The standard entropies of sulphur dioxide, sulphur trioxide and oxygen at $298K$

and $1$atm are $248\mathrm{.}5,256\mathrm{.}0$ and $205\mathrm{.}0J.K^{-1}.mo{l}^{-1}$ respectively. For the reaction

involving the formation of $S{O}_3,H{O}_{2}28K=-98\mathrm{.}32kJ.mo{l}^{-1}.$

$($i$)$ Calculate the equilibrium constant for the reaction at $298K$

$($ii$)$ If the pressure of the system is raised to $2$ atm what would be:

$($a$)$ the change in $G$ and

$($b$)$ the overall $G(rxn)$