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

Pb(s) l PbSO4 (s) l H2SO4 (aq) l PbO2(s), PbSO4(s) l 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 a balanced equation for the net cell reaction:

b)Look up standard potentials for the oxidation and the reduction reactions, then calculate the value of E0cell.

c) Calculate the value of deltaG0rxn

d) Calculate the value of Ecell at 25C is [H2SO4] = 10.0M

e) How many lead-acid cells are in a 12 V car battery? Round to the nearest integer.

A) Pb(s)+PbO2(s)+2SO4^2-(aq)+4H^4->2PbSO4(s)+2H2O(l)

B)2.04
C) -393.66
D)2.07
E)6

(a)Using the half reactions, you can sum them to determine the balanced equation.

(b)To find the E(0) cell, use the standard potentials with the correct signs and sum them
(c)To find the changeG^0 rxn, use the formula -nFE^0 and the E^0 calculated in (b)

a) The balanced equation for the net cell reaction is:

Pb(s) + PbO2(s) + 2H2SO4(aq) → 2PbSO4(s) + 2H2O(l)

b) The standard potentials for the oxidation and reduction reactions are:

Pb(s) → Pb2+(aq) + 2e- (oxidation) - E°red = -0.13 V
PbO2(s) + 4H+(aq) + 2e- → Pb2+(aq) + 2H2O(l) (reduction) - E°red = +1.69 V

The overall standard cell potential (E°cell) can be calculated by subtracting the reduction potential from the oxidation potential:

E°cell = E°red (reduction) - E°red (oxidation)
E°cell = +1.69 V - (-0.13 V)
E°cell = +1.82 V

c) The value of ΔG°rxn (standard Gibbs free energy change) can be calculated using the equation:

ΔG°rxn = -nFE°cell

Where n is the number of electrons transferred, and F is the Faraday constant (96,485 C/mol).

Since 2 electrons are transferred in the balanced equation, the value of ΔG°rxn is:

ΔG°rxn = -2 × 96,485 C/mol × 1.82 V
ΔG°rxn = -349,702 J/mol

d) To calculate Ecell at 25°C with [H2SO4] = 10.0 M, we can use the Nernst equation:

Ecell = E°cell - (0.0592 V/n) × log(Q)

Where Q is the reaction quotient, which can be calculated as:

Q = [PbSO4]^2 / [H2SO4]^2

At 25°C, the concentrations of solid species do not affect the reaction quotient. Therefore, the Q value can be expressed as:

Q = 1 / [H2SO4]^2

Substituting the values into the Nernst equation:

Ecell = 1.82 V - (0.0592 V/2) × log(1 / 10.0^2)
Ecell = 1.82 V - (0.0296 V) × log(0.01)
Ecell ≈ 1.82 V - (-0.059 V)
Ecell ≈ 1.88 V

e) A single lead-acid cell produces approximately 2 volts. Therefore, a 12 V car battery consists of approximately 12/2 = 6 lead-acid cells. Rounded to the nearest integer, there are 6 lead-acid cells in a 12 V car battery.

a) To write a balanced equation for the net cell reaction, we need to identify the oxidation and reduction reactions happening at each electrode.

Oxidation half-reaction: Pb(s) -> PbSO4(s) + 2e-
Reduction half-reaction: PbO2(s) + 4H+(aq) + 2e- -> PbSO4(s) + 2H2O(l)

To balance the electrons transferred in both reactions, we multiply the oxidation half-reaction by 2 and the reduction half-reaction by 1.

2Pb(s) + 2H2SO4(aq) + PbO2(s) -> 2PbSO4(s) + 2H2O(l) + 2Pb(s)

Simplifying the equation gives us:
Pb(s) + H2SO4(aq) + PbO2(s) -> 2PbSO4(s) + 2H2O(l)

b) To calculate the standard cell potential (E0cell), we need to look up the standard reduction potentials for the oxidation and reduction reactions.

The standard reduction potential values (E0red) are:
Pb2+(aq) + 2e- -> Pb(s) : E0red = -0.13 V
PbO2(s) + 4H+(aq) + 2e- -> PbSO4(s) + 2H2O(l) : E0red = 1.69 V

The standard cell potential (E0cell) is calculated by subtracting the oxidation potential (E0red) from the reduction potential (E0red) because the reduction potential is multiplied by -1 when it is a reduction reaction.

E0cell = E0red (reduction) - E0red (oxidation)
E0cell = (1.69 V) - (-0.13 V)
E0cell = 1.82 V

c) To calculate the standard Gibbs free energy change (ΔG0rxn), we can use the following equation:

ΔG0rxn = -nF E0cell

where n is the number of moles of electrons transferred in the balanced equation and F is the Faraday constant (approximately 96,485 C/mol).

From the balanced equation, we see that 2 moles of electrons are transferred.

ΔG0rxn = -2 * 96,485 C/mol * 1.82 V
ΔG0rxn = -349,913 J/mol

d) To calculate the cell potential (Ecell) at 25°C with a given concentration of H2SO4, we need to use the Nernst equation, which accounts for concentration differences:

Ecell = E0cell - (RT / nF) * ln(Q)

Where:
R = gas constant (8.314 J/mol·K)
T = temperature in Kelvin
n = moles of electrons transferred in the balanced equation
F = Faraday constant (96,485 C/mol)
Q = reaction quotient (the concentration of products over reactants)

Assuming standard conditions (1 M), the concentration of H2SO4 is 10.0 M. We plug all the values into the equation:

Ecell = 1.82 V - ((8.314 J/mol·K) * (298 K) / (2 * 96,485 C/mol)) * ln(1 / (10.0^2))
Ecell ≈ 1.57 V

e) A 12 V car battery typically consists of six lead-acid cells connected in series. Each cell has an average voltage of 2 V (at full capacity). Therefore,

Number of cells in a 12 V car battery = 12 V / 2 V = 6 cells (rounded to the nearest integer)

Hence, there are 6 lead-acid cells in a 12 V car battery.

And exactly what is your problem. Do you have the potentials.