Question

Given four reactions and their equilibrium constants.

$N_2{O}_2\rightleftharpoons 2NO,K_1;\frac{1}{2}{N}_2+\frac{1}{2}{O}_2\rightleftharpoons NO,K_2;$
$2NO\rightleftharpoons N_2+O_2,K_3;NO\rightleftharpoons \frac{1}{2}{N}_2+\frac{1}{2}{O}_2,K_4$
Correct relation between $K_1,K_2,K_{3}and{K}_4$ is:

• A. $(K_4{)}^2=K_3$
• B. $\sqrt{K_3}\times K_2=1$
  
• C. both a and b
• D. None of the above

Answer 1

The correct option is C both a and b

$N_2{O}_2\rightleftharpoons 2NO,K_1;\frac{1}{2}{N}_2+\frac{1}{2}{O}_2\rightleftharpoons NO,K_2;$
$2NO\rightleftharpoons N_2+O_2,K_3;NO\rightleftharpoons \frac{1}{2}{N}_2+\frac{1}{2}{O}_2,K_4$

Reaction 3 is obtained by multiplying the reaction 4 with 2
Hence, $(K_4{)}^2=K_3$
(a) is correct.

Reaction 3 is obtained by dividing reaction 2 by two and then reversing it Hence, $\sqrt{K_3}\times K_2$ = 1
(b) is true.

So both (a) and (b) are correct.

As (a) and (b) are already correct so (d) is ignored.