Why can't iodide be oxidised to iodate in acidic medium?
Permanganate oxidizes iodide to iodine $\ce{I2}$ at all pH values. In acidic conditions, the reaction is finished here. But in basic solution, the iodine $\ce{I2}$ is transformed into iodide and iodate according to $$\ce{3I2 + 6 OH^- -&gt; 5 I- + IO3^- + 3 H2O}$$The mixture  iodide + iodate reacts the other way as soon as the solution becomes acidic : $$\ce{5I^- + IO3^- + 6 H+ -&gt; 3 I2 + 3 H2O}$$