An equilibrium is established ${\mathrm{SO}}_2,{\mathrm{O}}_2$ and ${\mathrm{SO}}_3$ as ${\mathrm{SO}}_2\left(g\right)+\frac{1}{2}{\mathrm{O}}_2\left(g\right)\rightleftharpoons {\mathrm{SO}}_3\left(g\right)$ starting with 2 moles ${\mathrm{SO}}_2$ and $1.5$ moles ${\mathrm{O}}_2$ in 5 liter flask. The equilibrium mixture required $0.4$ moles of $KMn{O}_4$ in acidic medium. The value of $K_C^{\circ }$ is :