Pure acids in the liquid state are exceedingly poor conductors of electricity. The fact that aqueous solutions of acids conduct electricity is definite evidence of the existence of ions in these solutions. Acids undergo dissociation in aqueous solution to form H+ ions.
When electricity is passed through an aqueous solution of an acid, the H+ ions reach the cathode and each H+ ion picks up one electron from the cathode to form H2 gas. Because of this reaction, an aqueous solution of acid conducts electricity.
HCl(aq) → H+(aq) + Cl–(aq)
The solute to be dissolved by the solvent has fewer particles in it in an aqueous solution where water plays the role of solvent, making the particles travel in random motion. In simple words, due to the presence of ions, the aqueous solution of acid conduct electricity.