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
E = 0.057 V
To find the unknown concentration in the concentration cell, we can use the Nernst equation, which relates the electrode potential to the concentration of the ions involved.
The Nernst equation is given by:
Ecell = E°cell - (RT/nF) * ln(Q)
Where:
- Ecell is the cell potential
- E°cell is the standard cell potential
- R is the ideal gas constant (8.314 J/(mol*K))
- T is the temperature in Kelvin
- n is the number of electrons exchanged in the balanced redox reaction
- F is the Faraday constant (96,485 C/mol)
- Q is the reaction quotient, which is the ratio of product concentrations to reactant concentrations
In this case, the balanced redox reaction at both the anode and cathode is:
Pb2+(aq) + 2e^- -> Pb(s)
The number of electrons exchanged (n) is 2.
Given:
E = 0.057 V (cell potential)
E°cell is not provided, so we assume it to be 0 (considering standard hydrogen electrode as reference)
Now, we can rearrange the Nernst equation to solve for the unknown concentration (Pb2+ in this case). First, let's substitute the known values:
0.057 V = 0 V - (RT/(2F)) * ln(Q)
Next, let's rearrange the equation to solve for the unknown quantity (Q in this case):
ln(Q) = (2F/RT) * (0.057 V)
Now, let's calculate the value of Q:
Q = e^[(2F/RT) * (0.057 V)]
After obtaining the value of Q, we can equate it to the concentration ratio between the two compartments:
Q = [Pb2+(aq, ?)] / [Pb2+(aq, 0.1 M)]
Since we want to find the unknown concentration of Pb2+, we'll solve for [Pb2+(aq, ?)].
[Pb2+(aq, ?)] = Q * [Pb2+(aq, 0.1 M)]
Substituting the value of Q from the earlier calculation, we can find the unknown concentration.