The SO$3$ used in the manufacture of sulfuric acid is obtained by the oxidation of SO$2$ in the presence of an appropriate catalyst:

SO$2+0\mathrm{.}5$O$2$ SO$3$

If one starts with a feed of the composition shown below, determine the temperature at which the fluid must leave the reactor if the equilibrium effluent composition corresponds to $95\%$ conversion of the SO$2$ fed to the reactor.

O$2------>13$ mol$\%$ feed composition

N$2------>79$ mol$\%$ feed composition

SO$2----->8$ mol$\%$ feed composition

The effluent pressure is $2$ atm. At $600$C the standard Gibbs free$-$energy change for standard states of unit fugacity is known to be $3995$ cal$/$mol for the reaction as written above. For the temperature range of interest, the standard heat of reaction may be taken as a constant equal to $22,650$ cal$/$mol$.$