E° Value of a Daniell Cell Zn|Zn²⁺(aq)||Cu²⁺(aq)|Cu – Detailed Solution

Correct Answer: 1.10 V

The standard cell potential of the given Daniell cell is 1.10 V. To calculate this value correctly, we first need to identify which electrode acts as the anode and which electrode acts as the cathode. This identification is based on the standard reduction potentials of the two half-cells.

Understanding the Daniell Cell

A Daniell cell is a classic electrochemical or galvanic cell consisting of a zinc electrode immersed in a solution containing Zn²⁺ ions and a copper electrode immersed in a solution containing Cu²⁺ ions. The two half-cells are connected through a salt bridge, while the electrodes are connected externally through a conducting wire.

The cell is represented as:

Zn|Zn²⁺(aq)||Cu²⁺(aq)|Cu

According to the standard convention for writing an electrochemical cell, the electrode written on the left-hand side acts as the anode, where oxidation occurs, while the electrode written on the right-hand side acts as the cathode, where reduction occurs. Therefore, zinc is the anode and copper is the cathode in the Daniell cell.

Given Standard Reduction Potentials

The standard reduction potential of the zinc half-cell is:

E°(Zn²⁺/Zn) = −0.76 V

The standard reduction potential of the copper half-cell is:

E°(Cu²⁺/Cu) = +0.34 V

A species with a more positive standard reduction potential has a greater tendency to undergo reduction. Since the standard reduction potential of Cu²⁺/Cu is +0.34 V, which is more positive than −0.76 V for Zn²⁺/Zn, copper ions undergo reduction at the cathode. Zinc, therefore, undergoes oxidation at the anode.

Identifying the Anode and Cathode

Anode: Zinc Electrode

At the zinc electrode, metallic zinc loses two electrons and forms Zn²⁺ ions. Since loss of electrons is oxidation, the zinc electrode acts as the anode.

Zn(s) → Zn²⁺(aq) + 2e⁻

During the operation of the Daniell cell, the zinc electrode gradually dissolves into the solution because zinc atoms are converted into Zn²⁺ ions.

Cathode: Copper Electrode

At the copper electrode, Cu²⁺ ions present in the solution gain two electrons and are converted into metallic copper. Since gain of electrons is reduction, the copper electrode acts as the cathode.

Cu²⁺(aq) + 2e⁻ → Cu(s)

As the electrochemical reaction proceeds, copper metal is deposited on the copper electrode.

Formula for Calculating the Standard Cell Potential

When standard reduction potentials are provided for both electrodes, the standard cell potential is calculated using the following formula:

E°cell = E°cathode − E°anode

Here, E°cathode represents the standard reduction potential of the cathode and E°anode represents the standard reduction potential of the anode. It is important to use the given reduction potentials directly in this formula, including their positive or negative signs.

Step-by-Step Calculation of E°cell

For the given Daniell cell, copper is the cathode and zinc is the anode. Therefore:

E°cathode = E°(Cu²⁺/Cu) = +0.34 V

E°anode = E°(Zn²⁺/Zn) = −0.76 V

Substituting these values into the standard cell potential formula:

E°cell = E°cathode − E°anode

E°cell = (+0.34) − (−0.76)

Subtracting a negative value is equivalent to addition. Therefore:

E°cell = 0.34 + 0.76

E°cell = 1.10 V

Hence, the E° value of the Daniell cell, rounded off to two decimal places, is 1.10 V.

Overall Cell Reaction in the Daniell Cell

The oxidation half-reaction occurring at the zinc anode is:

Zn(s) → Zn²⁺(aq) + 2e⁻

The reduction half-reaction occurring at the copper cathode is:

Cu²⁺(aq) + 2e⁻ → Cu(s)

Adding the two half-reactions cancels the two electrons and gives the overall cell reaction:

Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

This reaction occurs spontaneously under standard conditions because the calculated standard cell potential is positive.

Why Is the Standard Cell Potential Positive?

The calculated value of E°cell is +1.10 V. A positive standard cell potential indicates that the overall redox reaction is thermodynamically spontaneous under standard conditions. In the Daniell cell, zinc has a stronger tendency to undergo oxidation, while Cu²⁺ ions have a stronger tendency to undergo reduction. This difference in electrode potentials drives the movement of electrons from the zinc electrode to the copper electrode through the external circuit.

The positive value of the standard cell potential also confirms that the assignment of zinc as the anode and copper as the cathode is correct. If the cell reaction were reversed, the sign of the cell potential would also reverse, giving −1.10 V.

Direction of Electron Flow in the Daniell Cell

Electrons are produced at the zinc anode during oxidation and travel through the external wire toward the copper cathode, where they are consumed during the reduction of Cu²⁺ ions. Therefore, the direction of electron flow is:

Zn electrode → Cu electrode

The salt bridge completes the electrical circuit by allowing the migration of ions between the two half-cells and maintaining electrical neutrality in both solutions.

Final Answer

Using the standard reduction potentials E°(Zn²⁺/Zn) = −0.76 V and E°(Cu²⁺/Cu) = +0.34 V:

E°cell = E°cathode − E°anode

E°cell = (+0.34) − (−0.76) = 1.10 V

Therefore, the E° value of the Daniell cell Zn|Zn²⁺(aq)||Cu²⁺(aq)|Cu, rounded off to two decimal places, is 1.10 V.qw5