College chemistry?

Question

Consider the voltaic cell, which is based on the cell reaction Zn(s)+Cu^ 2+ (aq)—> Zn^ 2+ (aq)+Cu(s).

under standard conditions what is the maximum electrical work, in joules, that the cell can accomplish if 53.0g of copper is plated out?

Answer 1

The maximum electrical work performed by a voltaic cell is give by ∆Gº = -nFEº

∆Gº = Gibbs Energy

n = moles of electrons transferred

F = Faraday = 96,485 C/mol

Eº = standard reduction potential

So, first, we must find Eº

Reduction half reaction (cathode): Cu2+(aq) + 2e- ==> Cu(s) ∆Eº = 0.34 V

Oxidation half reaction (anode): Zn(s) ===> Zn2+(aq) + 2e- ∆Eº = -0.76 V

Eº_cell = cathode - anode = 0.34 -(-0.76) = 1.10 V = 1.10 jolues/coulomb = 1.10 J/C

Next, let's find n, moles of electrons transferred:

53.0 g Cu(s) x 1 mol Cu/63.5 g Cu x 2 mol e-/mol Cu = 1.67 moles e-

Now, we can solve the equation for ∆Gº

∆Gº = -(1.67 mol e-)(96,495 C/mol e-)(1.10 J/C)

∆Gº = -177,243 J = - 177 kJ = max. electrical work

Note: the sign is negative indicating that the system (voltaic cell) is doing work on the surroundings.