For the reaction $SO_{2(g)} + \frac{1}{2}O_{2(g)} \rightleftharpoons SO_{3(g)}$,the relationship is given by $K_P = K_C(RT)^x$. Find the value of $x$.

Find out the value of $K_{c}$ for each of the following equilibria from the value of $K_{p}$:
$(i)$ $2 NOCl_{(g)} \longleftrightarrow 2 NO_{(g)} + Cl_{2(g)}$; $K_{p} = 1.8 \times 10^{-2}$ at $500 \ K$
$(ii)$ $CaCO_{3(s)} \longleftrightarrow CaO_{(s)} + CO_{2(g)}$; $K_{p} = 167$ at $1073 \ K$

When one mole of $A$ and one mole of $B$ were heated in a one-litre flask at $T \ K$,$0.5 \ mole$ of $C$ was formed at equilibrium for the reaction $A + B \rightleftharpoons C + D$. The equilibrium constant,$K_C$,is:

For the reversible reaction, $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$. When the partial pressure is measured in atmosphere, the value of $K_p$ at $500^{\circ}\text{C}$ is $1.44 \times 10^{-5}$. The value of $K_c$ when the concentration is expressed in $\text{mol L}^{-1}$ is:

At $800 \ K$ in a closed vessel,the molar concentrations of $N_2, O_2$ and $NO$ at equilibrium are $3.2 \times 10^{-3} \ M, 4.2 \times 10^{-3} \ M$ and $2.8 \times 10^{-3} \ M$ respectively. The approximate values of $K_{c}$ and $\frac{1}{K_{c}}$ for the following reaction are respectively: $N_{2(g)} + O_{2(g)} \rightleftharpoons 2 NO_{(g)}$

$A_{(g)} + 3B_{(g)} \rightleftharpoons 4C_{(g)}$. The starting concentrations of $A$ and $B$ are equal. At equilibrium,the concentrations of $A$ and $C$ are the same. The value of $K_c$ is: