A concentration cell consists of the same re- dox couples at the anode and the cathode, with different concentrations of the ions in the respective compartments. Find the un- known concentration for the following cell. Pb(s) | Pb2+(aq, ?) ||
Pb2+(aq, 0.1 M) | Pb(s) Answer in units of M
To find the unknown concentration in the concentration cell, we can use the Nernst equation. The Nernst equation is given by:
Ecell = E°cell - (RT/nF) * ln(Q)
Where:
Ecell = Cell potential (in volts)
E°cell = Standard cell potential (in volts)
R = Gas constant (8.314 J/(mol·K))
T = Temperature (in Kelvin)
n = Number of electrons transferred in the balanced redox reaction
F = Faraday constant (96485 C/mol)
Q = Reaction quotient
In this case, the cell consists of the same redox couple at the anode and cathode, which is the Pb/Pb2+ couple. The half-reactions involved are:
Anode: Pb(s) → Pb2+(aq) + 2e-
Cathode: Pb2+(aq) + 2e- → Pb(s)
The balanced equation for the overall cell reaction is:
Pb(s) + Pb2+(aq) → 2Pb2+(aq)
Since the same redox couple is used, the standard cell potential (E°cell) is 0 volts.
Now, let's use the Nernst equation to find the unknown concentration of Pb2+ in the first compartment (denoted as [Pb2+]).
Ecell = 0 - (RT/2F) * ln(Q)
Since Ecell is 0, the equation becomes:
0 = -(RT/2F) * ln(Q)
Q is the reaction quotient, which is equal to [Pb2+ in second compartment] / [Pb2+ in first compartment]. So, Q = [0.1 M] / [Pb2+].
The equation now becomes:
0 = -(RT/2F) * ln([0.1 M] / [Pb2+])
To solve for [Pb2+], rearrange the equation:
ln([0.1 M] / [Pb2+]) = 0
Taking the natural logarithm of both sides:
ln([0.1 M] / [Pb2+]) = ln(1)
Simplifying:
ln([0.1 M] / [Pb2+]) = 0
Since the natural logarithm of 1 is 0, we have:
[0.1 M] / [Pb2+] = 1
Solve for [Pb2+]:
[Pb2+] = [0.1 M]
Therefore, the unknown concentration in the first compartment is 0.1 M (Molar).