Electrode potential origin; Zn reduction potential

Electrode potential

The potential difference developed between a metal and the solution of its own ions at their interface, due to the tendency of the metal to lose or gain electrons.

Origin

A metal rod in a solution of its ions has two opposite tendencies. Metal atoms may go into solution as ions, leaving electrons on the rod (M → Mⁿ⁺ + ne⁻), so the rod becomes negative and attracts positive ions around it. Or ions of the solution may take electrons from the rod and deposit as metal, making the rod positive. Dynamic equilibrium is reached and an electrical double layer forms; the potential difference across it is the electrode potential.

Reduction potential of Zn²⁺/Zn

Reading: the question's "0.1 M H₂SO₄" has no Zn²⁺ given; I take the zinc in contact with 0.1 M Zn²⁺ solution (ZnSO₄). E°Zn/Zn²⁺ = +0.768 V is an oxidation potential, so E°(Zn²⁺/Zn) = −0.768 V.

Zn²⁺ + 2e⁻ → Zn
E = E° + (0.0591/n) log [Zn²⁺]
  = −0.768 + (0.0591/2) log (0.1)
  = −0.768 − 0.0296
  = −0.7976 V

Answer: E(Zn²⁺/Zn) ≈ −0.80 V.