Question

$$E_{\text {cathode }}^{\circ}=(2.71-2.310) V=+0.40 V$$VVV

Short answer

The standard potential of the cathode is \(0.40 V\).

Step-by-step solution

Understand the Given

This exercise works on the standard potential of a cathode in an electrochemical cell. The standard potential \(E_{cathode}^{\circ}\) is given by the formula \(E_{cathode}^{\circ}=E_{anode}^{0}-E_{cathode}^{0}\), where the standard potential of the anode and cathode are provided.

Substitute the Known Values

Substitute the given standard potentials into the standard cathode potential formula: \(E_{cathode}^{\circ} = 2.71 V - 2.310 V\).

Perform the Calculation

Perform the subtraction to calculate the standard potential of the cathode: \(E_{cathode}^{\circ} = 2.71 V - 2.310 V = 0.40 V\). The voltage is positive, indicating that the reaction can occur spontaneously under standard conditions.

Key concepts

Electrochemical Cell

An electrochemical cell is a device that facilitates the conversion of chemical energy into electrical energy through redox reactions. These cells comprise two electrodes immersed in an electrolyte solution. The electrode where oxidation occurs is called the anode, and the electrode where reduction occurs is known as the cathode. A typical electrochemical cell is divided into two half-cells:

• Anode Half-Cell: The site where the oxidation reaction occurs.
• Cathode Half-Cell: The site where the reduction reaction occurs.

The electrolyte solution allows ions to move between the two half-cells, maintaining charge balance while electrons flow through an external circuit from the anode to the cathode. This electron flow is what generates a current. If the overall reaction in the cell is spontaneous, the electrochemical cell can function without an external power source, making it practical for energy conversion in remote or standalone devices.

Cathode Potential

Cathode potential refers to the voltage associated with the reduction half-reaction occurring at the cathode. The standard electrode potential of a cathode, denoted as \( E_{cathode}^{\circ} \), is a measure of the tendency of a chemical species to acquire electrons, and thereby, get reduced. It is expressed in volts (V).

Cathode potential is determined using the standard hydrogen electrode (SHE) as a reference and is calculated by comparing the potential difference with a standard electrode under standard conditions (25°C, 1M concentration for each ion, and 1 atm pressure). In the context of the electrochemical cell, a high positive cathode potential indicates a strong tendency for the reduction to occur.

• A positive cathode potential means the cathode can easily gain electrons.
• This potential contributes to the overall voltage of the electrochemical cell and indicates how effectively electrons are pulled from the anode to the cathode.

Thus, a large positive \( E_{cathode}^{\circ} \) suggests that the reaction at the cathode is more spontaneous, contributing positively to the feasibility and efficiency of an electrochemical cell.

Anode Potential

Anode potential is the voltage associated with the oxidation half-reaction happening at the anode. In electrochemistry, it is essential as it helps to determine the direction and spontaneity of the electron flow in an electrochemical cell. Like the cathode, the standard electrode potential for an anode, \( E_{anode}^{\circ} \), is also measured against the SHE.

It is expressed in volts and is typically less positive than the potential of the cathode. Since the anode is where oxidation occurs (loss of electrons), it sets the pace for electrons to flow out towards the cathode. Negative or less positive anode potentials indicate a catalyst for electron donation:

• It doesn't mean the reaction at the anode is not worthwhile; rather, it denotes the need for an electron flow.
• The lower, more negative anode potential drives the conversion of chemical energy to electrical energy through electron movement.

Understanding anode potential is crucial for optimizing electrochemical cell performance and ensuring the efficiency of the redox reactions involved.