Chemical Equilibrium

For reaction : \(\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{3}(\mathrm{~g})\)

\(\mathrm{K}_{\mathrm{p}}=2 \times 10^{12}\) at \(27^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) pressure. The \(\mathrm{K}_{\mathrm{c}}\) for the same reaction is ____________ \(\times 10^{13}\). (Nearest integer)

(Given \(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\))