Question

For a general redox reaction} \[ \text{Anode: } \text{Red}_1 \rightarrow \text{Ox}_1^{n_1+} + n_1e^- \] \[ \text{Cathode: } \text{Ox}_2 + n_2e^- \rightarrow \text{Red}_2^{n_2-} \] Which of the following statement is incorrect?

• A. The overall reaction can be written as \( n_2\text{Red}_1 + n_1\text{Ox}_2 \rightarrow n_2\text{Ox}_1^{n_1+} + n_1\text{Red}_2^{n_2-} \)
• B. The electrons do not appear in the overall reaction because electrons produced at the anode are consumed at the cathode.
  

  

• C. In the Nernst equation plot, slope \( \propto \frac{1}{n} \), where \(n\) is number of electrons transferred in the redox reaction.
• D. If the reaction is carried out reversibly, the electrical work done is equal to the ratio of charge and potential difference through which charge is moved.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to identify the scientifically incorrect statement regarding redox reactions and electrochemical cells.
Step 2: Key Formula or Approach:
- Nernst equation: \(E = E^0 - \frac{2.303 RT}{nF} \log Q\).
- Electrical work: \(W = q \cdot \Delta V = nF \cdot E\).
Step 3: Detailed Explanation:
1. Statement A: Balanced redox reactions combine half-reactions such that electron gain equals electron loss. Correct.
2. Statement B: Electrons cancel out in the overall net cell reaction. Correct.
3. Statement C: From Nernst equation, \(\frac{E-E^0}{RT/F} = -\frac{2.303}{n} \log Q\). Thus slope is \(-2.303/n\), which is proportional to \(1/n\). Correct.
4. Statement D: Electrical work \(W\) is the PRODUCT of charge (\(q\)) and potential difference (\(\Delta V\)), not their ratio. Incorrect.
Step 4: Final Answer:
Statement (D) is the incorrect statement.