For reaction: SO _ 2 ( g ) + (1)/(2) O _ 2 ( g ) ⇌ SO _ 3 ( g ) K _...

For reaction: ${SO}_{2 ( g )} + \dfrac{1}{2}{O}_{2 ( g )} ⇌ {SO}_{3 ( g )}$

${K}_{p} = 2 \times {10}^{12}$ at $300K$ and $1atm$ pressure.

The relation between equilibrium constant in terms of pressures ${K}_{p}$ and equilibrium constant in terms of concentration ${K}_{c}$ is

${K}_{p} = {K}_{c} \times ( RT{)}^{∆ ng}$

$⇒ 2 \times {10}^{12} = {K}_{c} \times ( 0 . 082 \times 300{)}^{- \dfrac{1}{2}}$

$⇒ {K}_{C} = 9 . 92 \times {10}^{12}$

$⇒ {K}_{C} = 0 . 992 \times {10}^{13}$

So, answer is 1.