Consider the following reversible chemical reactions:
$A_{2(g)} + B_{2(g)} \overset {K_1} \leftrightarrows 2AB_{(g)} ......(1)$
$6AB_{(g)} \overset {K_2} \leftrightarrows 3A_{2(g)} + 3B_{2(g)} ......(2)$
The relation between $K_1$ and $K_2$ is:

The gas phase reaction $2A_{(g)} \rightleftharpoons A_{2(g)}$ at $400 \ K$ has $\Delta G^{\circ} = +25.2 \ kJ \ mol^{-1}$. The equilibrium constant $K_{C}$ for this reaction is $...... \times 10^{-2}$. (Round off to the nearest integer) $[$Use: $R = 8.3 \ J \ mol^{-1} \ K^{-1}$,$\ln 10 = 2.3$,$\log_{10} 2 = 0.30$,$1 \ atm = 1 \ bar]$ $[$antilog $(-3.3) = 5.01 \times 10^{-4}]$

Consider the equilibrium,$H_2 + I_2 \rightleftharpoons 2 HI$. Calculate the equilibrium constant of the reverse reaction when the equilibrium concentrations of $H_2$,$I_2$,and $HI$ are $1.14 \times 10^{-2} \ mol \ L^{-1}$,$0.12 \times 10^{-2} \ mol \ L^{-1}$,and $2.52 \times 10^{-2} \ mol \ L^{-1}$,respectively.

At $1000\, K$ and $2\, atm$ pressure,a gaseous mixture of $CO$ and $CO_{2}$ in equilibrium with solid carbon has $84\%$ $CO_{(g)}$ by mass. Calculate $K_{p}$ for the reaction: $C_{(s)} + CO_{2_{(g)}} \rightleftharpoons 2CO_{(g)}$ at this temperature.

For the reaction $SO_{2(g)} + 1/2 O_{2(g)} \rightleftharpoons SO_{3(g)}$,the equilibrium constant is $K_1$ at $298 \, K$. For the reaction $2SO_{3(g)} \rightleftharpoons 2SO_{2(g)} + O_{2(g)}$ at the same temperature,the equilibrium constant is $K_2$. Then,which of the following is correct?

$1.1 \ mol$ of $A$ are mixed with $2.2 \ mol$ of $B$ and the mixture is kept in a $1 \ L$ vessel till the equilibrium is established in the reaction. If the molar concentration of $C$ at the equilibrium point is $0.2 \ M$,then find the value of the equilibrium constant $(K_c)$ for the reaction: $A + 2B \rightleftharpoons 2C + D$