Calculate Ecell forthe following electrochemical cell at 25 C

Pt(s) |H2(g, 1.00 bar) |H
+
(aq, 1.00 M) || Pb2+(aq, 0.150 M) | Pb(s)

Look up Eo for H2 ==> 2H^+ + 2e Eo = 0

Calculate Eo for the Pb half cell.
E = Eo Pb + (0.0592/2)log(1/0.15)
Then Ecell = EoH2 + EoPb

To calculate the cell potential (Ecell) for the given electrochemical cell, we need to use the Nernst equation. The Nernst equation is given by:

Ecell = E°cell - (RT / nF) * ln(Q)

Where:
Ecell: Cell potential
E°cell: Standard cell potential at standard conditions
R: Gas constant (8.314 J/(mol⋅K))
T: Temperature in Kelvin
n: Number of electrons transferred in the balanced chemical equation
F: Faraday constant (96485 C/mol)
ln: Natural logarithm
Q: Reaction quotient

First, let's determine the balanced chemical equation for the cell reaction:

Pb2+(aq) + 2e- → Pb(s) ---- (1)
2H+(aq) + 2e- → H2(g) ---- (2)

Adding equation (1) and equation (2) cancels out the electrons:

Pb2+(aq) + 2H+(aq) → Pb(s) + H2(g)

The standard cell potential (E°cell) can be found using standard reduction potentials. The reduction half-reactions and their standard reduction potentials are:

Pb2+(aq) + 2e- → Pb(s) E° = -0.13 V (from reduction potential table)
2H+(aq) + 2e- → H2(g) E° = 0 V (by convention)

The standard cell potential (E°cell) is the sum of the reduction potentials:

E°cell = E°(cathode) - E°(anode)
= 0 V - (-0.13 V)
= 0.13 V

Now, we can calculate the reaction quotient (Q) using the concentrations of the species involved:

Q = [Pb2+(aq)] / [H+(aq)]^2

Given:
[Pb2+(aq)] = 0.150 M
[H+(aq)] = 1.00 M

Q = 0.150 / (1.00)^2
= 0.150

Plugging in the values into the Nernst equation:

Ecell = E°cell - (RT / nF) * ln(Q)

Since the concentration of H2(g) is constant (1.00 bar) in the cell, we can assume that Q is equal to 1. Therefore, ln(Q) is equal to 0 and can be ignored, simplifying the equation to:

Ecell = E°cell

Thus, the cell potential (Ecell) for the given electrochemical cell at 25°C is 0.13 V.