In a cell that utilizes the reaction $\mathrm{Zn}\left(\mathrm{s}\right)+2{\mathrm{H}}^{+}\left(\mathrm{aq}\right)\to {\mathrm{Zn}}^{2+}\left(\mathrm{aq}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)$ addition of ${\mathrm{H}}_2\mathrm{SO}4$ to cathode compartment, will

For the reaction $\mathrm{Zn}\left(\mathrm{s}\right)+2{\mathrm{H}}^{+}\left(\mathrm{aq}\right)\to {\mathrm{Zn}}^{2+}\left(\mathrm{aq}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)$ we have $E_{\text{cell }}=E_{\text{cell }}^{\circ }-\frac{RT}{nF}\ln \frac{\left.\left(\left[{\mathrm{Zn}}^{2+}\right]/c^{\circ }\right)\left(p_{{\mathrm{H}}_2}/p^{\circ }\right)\right]}{{\left(\left[{\mathrm{H}}^{+}\right]/c^{\circ }\right)}^2}$On adding ${\mathrm{H}}_2{\mathrm{SO}}_4$ , the [${\mathrm{H}}^{+}$] increases. This will increase the value of E cell and the reaction proceeds more to right side of the reaction ( Le- Chatelier principle).