The cell diagram for the lead-acid cell that is used in automobile and truck bat

Question

The cell diagram for the lead-acid cell that is used in automobile and truck batteries is Pb(s) I PbSO4(s) I H2SO4(aq) I PbO2(s), PbSO4(s) I Pb(s)   where the comma between PbO2(s) and PbSO4(s) denotes a heterogeneous mixture of the two solids and the right-hand lead electrode is nonreactive. (a) Write the balanced equation for the net cell reaction. (b) Look up standard potentials for the oxidation and the reduction reactions, then calculate the value of E°cell. (c) Calculate the value of G°rxn. (d) Calculate the value of Ecell at 25°C if [H2SO4] = 10.0 M. (e) How many lead-acid cells are in a 12 V car battery? Round to the nearest integer.

Explanation / Answer

(a)
Pb(s)+SO4(2-) (aq) -------> PbSO4(s) + 2e-
PbO2(s) + SO4(2-) (aq) + 4H+ (aq) + 2e- -------> PbSO4 (s) + 2H2O (l)
Net reaction: Pb(s)+PbO2(s)+2SO4(2-) (aq) + 4H+ --> 2PbSO4 (s) + 2H2O (l)

(b)
1.6913V - (-0.3588V)= 2.0501V = 2.05 V


(c) Use the formula

deltaG= -nFE(cell) equation
deltaG= -(2)(96.485 kJ/V x mol)(2.05V)
= -395.58 kJ/mol

(d) Using formula
Ecell= Ecell(standard)- (0.0592V/n)(logQ)
Ecell= 2.05 V- (0.0592/2)(log(10))
=2.02 V

E) There are six lead-acid cells are in a 12 V car battery

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