The theoretical energy consumption per kg of aluminum and

Question

Aluminum metal is produced by electrolysis of alumina dissolved in a mixture of molten fluorides at 970 ^oC. The free enthalpy (Gibbs function) change for the reaction:

Al₂O_{3 (soln)} + 3/2C_(c) = 2Al_(l) + 3/2CO_{2 (g)}

under these conditions is: DG = 698.7 kJ/mol. The observed cell voltage is 4.5 volts and the cathodic current efficiency is 90%.

Calculate:    

a) the reversible cell voltage (E_rev);

b) the theoretical energy consumption per kg of aluminum;

c) the current required for the production of 1 metric ton of aluminum per day;

d) the electrical energy actually required per metric ton of aluminum;

e) the voltages efficiency and the energy efficiency of the process.

f) the amount of heat dissipated in the process assuming that the enthalpy required for the reaction above is D_rH = 1,263.77 kJ mol^-1.