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JIPMER 2007
Exam
JIPMER
Year
2007
Subject
Chemistry
Chapter
Chemical Equilibrium

JIPMER 2007 · Chemistry · Chemical Equilibrium

Equilibrium constants K_1 and K_2 for the following equilibria...

Equilibrium constants K1K_1 and K2K_2 for the following equilibria NO(g)+12O2⇌K1NO2(g)\mathrm{NO}(g)+\frac{1}{2} \mathrm{O}_2 \stackrel{K_1}{\rightleftharpoons} \mathrm{NO}_2(g) and 2NO2(g)⇌K22NO(g)+O2(g)2 \mathrm{NO}_2(g) \stackrel{K_2}{\rightleftharpoons} 2 \mathrm{NO}(g)+\mathrm{O}_2(g) are related as

Options

  1. AK2=1K1K_2=\frac{1}{K_1}
  2. BK2=K12K_2=K_1^2
  3. CK2=K12K_2=\frac{K_1}{2}
  4. DK2=1K12K_2=\frac{1}{K_1^2}

Correct answer

D. K2=1K12K_2=\frac{1}{K_1^2}

Step-by-step solution

(i) NO(g)+12O2(g)⇌K1NO2(g)\mathrm{NO}(g)+\frac{1}{2} \mathrm{O}_2(g) \stackrel{K_1}{\rightleftharpoons} \mathrm{NO}_2(g) So K1=[NO2][NO][O2]12...(i)K_1=\frac{\left[\mathrm{NO}_2\right]}{[\mathrm{NO}]\left[\mathrm{O}_2\right]^{\frac{1}{2}}}...(i) (ii) 2NO2(g)⇌K22NO+O2(g)2 \mathrm{NO}_2(g) \stackrel{K_2}{\rightleftharpoons} 2 \mathrm{NO}+\mathrm{O}_2(g) So K2=[NO]2[O2][NO2]2...(ii)K_2=\frac{[\mathrm{NO}]^2\left[\mathrm{O}_2\right]}{\left[\mathrm{NO}_2\right]^2}...(ii) From Eq. (i) K12=[NO2]2[ NO ]2[O2]K_1^2=\frac{\left[\mathrm{NO}_2\right]^2}{\left[\mathrm{\text{ NO }]}^2\left[\mathrm{O}_2\right]\right.}oror\frac{1}{K_1^2}=\frac{\left[\mathrm{NO}\right]^2\left[\mathrm{O}_2\right]}{\left[\mathrm{NO}_2\right]^2}...(iii) From Eqs. (ii) and (iii) K2=1K12K_2=\frac{1}{K_1^2}
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