2.4.4 Determination of Cell Potential

In the previous section, we learned how to measure the potential of a single half-cell relative to the Standard Hydrogen Electrode (SHE). Now, we will learn how to determine the overall cell potential (E⁰_cell) of a galvanic cell made from any two half-cells. The cell potential is the driving force that pushes electrons through the external circuit, and its value tells us whether a reaction is spontaneous.

Main Idea

The cell potential is determined by combining the standard reduction potentials of the two half-cells. The half-cell with the greater (more positive) reduction potential undergoes reduction and acts as the cathode. The half-cell with the smaller (more negative) reduction potential undergoes oxidation and acts as the anode. The overall cell potential is the difference between these two potentials: E⁰_cell = E⁰_cathode - E⁰_anode

Core Concept

The core concept is that the overall cell potential is the algebraic difference between the standard reduction potentials of the two half-cells. A positive E⁰_cell indicates that the reaction is spontaneous (feasible) in the forward direction. A negative E⁰_cell means the reaction is non-spontaneous, and the reverse reaction would be spontaneous instead.

Detailed Explanation

The textbook explains the method to determine the cell potential step-by-step.

Step 1: Identify the Two Half-Cells and Their Standard Reduction Potentials

A cell reaction consists of two half-reactions. You are given (or can look up) the standard reduction potentials for each half-cell.

• Zn^{2+} + 2e^- \rightarrow Zn\) \(E⁰ = -0.76 V
• Cu^{2+} + 2e^- \rightarrow Cu\) \(E⁰ = +0.34 V

Step 2: Identify the Cathode and Anode

• Reduction takes place in the half-cell having the greater value of reduction potential.
• In this case, copper (+0.34 V) has the greater reduction potential, so copper is the cathode.
• Oxidation takes place in the half-cell having the smaller value of reduction potential.
• Zinc (-0.76 V) has the smaller reduction potential, so zinc is the anode.

Step 3: Reverse the Anode Half-Reaction

The equation of the half-cell reaction having a smaller value of reduction potential is reversed and added to the equation of the half-cell having a greater value of reduction potential. The sum of these two equations represents the cell reaction.

- Cathode (reduction): Cu^{2+} + 2e^- \rightarrow Cu - Anode (oxidation, reversed): Zn \rightarrow Zn^{2+} + 2e^- - Overall Cell Reaction: Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu

Step 4: Calculate the Standard Cell Potential

Standard cell potential E⁰_cell or emf of the cell is the algebraic difference between the respective standard reduction potentials of the two half-cells.

E⁰_cell = E⁰_cathode - E⁰_anode

Substitute the values: E⁰_cell = (+0.34 V) - (-0.76 V) E⁰_cell = +0.34 + 0.76 E⁰_cell = +1.10 V

Since the value is positive, the reaction is spontaneous.

Key Note from the Textbook

The standard reduction potential values of reactions do not change when the coefficients of the half-reactions are multiplied to balance the electrons. The potential is an intensive property (like temperature or density); it does not depend on the amount of substance.

Intermediate Level

• Look up the standard reduction potentials for both half-cells.
• The half-cell with the more positive E⁰ value is the cathode (reduction).
• The half-cell with the more negative E⁰ value is the anode (oxidation).
• Use the formula E⁰_cell = E⁰_cathode - E⁰_anode.
• If E⁰_cell is positive, the reaction is spontaneous. If negative, it is non-spontaneous.

This method allows you to predict whether a redox reaction will occur and to calculate the voltage of a battery made from any two half-cells.

Important Points

• - Cathode: The half-cell with the greater (more positive) reduction potential.
• - Anode: The half-cell with the smaller (more negative) reduction potential.
• - Formula: E⁰_cell = E⁰_cathode - E⁰_anode.
• - A positive E⁰_cell means the reaction is spontaneous.
• - A negative E⁰_cell means the reaction is non-spontaneous (the reverse reaction is spontaneous).
• - The cell reaction is obtained by reversing the anode half-reaction and adding it to the cathode half-reaction.
• - The E⁰ value is an intensive property and is not multiplied by the coefficients.

Remember

• - E°cell = E°cathode - E°anode.
• - Cathode = more positive reduction potential.
• - Anode = more negative reduction potential.
• - Positive E°cell → Spontaneous.
• - Negative E°cell → Non-spontaneous.
• - Reverse the anode half-reaction to get the oxidation reaction.
• - Do not multiply E⁰ values by stoichiometric coefficients.

Common Mistakes

• - Adding the potentials instead of subtracting them. The correct formula is E⁰_cell = E⁰_cathode - E⁰_anode.
• - Reversing the formula. A common mistake is to do E⁰_anode - E⁰_cathode, which gives the wrong sign and the wrong conclusion about spontaneity.
• - Multiplying the E⁰ value by the coefficients. Students often think they need to multiply the potential by the number of electrons transferred to balance the equation. This is incorrect; the potential is an intensive property.
• - Forgetting to reverse the anode half-reaction. The cell reaction is the sum of the reduction half-reaction (as written) and the oxidation half-reaction (the reverse of the reduction half-reaction).
• - Assuming a positive cell potential always means the reaction is fast. A positive E⁰_cell means the reaction is thermodynamically favorable, but it may be kinetically slow (it might need a catalyst).

Quick Revision

The cell potential is determined by combining the standard reduction potentials of two half-cells. The half-cell with the more positive reduction potential is the cathode (reduction), and the one with the more negative reduction potential is the anode (oxidation). The standard cell potential is calculated using the formula E⁰_cell = E⁰_cathode - E⁰_anode. A positive value indicates that the reaction is spontaneous. The cell reaction is obtained by reversing the anode half-reaction and adding it to the cathode half-reaction. The E⁰ values are not multiplied by the coefficients when balancing the electron transfer.

60-Second Revision

To determine cell potential, identify the cathode (more positive reduction potential) and the anode (more negative reduction potential). Use the formula E⁰_cell = E⁰_cathode - E⁰_anode. A positive result means the reaction is spontaneous. The cell reaction is the sum of the reduction half-reaction and the reversed oxidation half-reaction. Remember that E⁰ values are intensive properties and are not multiplied by the coefficients.

Frequently Asked Questions (FAQs)

Q1. How can you deduce the feasibility of a redox reaction using electrode potentials? Answer: The feasibility of a redox reaction can be deduced by calculating the standard cell potential (E⁰_cell). If E⁰_cell is positive, the reaction is feasible (spontaneous) in the forward direction. If E⁰_cell is negative, the reaction is not feasible as written, and the reverse reaction would be spontaneous.

Q2. Which half-cell acts as the cathode and which acts as the anode? Answer: The half-cell with the greater (more positive) standard reduction potential acts as the cathode (where reduction occurs). The half-cell with the smaller (more negative) standard reduction potential acts as the anode (where oxidation occurs).

• Q3. What is the formula for calculating the standard cell potential?
• Answer: The standard cell potential is calculated using the formula:
• E⁰_cell = E⁰_cathode - E⁰_anode
• where E⁰_cathode and E⁰_anode are the standard reduction potentials of the cathode and anode half-cells, respectively.

Q4. Why don't the standard reduction potential values change when you multiply the half-reaction by a coefficient? Answer: Standard reduction potentials are intensive properties, meaning they do not depend on the amount of substance. They represent the potential difference per unit charge, so they are independent of the stoichiometric coefficients used to balance the electron transfer.

• Q5. If the standard reduction potential of zinc is -0.76 V and that of copper is +0.34 V, what is the cell potential of the Zn-Cu cell?
• Answer: The copper half-cell (+0.34 V) is the cathode, and the zinc half-cell (-0.76 V) is the anode.
• E⁰_cell = 0.34 - (-0.76) = 0.34 + 0.76 = 1.10 V
• The positive value indicates a spontaneous reaction.

Q6. What does a negative standard cell potential indicate? Answer: A negative standard cell potential indicates that the reaction is non-spontaneous in the direction written. The reverse reaction would be spontaneous, meaning the actual cell would operate in the opposite direction.

Q7. How do you write the overall cell reaction from two half-reactions? Answer: The overall cell reaction is obtained by adding the reduction half-reaction (at the cathode) and the oxidation half-reaction (the reverse of the reduction half-reaction at the anode). The electrons on both sides must cancel out.

• Q8. What is the relationship between cell potential and Gibbs free energy?
• Answer: The relationship is given by:
• Δ G⁰ = -nFE⁰_cell
• A positive E⁰_cell corresponds to a negative Δ G⁰, indicating a spontaneous reaction.

Q9. Can a cell with a positive cell potential still not work in practice? Answer: Yes. A positive cell potential means the reaction is thermodynamically feasible (spontaneous), but it might be kinetically slow. A high activation energy or the presence of an overpotential could prevent the reaction from occurring at a noticeable rate.

Multiple Choice Questions (MCQs)

• Q1. In a galvanic cell, which half-cell acts as the cathode?
• A. The half-cell with the more negative reduction potential
• B. The half-cell with the more positive reduction potential
• C. The half-cell where oxidation occurs
• D. The half-cell that loses electrons
• Correct Answer: B
• Explanation: Reduction occurs at the cathode, and the half-cell with the more positive reduction potential has a greater tendency to be reduced.

• Q2. What is the formula for the standard cell potential?
• A. E⁰_cell = E⁰_anode - E⁰_cathode
• B. E⁰_cell = E⁰_cathode + E⁰_anode
• C. E⁰_cell = E⁰_cathode - E⁰_anode
• D. E⁰_cell = E⁰_anode + E⁰_cathode
• Correct Answer: C
• Explanation: The standard cell potential is the algebraic difference between the standard reduction potentials of the cathode and the anode.

• Q3. For a spontaneous reaction, what should be the sign of E⁰_cell?
• A. Negative
• B. Zero
• C. Positive
• D. It depends on the reaction
• Correct Answer: C
• Explanation: A positive cell potential indicates that the reaction is spontaneous under standard conditions.

• Q4. In a cell with zinc and copper half-cells, which electrode is the anode?
• A. Copper (E° = +0.34 V)
• B. Zinc (E° = -0.76 V)
• C. Both are anodes
• D. Neither is an anode
• Correct Answer: B
• Explanation: Zinc has the more negative reduction potential, so it undergoes oxidation and acts as the anode.

• Q5. If the standard reduction potential of silver is +0.80 V and that of zinc is -0.76 V, what is the cell potential?
• A. 0.04 V
• B. 1.56 V
• C. -1.56 V
• D. 0.80 V
• Correct Answer: B
• Explanation: E⁰_cell = 0.80 - (-0.76) = 0.80 + 0.76 = 1.56 V.

• Q6. Why are standard reduction potential values not multiplied by stoichiometric coefficients?
• A. Because they are intensive properties.
• B. Because they are extensive properties.
• C. Because it would make the cell potential too large.
• D. Because it would make the cell potential negative.
• Correct Answer: A
• Explanation: Standard reduction potentials are intensive properties and do not depend on the amount of substance.

Q7. What is the overall cell reaction for the Zn-Cu cell? A. Zn^{2+} + Cu \rightarrow Zn + Cu^{2+} B. Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu C. Zn + Cu \rightarrow Zn^{2+} + Cu^{2+} D. Zn^{2+} + Cu^{2+} \rightarrow Zn + Cu Correct Answer: B Explanation: Zinc is oxidized to Zn^{2+} and copper ions are reduced to Cu, giving the overall reaction Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu.

• Q8. What does a negative cell potential indicate?
• A. The reaction is spontaneous.
• B. The reaction is non-spontaneous.
• C. The cell is at equilibrium.
• D. The cell is a galvanic cell.
• Correct Answer: B
• Explanation: A negative cell potential indicates that the reaction is non-spontaneous in the direction written. The reverse reaction would be spontaneous.

Q9. In the formula E⁰_cell = E⁰_cathode - E⁰_anode, what does E⁰_anode represent? A. The standard oxidation potential of the anode B. The standard reduction potential of the anode C. The standard cell potential D. The standard reduction potential of the cathode Correct Answer: B Explanation: The formula uses the standard reduction potentials for both half-cells, so E⁰_anode is the standard reduction potential of the half-cell acting as the anode.

Q10. To obtain the cell reaction, you must: A. Add the two reduction half-reactions. B. Add the reduction half-reaction and the reversed oxidation half-reaction. C. Subtract the reduction half-reaction from the oxidation half-reaction. D. Multiply the two half-reactions. Correct Answer: B Explanation: The cell reaction is the sum of the reduction half-reaction at the cathode and the oxidation half-reaction (the reverse of the reduction half-reaction) at the anode.

Multiple Choice Questions (MCQs)

• Q1. In a galvanic cell, the half-cell with the more positive reduction potential acts as the:
• A. Anode
• B. Cathode
• C. Salt bridge
• D. Voltmeter
• Correct Answer: B
• Explanation: The half-cell with the more positive reduction potential has a greater tendency to be reduced and acts as the cathode.

• Q2. What is the standard cell potential (E⁰_cell) for a cell made from Zn and Cu half-cells?
• A. 1.10 V
• B. -1.10 V
• C. 0.34 V
• D. -0.76 V
• Correct Answer: A
• Explanation: E⁰_cell = (+0.34 V) - (-0.76 V) = +1.10 V.

• Q3. If the standard reduction potential of a half-cell is -0.44 V, and it is connected to a SHE (0.00 V), which electrode is the cathode?
• A. The half-cell with -0.44 V
• B. SHE
• C. Both
• D. Neither
• Correct Answer: B
• Explanation: The SHE has the more positive reduction potential (0.00 V), so it is the cathode. The half-cell with -0.44 V is the anode.

• Q4. What does a positive E⁰_cell indicate?
• A. The reaction is non-spontaneous.
• B. The reaction is spontaneous.
• C. The reaction is at equilibrium.
• D. The cell is an electrolytic cell.
• Correct Answer: B
• Explanation: A positive cell potential indicates a spontaneous redox reaction.

• Q5. Which of the following is the correct formula for calculating standard cell potential?
• A. E⁰_cell = E⁰_anode - E⁰_cathode
• B. E⁰_cell = E⁰_cathode + E⁰_anode
• C. E⁰_cell = E⁰_cathode - E⁰_anode
• D. E⁰_cell = E⁰_cathode × E⁰_anode
• Correct Answer: C
• Explanation: The standard cell potential is the difference between the reduction potential of the cathode and the anode.

• Q6. In the Zn-Cu cell, which electrode is the anode?
• A. Cu (E° = +0.34 V)
• B. Zn (E° = -0.76 V)
• C. Both are anodes
• D. Neither is an anode
• Correct Answer: B
• Explanation: Zinc has the more negative reduction potential, so it is oxidized and acts as the anode.

• Q7. Why is the standard reduction potential of an electrode not multiplied when balancing the cell reaction?
• A. Because it is an intensive property.
• B. Because it is an extensive property.
• C. Because it would make the calculation too complicated.
• D. Because it is always zero.
• Correct Answer: A
• Explanation: Intensive properties, like potential, do not depend on the amount of substance, so they are not multiplied by coefficients.

• Q8. What is the overall cell reaction for a cell with a Zn anode and a Cu cathode?
• A. Zn^{2+} + Cu \rightarrow Zn + Cu^{2+}
• B. Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu
• C. Zn + Cu \rightarrow Zn^{2+} + Cu^{2+}
• D. Zn^{2+} + Cu^{2+} \rightarrow Zn + Cu
• Correct Answer: B
• Explanation: Zinc is oxidized (anode) and copper is reduced (cathode), giving the overall reaction Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu.

• Q9. What is the relationship between E⁰_cell and Δ G⁰?
• A. Δ G⁰ = nFE⁰_cell
• B. Δ G⁰ = -nFE⁰_cell
• C. Δ G⁰ = -FnE⁰_cell
• D. Δ G⁰ = nE⁰_cell/F
• Correct Answer: B
• Explanation: The relationship is Δ G⁰ = -nFE⁰_cell. A positive E⁰_cell gives a negative Δ G⁰, meaning spontaneity.

• Q10. If the standard reduction potentials of two half-cells are -0.25 V and +0.80 V, which is the anode?
• A. The half-cell with -0.25 V
• B. The half-cell with +0.80 V
• C. Both
• D. Neither
• Correct Answer: A
• Explanation: The half-cell with the more negative (or smaller) reduction potential is the anode, where oxidation occurs.