The equilibrium mixture for $2{\mathrm{SO}}_{2\left(\mathrm{g}\right)}+{\mathrm{O}}_{2\left(\mathrm{g}\right)}\iff 2{\mathrm{SO}}_{3\left(\mathrm{g}\right)}$ present in 1litre vessel at 600°C contains 0.50, 0.12 and 5.0 mole of ${\mathrm{SO}}_2,{\mathrm{O}}_2\&{\mathrm{SO}}_3$respectively.

a) Calculate ${\mathrm{K}}_{\mathrm{C}}$ for the given change at 600°C

b) Calculate KP

c) How many mole of ${\mathrm{O}}_2$ must be forced into the equilibrium vessel at 600°C in order to increase the concentration of ${\mathrm{SO}}_3$ to 5.2 mole?