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.