(a)
Equilibrium constant for the reaction,
$SO_{2}(g) + \frac{1}{2}O_{2} \rightleftharpoons SO_{3}(g)$
$K_{c} = \frac{1}{4.9 \times 10^{- 2}}$
and for $2SO_{2} + O_{2} \rightleftharpoons 2SO_{3}(g)\$
$K_{c} = \left( \frac{1}{4.9 \times 10^{- 2}} \right)^{2}$
$= \frac{10^{4}}{(4.9)^{2}} = 416.49$