Question

For the given Nernst equation
$E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln \left[ \frac{\text{[Mg$^{2+}$]}}{\text{[Ag$^+$]}} \right]$
Which of the following representation is correct?

• A. Ag$^+$|Ag||Mg$^{2+}$|Mg
• B. Mg$^{2+}$|Mg||Ag|Ag$^+$
• C. Mg|Mg$^{2+}$||Ag$^+ $|Ag
• D. Mg|Mg$^{2+}$||Ag|Ag$^+$

Hint:

Key Exam Tip:
In electrochemical cell notation:
• Anode (oxidation) is written first: Reduced form | Oxidized form.
• Cathode (reduction) is written second: Oxidized form | Reduced form.
• A single vertical line (|) separates phases (e.g., electrode and solution).
• A double vertical line (||) separates the anode and cathode compartments, representing the salt bridge. The Nernst equation's reaction quotient ($Q$) directly reveals which species are oxidized and reduced, and thus the anode and cathode half-cells.

Answer 1

The Correct Option is C

The Nernst equation relates the cell potential ($E_{\text{cell}}$) of an electrochemical cell to the standard cell potential ($E^\circ_{\text{cell}}$) and the concentrations of the ions involved. The general form of the Nernst equation for a redox reaction is: $E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q$ where $Q$ is the reaction quotient. The given Nernst equation is: $E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln \left[ \frac{\text{[Mg$^{2+}$]}}{\text{[Ag$^+$]}} \right]$ In this equation, the term inside the logarithm, $\frac{\text{[Mg$^{2+}$]}}{\text{[Ag$^+$]}}$, represents the reaction quotient ($Q$). The reaction quotient is written as (products)/(reactants), considering the stoichiometric coefficients. The expression $\ln \left[ \frac{\text{[Mg$^{2+}$]}}{\text{[Ag$^+$]}} \right]$ indicates that Mg$^{2+}$ is in the numerator (likely a product of oxidation) and Ag$^+$ is in the denominator (likely a reactant in reduction). A cell representation in shorthand notation is written as: Anode | Anode Solution || Cathode Solution | Cathode The anode is where oxidation occurs, and the cathode is where reduction occurs. The species in the cell notation are written in the form of: Reduced form | Oxidized form (for anode) and Oxidized form | Reduced form (for cathode). From the reaction quotient $\frac{\text{[Mg$^{2+}$]}}{\text{[Ag$^+$]}}$, we can infer the half-reactions:
• Anode (Oxidation): Mg $\rightarrow$ Mg$^{2+}$ + 2e$^-$ (Mg is oxidized to Mg$^{2+}$)
• Cathode (Reduction): Ag$^+$ + e$^-$ $\rightarrow$ Ag (Ag$^+$ is reduced to Ag) Now let's construct the cell notation:
• Anode half-cell: Reduced form is Mg, oxidized form is Mg$^{2+}$. So, it's Mg | Mg$^{2+}$.
• Cathode half-cell: Oxidized form is Ag$^+$, reduced form is Ag. So, it's Ag$^+$ | Ag. Connecting these with the salt bridge (||): Anode || Cathode Mg | Mg$^{2+}$ || Ag$^+$ | Ag Let's check the given options: (a) Ag$^+$|Ag||Mg$^{2+}$|Mg: This represents Ag as anode and Mg as cathode, which is incorrect based on the reaction quotient. (b) Mg$^{2+}$|Mg||Ag|Ag$^+$: This representation is incorrect in how it writes the half-cells. The reduced form should be on the left for the anode, and the oxidized form on the left for the cathode. (c) Mg|Mg$^{2+}$||Ag$^+ $|Ag: This representation correctly shows Mg as the anode (oxidation) and Ag as the cathode (reduction), with the correct species in their respective states. (d) Mg|Mg$^{2+}$||Ag|Ag$^+$: This representation is incorrect in how it writes the cathode half-cell. Therefore, the correct representation of the cell is Mg|Mg$^{2+}$||Ag$^+ $|Ag. Final Answer: \(\boxed{c}\)