A chemist designs a galvanic cell that uses these two half-reactions:

half-reaction standard reduction potential
MnO4⁻ (aq) + 8H⁺ (aq) + 5e⁻ → Mn(aq)²⁺ + 4H2O (l) E⁰red = +1.51V
Fe³⁺ (aq) +e⁻ → Fe²⁺(aq) E⁰red = +0.771V

Answer the following questions about this cell.
(a) Write a balanced equation for the half-reaction that happens at the cathode.
(b) Write a balanced equation for the half-reaction that that happens at the anode.
(c) Write a balanced equation for the overall reaction that powers the cell. Be sure the reaction is spontaneous as written.