For the reaction $SO_{3(g)} \rightleftharpoons SO_{2(g)} + \frac{1}{2}O_{2(g)}$,the equilibrium constant $K_C = 4.9 \times 10^{-2}$. Calculate the $K_C$ for the reaction $2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$.

$2N_2O_{4(g)} \rightleftharpoons 4NO_{2(g)}$ has $K_p = 0.15 \, atm$ at $298 \, K$. Calculate $K_p$ in $torr$ and $K_c$ in $mol \, L^{-1}$. ($1 \, atm = 760 \, torr$; $R = 0.082 \, L \, atm \, mol^{-1} \, K^{-1}$).

For the reaction $2NOCl_{(g)} \rightleftharpoons 2NO_{(g)} + Cl_{2(g)}$,the value of equilibrium constant $K_p$ is $0.033 \ bar$ at $1060 \ K$. Calculate the value of $K_c$.

Given the equilibria:
$I: A + 2B \rightleftharpoons C ; K_{eq} = K_1$
$II: C + D \rightleftharpoons 3A ; K_{eq} = K_2$
$III: 6B + D \rightleftharpoons 2C ; K_{eq} = K_3$
Which of the following relations is correct?

The reaction rate for the reaction $[PtCl_4]^{2-} + H_2O \rightleftharpoons [Pt(H_2O)Cl_3]^- + Cl^-$ was measured as a function of concentrations of different species. It was observed that $\frac{-d[[PtCl_4]^{2-}]}{dt} = 4.8 \times 10^{-5} [[PtCl_4]^{2-}] - 2.4 \times 10^{-3} [[Pt(H_2O)Cl_3]^-] [Cl^-]$,where square brackets are used to denote molar concentrations. The equilibrium constant $K_c = ...$. (Nearest integer)

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 $(-3.3) = 5.01 \times 10^{-4}]$