Question

If the 0.05 molar solution of ${{M}^{+}}$ is replaced by 0.0025 molar ${{M}^{+}}$ solution, then the magnitude of the cell potential would be:
(A) 35mV
(B) 70mV
(C) 140mV
(D) 700mV

Answer 1

Hint: The cell potential of an electrochemical cell is the potential difference occurring between the two electrodes of the cell, and arises due to the transfer of electrons through the external circuit of a cell that has not reached equilibrium.

Complete step by step answer:
The Nernst equation is an equation that relates the reduction potential of an electrochemical reaction (half-cell or full cell reaction) to the standard electrode potential, temperature, and activities (often approximated by concentrations) of the chemical species undergoing reduction and oxidation.
\[{{E}_{cell}}={{E}^{{}^\circ }}_{cell}-\frac{RT}{nF}\ln Q\]

A concentration cell is an electrolytic cell that is composed of two half-cells with the same electrodes, but differing in concentrations. A concentration cell acts to dilute the more concentrated solution and concentrate the more dilute solution, creating a voltage as the cell reaches an equilibrium.
Concentration cells consist of anode and cathode compartments that are identical except for the concentrations of the reactant. Because ΔG = 0 at equilibrium, the measured potential of a concentration cell is zero at equilibrium (the concentrations are equal).
Therefore, ${{E}^{{}^\circ }}_{cell}$= 0, for every concentration cell,
\[\begin{align}
 & {{E}_{cell}}={{E}^{{}^\circ }}_{cell}-\frac{RT}{nF}\ln Q \\
 & {{E}_{cell}}=0-\frac{0.059}{1}\log [0.0025] \\
 & {{E}_{cell}}=153mV \\
\end{align}\]
The obtained value is 153mV which is close to the 140mV among the given options.
So, the correct answer is “Option C”.

Note: Electrolyte Concentration cells consist of identical electrodes immersed in the solutions of the same electrolytes but with varying concentrations. In these cells, the electrolyte tends to diffuse from higher concentration solutions towards solutions of lower concentration.