(D) For reaction $(i)$: $N_2 + 2O_2 \rightleftharpoons 2NO_2$ with equilibrium constant $K_1$.For reaction $(ii)$: $2NO_2 \rightleftharpoons N_2 + 2O_

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(D) For reaction $(i)$: $N_2 + 2O_2 \rightleftharpoons 2NO_2$ with equilibrium constant $K_1$.For reaction $(ii)$: $2NO_2 \rightleftharpoons N_2 + 2O_2$,which is the reverse of $(i)$,so $K_2 = 1/K_1$.For reaction $(iii)$: $NO_2 \rightleftharpoons 1/2 N_2 + O_2$,which is half of reaction $(ii)$,so $K_3 = (K_2)^{1/2} = \sqrt{K_2}$.From $K_2 = 1/K_1$,we get $K_1 = 1/K_2$.From $K_3 = \sqrt{K_2}$,we get $K_3^2 = K_2$,so $K_2 = K_3^2$.Substituting $K_2$ in $K_1 = 1/K_2$,we get $K_1 = 1/K_3^2$.

Class 11 Chemistry 6-1.Equilibrium (Chemical Equilibrium)Law of equilibrium and Equilibrium constant

Medium

The equilibrium constants for the reactions $(i)$,$(ii)$,and $(iii)$ are $K_1$,$K_2$,and $K_3$ respectively. Which of the following is the correct relationship?
$(i)$ $N_2 + 2O_2 \rightleftharpoons 2NO_2$
$(ii)$ $2NO_2 \rightleftharpoons N_2 + 2O_2$
$(iii)$ $NO_2 \rightleftharpoons 1/2 N_2 + O_2$

A
$K_1 = \sqrt{K_2} = K_3$
B
$K_1 = 1/K_2 = 1/K_3$
C
$K_1 = K_2^2 = K_3$
D
$K_1 = 1/K_2 = 1/(K_3)^2$

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The equilibrium constant for the given reaction is $100$.
$N_{2(g)} + 2 O_{2(g)} \rightleftharpoons 2 NO_{2(g)}$
What is the equilibrium constant for the reaction given below?
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The equilibrium constants for the reactions $(i)$,$(ii)$,and $(iii)$ are $K_1$,$K_2$,and $K_3$ respectively. Which of the following is the correct relationship?$(i)$ $N_2 + 2O_2 \rightleftharpoons 2NO_2$$(ii)$ $2NO_2 \rightleftharpoons N_2 + 2O_2$$(iii)$ $NO_2 \rightleftharpoons 1/2 N_2 + O_2$

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$4.5 \text{ moles}$ each of hydrogen and iodine is heated in a sealed $10 \text{ litre}$ vessel. At equilibrium,$3 \text{ moles}$ of $HI$ were found. The equilibrium constant for $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$ is .......

The figure shows the change in concentration of species $A$ and $B$ as a function of time. The equilibrium constant $K_C$ for the reaction $2A_{(g)} \rightleftharpoons B_{(g)}$ is

The equilibrium constant for the given reaction is $100$.$N_{2(g)} + 2 O_{2(g)} \rightleftharpoons 2 NO_{2(g)}$What is the equilibrium constant for the reaction given below?$NO_{2(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + O_{2(g)}$

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The equilibrium constants for the reactions $(i)$,$(ii)$,and $(iii)$ are $K_1$,$K_2$,and $K_3$ respectively. Which of the following is the correct relationship?
$(i)$ $N_2 + 2O_2 \rightleftharpoons 2NO_2$
$(ii)$ $2NO_2 \rightleftharpoons N_2 + 2O_2$
$(iii)$ $NO_2 \rightleftharpoons 1/2 N_2 + O_2$

The equilibrium constant for the given reaction is $100$.
$N_{2(g)} + 2 O_{2(g)} \rightleftharpoons 2 NO_{2(g)}$
What is the equilibrium constant for the reaction given below?
$NO_{2(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + O_{2(g)}$