(D) For the first equilibrium: $AB \rightleftharpoons A^{+} + B^{-}$,$K_1 = \frac{[A^{+}][B^{-}]}{[AB]}$For the second equilibrium: $AB + B^{-} \right

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inversely proportional to the square of $[B^{-}]$

(D) For the first equilibrium: $AB \rightleftharpoons A^{+} + B^{-}$,$K_1 = \frac{[A^{+}][B^{-}]}{[AB]}$For the second equilibrium: $AB + B^{-} \rightleftharpoons AB_2^-$,$K_2 = \frac{[AB_2^-]}{[AB][B^{-}]}$Dividing $K_1$ by $K_2$,we get:$\frac{K_1}{K_2} = \frac{[A^{+}][B^{-}]}{[AB]} \times \frac{[AB][B^{-}]}{[AB_2^-]} = \frac{[A^{+}][B^{-}]^2}{[AB_2^-]}$Rearranging the expression to find the ratio $\frac{[A^{+}]}{[AB_2^-]}$:$\frac{[A^{+}]}{[AB_2^-]} = \frac{K_1}{K_2} \times \frac{1}{[B^{-}]^2}$Thus,the ratio $\frac{[A^{+}]}{[AB_2^-]}$ is inversely proportional to the square of $[B^{-}]$.

Class 11 Chemistry 6-1.Equilibrium (Chemical Equilibrium)Mix Examples- 6-1.Equilibrium (Chemical Equilibrium)

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Two equilibria,$AB \rightleftharpoons A^{+} + B^{-}$ and $AB + B^{-} \rightleftharpoons AB_2^-$,are simultaneously maintained in a solution with equilibrium constants $K_1$ and $K_2$ respectively. The ratio of $[A^{+}]$ to $[AB_2^-]$ in the solution is

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A
directly proportional to $[B^{-}]$
B
inversely proportional to $[B^{-}]$
C
directly proportional to the square of $[B^{-}]$
D
inversely proportional to the square of $[B^{-}]$

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Mix Examples- 6-1.Equilibrium (Chemical Equilibrium)

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In a $10 \ L$ vessel,$SO_3, SO_2$,and $O_2$ gases are present at a definite temperature with $K_c = 100$. For the reaction $2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$,if $SO_3$ and $SO_2$ are present in the same number of moles at equilibrium,find the moles of $O_2$. If $SO_3$ is double the moles of $SO_2$,what is the number of moles of $O_2$?

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The incorrect expression among the following is:

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At $67\,^{\circ}C$ and $1\ bar$ pressure,dinitrogen tetraoxide is $50\%$ dissociated into nitrogen dioxide. $\Delta G^{\circ}$ for the process $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$ is $(R = \frac{25}{3} \ J \ K^{-1} \ mol^{-1}, \ln 2 = 0.7, \ln 3 = 1.1)$.

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The two substances $A$ and $B$ are in equilibrium with $C$ and $D$ as $2A + B \rightleftharpoons 3C + 2D$. If the initial pressure of $A$ and $B$ are in the ratio of $4:1$ and at equilibrium,the partial pressures of $A$ and $D$ are equal,find the correct relation.

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When $5.1 \ g$ of solid $NH_4HS$ is introduced into a two litre evacuated flask at $27^{\circ}C$,$20\%$ of the solid decomposes into gaseous ammonia and hydrogen sulphide. The $K_p$ for the reaction at $27^{\circ}C$ is $x \times 10^{-2}$.
The value of $x$ is ....... . (Integer answer)
[Given $R=0.082 \ L \ atm \ K^{-1} \ mol^{-1}$]

MediumJEE MAIN 2021

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Two equilibria,$AB \rightleftharpoons A^{+} + B^{-}$ and $AB + B^{-} \rightleftharpoons AB_2^-$,are simultaneously maintained in a solution with equilibrium constants $K_1$ and $K_2$ respectively. The ratio of $[A^{+}]$ to $[AB_2^-]$ in the solution is

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The incorrect expression among the following is:

At $67\,^{\circ}C$ and $1\ bar$ pressure,dinitrogen tetraoxide is $50\%$ dissociated into nitrogen dioxide. $\Delta G^{\circ}$ for the process $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$ is $(R = \frac{25}{3} \ J \ K^{-1} \ mol^{-1}, \ln 2 = 0.7, \ln 3 = 1.1)$.

The two substances $A$ and $B$ are in equilibrium with $C$ and $D$ as $2A + B \rightleftharpoons 3C + 2D$. If the initial pressure of $A$ and $B$ are in the ratio of $4:1$ and at equilibrium,the partial pressures of $A$ and $D$ are equal,find the correct relation.

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