\(\mathrm{H}_2 \mathrm{SO}_4\) is an oxidising agent. It oxidises \(\mathrm{HI}\) produced during the reaction to \(\mathrm{I}_2\) and thus prevents the reaction between an alcohol and HI to form alkyl iodide. To prevent this, a non-oxidising acid like \(\mathrm{H}_3 \mathrm{PO}_4\) is used.
\(2 \mathrm{KI}+\mathrm{H}_2 \mathrm{SO}_4 \rightarrow 2 \mathrm{KHSO}_4+2 \mathrm{HI} ; 2 \mathrm{HI}+\mathrm{H}_2 \mathrm{SO}_4 \rightarrow \mathrm{H}_2 \mathrm{O}+\mathrm{I}_2+\mathrm{SO}_2\)
\(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH}+\mathrm{KI}+\mathrm{H}_3 \mathrm{PO}_4 \stackrel{\Delta}{\longrightarrow}\)
\(\mathrm{CH}_3 \mathrm{CH}_2-\mathrm{I}+\mathrm{KH}_2 \mathrm{PO}_4+\mathrm{H}_2 \mathrm{O}\)