The gas leaving a pyrites roaster in a sulphuric acid plant has the following composition. SO$2=7\%,$ O$2=10\mathrm{.}5\%,$ SO$3=0\mathrm{.}8\%,$ N$2=81\mathrm{.}7\%.$ The heat capacity $($CP$,$ kJ$/$kmol$-$K$)$ of the gases varies with temperature $($T$,$ in K$)$ is given below:

O$2=25\mathrm{.}74+12\mathrm{.}98$x$10–3$ T$–3\mathrm{.}864$x$10–6$ T$2$

N$2=27\mathrm{.}03+5\mathrm{.}815$x$10–3$ T$–0\mathrm{.}289$x$10–6$ T$2$

SO$3=34\mathrm{.}33+42\mathrm{.}86$x$10–3$ T$–14\mathrm{.}298$x$10–6$ T$2$

SO$2=25\mathrm{.}74+57\mathrm{.}96$x$10–3$ T$–38\mathrm{.}11$x$10–6$ T$2$

Calculate the enthalpy of the gas mixture at $750$ K with reference to a base temperature of $298$ K