2.4.2 Cell Potential

A galvanic cell is a device that converts the chemical energy of a spontaneous redox reaction into electrical energy. The ability of a cell to do this is measured by its cell potential. This section explains what cell potential is, how it is generated, and how it is calculated using standard reduction potentials.

Definition

The cell potential (E_cell) for a galvanic cell is literally the potential of the cell to do work on its surroundings by driving an electric current through a wire. It is the measure of the voltage (or electromotive force, emf) produced by the cell.

Simple Explanation: It is the "push" or "force" that drives the electrons through the external circuit, from the anode to the cathode.

Core Concept

The core concept is that the cell potential is the difference between the electrical potentials of the two half-cells. Each half-cell has its own potential, which is a measure of its tendency to undergo reduction. The overall cell potential is generated because these two half-cells have different tendencies. The electrons will flow spontaneously from the half-cell with the lower reduction potential (the anode) to the half-cell with the higher reduction potential (the cathode).

Detailed Explanation

How Cell Potential is Generated

When a piece of zinc metal is dipped in a solution of copper(II) sulphate, a spontaneous reaction occurs. Electrons flow directly from the zinc rod to the copper ions in the solution. If this electron transfer is directed through an external circuit (by separating the half-cells), the spontaneous redox reaction can be used to generate an electric current.

The force with which electrons are pushed to flow through the wire from the anode to the cathode is called the electromotive force (emf) or cell potential. It is measured in volts (V).

The emf produced by the galvanic cell is called cell potential (E⁰_cell). It depends upon the difference in the electrode potentials of the two half-cells joined in series.

Standard Conditions

• Concentration of solutions: 1 mol dm⁻³
• Temperature: 25°C (298 K)
• Pressure of gases: 1 atm

Under these standard conditions, the reaction with a more negative E⁰ value occurs as oxidation (anode reaction), and the reaction with a more positive E⁰ value occurs as reduction (cathode reaction).

Calculating Standard Cell Potential

The standard cell potential is the algebraic difference between the respective standard reduction potentials of the two half-cells.

The formula is: E⁰_cell = E⁰_cathode - E⁰_anode

• E⁰_cathode is the standard reduction potential of the reduction half-cell.
• E⁰_anode is the standard reduction potential of the oxidation half-cell.

Important: The cell potential has a positive value for any spontaneous redox reaction. A negative value means the reaction is non-spontaneous in that direction.

Example Calculation

Consider a galvanic cell made from a zinc electrode in a 1 M ZnSO_4 solution and a copper electrode in a 1 M CuSO_4 solution.

• E⁰_Cu²⁺/Cu = +0.34 V
• E⁰_Zn²⁺/Zn = -0.76 V

Since copper has the more positive reduction potential, it will act as the cathode (reduction occurs here). Zinc has the more negative reduction potential, so it will act as the anode (oxidation occurs here).

E⁰_cell = E⁰_cathode - E⁰_anode \] \[ E⁰_cell = (+0.34 V) - (-0.76 V) \] \[ E⁰_cell = +0.34 + 0.76 \] \[ E⁰_cell = +1.10 V

The positive value indicates that the reaction is spontaneous.

Measurement of Cell Potential

The potential of a galvanic cell can be measured with a voltmeter. However, a single half-cell potential or the electrode potential cannot be measured directly. This is because one half-cell reaction cannot occur without a simultaneous reaction in another half-cell.

To measure the relative half-cell potential (electrode potential), it is coupled with the Standard Hydrogen Electrode (SHE) as a reference electrode, which has a standard potential of 0.00 volt.

Intermediate Level

The cell potential is determined by the difference in standard reduction potentials of the two half-cells. The half-cell with the more positive reduction potential has a greater tendency to be reduced and acts as the cathode. The half-cell with the more negative reduction potential has a greater tendency to be oxidized and acts as the anode. The formula E⁰_cell = E⁰_cathode - E⁰_anode calculates the net driving force of the reaction. A positive E⁰_cell means the reaction is thermodynamically favorable (spontaneous) under standard conditions.

Important Points

• - Cell Potential (E⁰_cell): The potential of a galvanic cell to drive a current.
• - Formula: E⁰_cell = E⁰_cathode - E⁰_anode.
• - Standard Conditions: 1 M concentration, 25°C, 1 atm pressure.
• - Spontaneous Reaction: Has a positive cell potential.
• - Anode: The half-cell with the more negative reduction potential.
• - Cathode: The half-cell with the more positive reduction potential.
• - Measurement: A single electrode potential cannot be measured directly; it is measured relative to the SHE.

Remember

• - E°cell = E°cathode - E°anode.
• - Positive E°cell → Spontaneous.
• - Negative E°cell → Non-spontaneous.
• - Anode: Lower (more negative) reduction potential.
• - Cathode: Higher (more positive) reduction potential.
• - SHE is the reference (0.00 V).
• - Electrons flow from anode to cathode.

Common Mistakes

• - Adding the potentials instead of subtracting. Use the formula E⁰_cell = E⁰_cathode - E⁰_anode.
• - Using the oxidation potential instead of the reduction potential. Standard tables provide reduction potentials. Always use these values in the formula.
• - Reversing the formula. A common mistake is to do E⁰_anode - E⁰_cathode, which gives the wrong sign. The formula is always E⁰_cathode - E⁰_anode.
• - Forgetting that a positive value means spontaneous. A negative E⁰_cell means the reaction is non-spontaneous in the direction written.
• - Assuming that a more negative electrode potential means a more negative cell potential. The cell potential is a difference; the more negative the anode potential, the more positive the cell potential.

Quick Revision

The cell potential is the voltage produced by a galvanic cell. It is the difference between the standard reduction potential of the cathode (where reduction occurs) and the anode (where oxidation occurs). The formula is E⁰_cell = E⁰_cathode - E⁰_anode. A positive value of E⁰_cell indicates a spontaneous reaction. The half-cell with the more positive reduction potential acts as the cathode, and the one with the more negative reduction potential acts as the anode. The standard hydrogen electrode (SHE) is the reference (0.00 V) for all measurements.

60-Second Revision

Cell potential (E⁰_cell) is the voltage of a galvanic cell. It is calculated using the formula E⁰_cell = E⁰_cathode - E⁰_anode. The cathode is the half-cell with the more positive reduction potential (where reduction occurs), and the anode is the half-cell with the more negative reduction potential (where oxidation occurs). A positive cell potential indicates a spontaneous reaction. The measurement is relative to the Standard Hydrogen Electrode (SHE) with a potential of 0.00 V.

Frequently Asked Questions (FAQs)

Q1. What is the cell potential? Answer: The cell potential is the potential of a galvanic cell to do work on its surroundings by driving an electric current through a wire. It is the voltage or electromotive force (emf) produced by the cell, and it depends on the difference in the electrode potentials of the two half-cells.

Q2. What is the standard cell potential? Answer: The standard cell potential (E⁰_cell) is the cell potential measured under standard conditions: 1 mol dm⁻³ concentration for solutions, 1 atm pressure for gases, and a temperature of 25°C (298 K).

Q3. How is the standard cell potential calculated? Answer: The standard cell potential is the algebraic difference between the standard reduction potentials of the two half-cells. The formula is E⁰_cell = E⁰_cathode - E⁰_anode.

Q4. Which electrode is the cathode? Answer: The cathode is the electrode where reduction occurs. In a galvanic cell, it is the electrode with the more positive (or less negative) standard reduction potential.

Q5. Which electrode is the anode? Answer: The anode is the electrode where oxidation occurs. In a galvanic cell, it is the electrode with the more negative (or less positive) standard reduction potential.

Q6. Why is a single electrode potential impossible to measure? Answer: A single electrode potential cannot be measured directly because a half-cell reaction cannot occur without a simultaneous reaction in another half-cell. The potential is always measured as a difference between two half-cells.

Q7. What does a positive cell potential indicate? Answer: A positive cell potential indicates that the redox reaction is spontaneous under the given conditions. The reaction will proceed in the forward direction to produce electrical energy.

• Q8. What does a negative cell potential indicate?
• Answer: A negative cell potential indicates that the reaction is non-spontaneous in the direction written. The reverse reaction would be spontaneous.

Q9. Why is the SHE used as a reference? Answer: The SHE is used as a reference because its electrode potential is arbitrarily assigned a value of exactly 0.00 V. This allows all other electrode potentials to be measured and compared relative to a common standard.

Q10. How is the cell potential measured? Answer: The cell potential is measured using a voltmeter connected between the two electrodes of the cell. The voltmeter measures the potential difference (voltage) between the anode and the cathode.

Multiple Choice Questions (MCQs)

• Q1. What is the cell potential of a galvanic cell?
• A. The potential of the anode alone
• B. The potential of the cathode alone
• C. The difference between the electrode potentials of the two half-cells
• D. The sum of the electrode potentials of the two half-cells
• Correct Answer: C
• Explanation: The cell potential is the difference between the reduction potential of the cathode and the anode.

• Q2. What is the formula for 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 standard reduction potential of the cathode and that of the anode.

• Q3. For a spontaneous redox reaction, the cell potential must be:
• A. Negative
• B. Zero
• C. Positive
• D. Equal to 1 V
• Correct Answer: C
• Explanation: A positive cell potential indicates that the reaction is spontaneous. A negative value means it is non-spontaneous.

• Q4. Under standard conditions, which electrode has a more negative reduction potential?
• A. The cathode
• B. The anode
• C. Both have the same potential
• D. It depends on the concentration
• Correct Answer: B
• Explanation: The electrode with the more negative reduction potential is the anode, where oxidation occurs.

• Q5. If E⁰_cathode is +0.80 V and E⁰_anode is -0.76 V, what is E⁰_cell?
• A. 0.04 V
• B. 1.56 V
• C. -1.56 V
• D. 0.76 V
• Correct Answer: B
• Explanation: E⁰_cell = E⁰_cathode - E⁰_anode = 0.80 - (-0.76) = 1.56 V.

• Q6. Which electrode is the site of reduction?
• A. The anode
• B. The cathode
• C. The salt bridge
• D. The voltmeter
• Correct Answer: B
• Explanation: Reduction occurs at the cathode, where the electrode has a more positive reduction potential.

• Q7. What is the standard potential of the hydrogen electrode?
• A. 0 V
• B. 1 V
• C. -1 V
• D. 0.5 V
• Correct Answer: A
• Explanation: The standard hydrogen electrode (SHE) is defined as having a potential of exactly 0.00 V.

• Q8. What instrument is used to measure the cell potential?
• A. Ammeter
• B. Voltmeter
• C. Thermometer
• D. Barometer
• Correct Answer: B
• Explanation: A voltmeter is used to measure the potential difference (voltage) between the two electrodes of a cell.

• Q9. The cell potential depends on the difference in the:
• A. Mass of the electrodes
• B. Concentration of the electrolyte
• C. Electrode potentials of the two half-cells
• D. Temperature of the solution
• Correct Answer: C
• Explanation: The cell potential is determined by the difference in the electrode potentials of the two half-cells.

Q10. What happens to the cell potential if the concentration of the electrolyte changes? A. It remains the same B. It changes C. It becomes zero D. It becomes negative Correct Answer: B Explanation: The cell potential depends on the concentration of the ions involved in the reaction. Changes in concentration will alter the cell potential (as described by the Nernst equation).

Multiple Choice Questions (MCQs)

• Q1. What does cell potential measure?
• A. The current flowing through the circuit
• B. The voltage produced by the cell
• C. The resistance of the wire
• D. The mass of the electrodes
• Correct Answer: B
• Explanation: Cell potential is the voltage or electromotive force (emf) produced by a galvanic cell.

• Q2. The standard cell potential is calculated under which of the following conditions?
• A. 1 M concentration, 25°C, 1 atm pressure
• B. 0.1 M concentration, 0°C, 2 atm pressure
• C. 1 M concentration, 100°C, 1 atm pressure
• D. 0.01 M concentration, 25°C, 0.5 atm pressure
• Correct Answer: A
• Explanation: Standard conditions are 1 mol dm⁻³ concentration, 298 K (25°C), and 1 atm pressure.

• Q3. 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: The cathode is the half-cell with the more positive reduction potential, where reduction occurs.

Q4. 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 reduction potential of the cathode D. The standard cell potential Correct Answer: B Explanation: The formula uses standard reduction potentials for both half-cells, so E⁰_anode is the standard reduction potential of the half-cell acting as the anode.

• Q5. What is the cell potential for a cell made from a zinc electrode and a copper electrode?
• A. +0.34 V
• B. -0.76 V
• C. +1.10 V
• D. -1.10 V
• Correct Answer: C
• Explanation: E⁰_cell = E⁰_cathode - E⁰_anode = (+0.34 V) - (-0.76 V) = +1.10 V.

• Q6. If the cell potential is negative, the reaction is:
• A. Spontaneous
• B. Non-spontaneous
• C. At equilibrium
• D. Always explosive
• 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.

• Q7. Which of the following statements about the SHE is correct?
• A. It has a positive electrode potential.
• B. It is used as a reference electrode with a potential of 0.00 V.
• C. It is a type of cathode.
• D. It cannot be used to measure the potential of other half-cells.
• Correct Answer: B
• Explanation: The SHE is a reference electrode with an assigned potential of 0.00 V. It is used to measure the relative potentials of other half-cells.

Q8. What is the relationship between cell potential and Gibbs free energy? A. Δ G = nFE_cell B. Δ G = -nFE_cell C. Δ G = nE_cell/F D. Δ G = -FnE_cell Correct Answer: B Explanation: The relationship is Δ G = -nFE_cell. A positive cell potential corresponds to a negative Gibbs free energy change, indicating spontaneity.

• Q9. Electrons flow in the external circuit from:
• A. Cathode to anode
• B. Anode to cathode
• C. Salt bridge to cathode
• D. Anode to salt bridge
• Correct Answer: B
• Explanation: Electrons are released at the anode (oxidation) and travel through the external wire to the cathode (reduction).

• Q10. In the Daniell cell, which electrode is the anode?
• A. Copper
• B. Zinc
• C. Hydrogen
• D. Silver
• Correct Answer: B
• Explanation: Zinc is oxidized and acts as the anode, while copper ions are reduced at the copper cathode.