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 this concentration cell, we can apply the Nernst equation. The Nernst equation is given by:
E_cell = E°_cell - (0.0592 V/n) * log(Q)
In this case, since the anode and cathode have the same redox couple, their standard cell potential (E°_cell) is 0 V.
E_cell = 0 V - (0.0592 V) * log(Q)
Q represents the reaction quotient, which is the ratio of concentrations of products to reactants raised to their stoichiometric coefficients.
In this case, the reaction at both the anode and cathode is:
Pb(s) -> Pb2+(aq)
Since the concentration of Pb2+ at the anode is unknown and Pb2+ at the cathode is 0.1 M, the reaction quotient (Q) can be represented as:
Q = [Pb2+]_anode / [Pb2+]_cathode
Substituting the values into the Nernst equation:
0 V = 0 - (0.0592 V) * log([Pb2+]_anode / 0.1 M)
To solve for the unknown concentration [Pb2+]_anode, we rearrange the equation:
log([Pb2+]_anode / 0.1 M) = 0
Since log(1) = 0, the equation becomes:
[Pb2+]_anode / 0.1 M = 1
Solving for [Pb2+]_anode:
[Pb2+]_anode = 0.1 M
Therefore, the unknown concentration in this concentration cell is 0.1 M.