 \longrightarrow 4 \mathrm{NO}+6 \mathrm{H}_2 \mathrm{O} ; \mathrm{K}=\text{ ? } \\ & \text{ or } 2 \mathrm{NH}_3+\frac{5}{2} \mathrm{O}_2 \longrightarrow 2 \mathrm{NO}+3 \mathrm{H}_2 \mathrm{O} \end{aligned} For this equation K=[NO]2[H2O]3[NH3]2[O2]5/2\mathrm{K}=\frac{[\mathrm{NO}]^2\left[\mathrm{H}_2 \mathrm{O}\right]^3}{\left[\mathrm{NH}_3\right]^2\left[\mathrm{O}_2\right]^{5 / 2}} but K1=[NH3]2[N2][H2]3K2=[NO]2[N2][O2]K3=[H2O][H2][O2]1/2K3=[H2O3[H2]3[O2]3/2\begin{aligned} \mathrm{K}_1 & =\frac{\left[\mathrm{NH}_3\right]^2}{\left[\mathrm{ N}_2\right]\left[\mathrm{H}_2\right]^3} \\ \mathrm{ K}_2 & =\frac{[\mathrm{NO}]^2}{\left[\mathrm{ N}_2\right]\left[\mathrm{O}_2\right]} \\ \mathrm{K}_3 & =\frac{\left[\mathrm{H}_2 \mathrm{O}\right]}{\left[\mathrm{H}_2\right]\left[\mathrm{O}_2\right]^{1 / 2}} \\ \mathrm{ K}_3 & =\frac{\left[\mathrm{H}_2 \mathrm{O}^3\right.}{\left[\mathrm{H}_2\right]^3\left[\mathrm{O}_2\right]^{3 / 2}} \end{aligned} Now K2⋅K33K1=[NO]2[N2][O2]×[H2O]3[H2]3[O2]3/2×[N2][H2]3[NH3]2=[NO]2[H2O]3[NH3]2[O2]5/2=K∴K=K2⋅K33K1\begin{aligned} & \frac{\mathrm{K}_2 \cdot \mathrm{K}_3{ }^3}{\mathrm{ K}_1} =\frac{[\mathrm{NO}]^2}{\left[\mathrm{ N}_2\right]\left[\mathrm{O}_2\right]} \times \frac{\left[\mathrm{H}_2 \mathrm{O}\right]^3}{\left[\mathrm{H}_2\right]^3\left[\mathrm{O}_2\right]^{3 / 2}} \times \frac{\left[\mathrm{N}_2\right]\left[\mathrm{H}_2\right]^3}{\left[\mathrm{NH}_3\right]^2} \\ & =\frac{[\mathrm{NO}]^2\left[\mathrm{H}_2 \mathrm{O}\right]^3}{\left[\mathrm{NH}_3\right]^2\left[\mathrm{O}_2\right]^{5 / 2}}=\mathrm{K} \\ & \therefore \mathrm{K}=\frac{\mathrm{K}_2 \cdot \mathrm{K}_3{ }^3}{\mathrm{ K}_1} \end{aligned}
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