Cell Potential

Cell Potential is the difference in electrical potential between an electrochemical cell’s two electrodes. An electrochemical cell is a device that uses an electrochemical reaction to transform chemical energy into electrical energy. The differential in electron affinities between the two electrodes and the electrolytes’ reactivity are what cause the cell potential.
Electrons will move from the metal with lower electron affinity to the metal with higher electron affinity when two different metals are in contact, creating an electrical potential difference.

What is Cell Potential?

The cell potential is a measure of the ability of the cell to do work and is related to the Gibbs free energy change (ΔG) of the electrochemical reaction. 

A positive cell potential indicates that the reaction is spontaneous and can generate electrical energy, while a negative cell potential indicates that the reaction is non-spontaneous and requires an external source of energy to occur.

The cell potential is an important parameter in many electrochemical processes, including batteries, fuel cells, and corrosion. 

It can be measured experimentally using a voltmeter and can be predicted theoretically using the Nernst equation, which relates the cell potential to the concentrations of the reactants and products involved in the electrochemical reaction.

The image discussed below shows the structure of the Galvanic Cell for which we find the cell potential is calculated.

Types of Cell Potential

There are two main types of cell potential: 

• Standard Cell Potential
• Non-Standard Cell Potential

Standard Cell Potential

• The cell potential that would be measured under typical conditions of 1 atm pressure, 25°C temperature, and 1 M concentration of all species participating in the electrochemical reaction is known as the standard cell potential (E°cell).
• Standard cell potentials are tabulated in reference books and used to forecast an electrochemical reaction’s direction and determine the reaction’s equilibrium constant. The Nernst equation can be used with standard concentrations to determine the standard cell potential.

Non-Standard Cell Potential

• Non-standard cell potential is the cell potential that is measured under non-standard conditions, such as different concentrations of the species involved in the electrochemical reaction, temperature, and pressure. 
• Nernst equation, which considers the impact of the non-standard conditions on the cell potential, relates the non-standard cell potential to the standard cell potential.
• Non-standard cell potentials can be used to predict the direction and extent of an electrochemical reaction under specific conditions and to calculate the reaction quotient of the reaction.

Cell Potential Formula

The cell potential formula is widely used to find the electric potential of the cell. The diagram given below shows the cell potential formula.

Read, More

• Electrochemical Cells
• Galvanic Cells
• Redox Reactions and Electrode Processes

Solved Examples on Cell Potential

Example 1: An example of cell potential can be demonstrated using the redox reaction between zinc (Zn) and copper (Cu) in an electrochemical cell. The overall reaction can be written as:

Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

The standard reduction potential of Cu²⁺/Cu is +0.34 V, while the standard reduction potential of Zn²⁺/Zn is -0.76 V. Therefore, the Cu²⁺/Cu half-reaction will act as the cathode half-reaction and the Zn²⁺/Zn half-reaction will act as the anode half-reaction.

Solution:

The cell potential can be calculated using the formula:

E_cell = E°_cathode – E°_anode

E°_cathode = +0.34 V (Cu²⁺/Cu)
E°_anode = -0.76 V (Zn²⁺/Zn)

Ecell = +0.34 V – (-0.76 V) = +1.10 V

The positive value of the cell potential indicates that the reaction is spontaneous in the forward direction, i.e., Zn(s) is oxidized and Cu²⁺(aq) is reduced. The reaction proceeds until the concentrations of the reactants and products reach equilibrium.

To measure the actual cell potential under non-standard conditions, the Nernst equation can be used. For example, if the concentrations of Cu²⁺ and Zn²⁺ are both 1.00 M and the cell is at 25°C, the cell potential can be calculated as,

E_cell = E°_cell – (RT/nF) ln(Q)

Q = [Cu⁺²]/[Zn⁺²] = 1.00/1.00 = 1.00

Plugging in the values, we get

E_cell = +1.10 V – (0.0257 V) ln(1.00) = +1.10 V

Thus, the cell potential is the same as the standard cell potential under these conditions.

Example 2: Consider the following reaction: Cu(s) + Ag⁺(aq) -> Cu²⁺(aq) + Ag(s)

Standard reduction potentials are,

• Cu²⁺(aq) + 2e^– -> Cu(s)                (E° = +0.34 V)
• Ag⁺(aq) + e^– -> Ag(s)                  (E° = +0.80 V)

A) Write the balanced equation for the cell reaction and calculate the standard cell potential. 

B) If the initial concentrations of Cu2+ and Ag+ are both 0.1 M and the cell operates at standard conditions, calculate the cell potential.

C) If the initial concentration of Cu2+ is 1 M and the initial concentration of Ag+ is 0.1 M, calculate the cell potential.

Solution:

A) The balanced equation for the cell reaction is,

Cu(s) + 2Ag⁺(aq) -> Cu²⁺(aq) + 2Ag(s)

Standard cell potential is calculated using the formula:

E°_cell = E°_reduction (reduced species) – E°_reduction (oxidized species)

E°_cell = E°Ag⁺ – E°Cu²⁺

E°_cell = 0.80 V + 0.34 V – 0.34 V – 0.80 V

E°_cell = -0.50 V

B) If the initial concentrations of Cu2+ and Ag+ are both 0.1 M, the cell operates at standard conditions and the Nernst equation can be used:

E_cell = E°_cell – (RT/nF)lnQ

At standard conditions, Q = 1 and lnQ = 0, so:

E_cell = E°_cell = -0.50 V

C) If the initial concentration of Cu²⁺ is 1 M and the initial concentration of Ag⁺ is 0.1 M, the reaction quotient Q is:

Q = [Cu²⁺][Ag⁺]²/ [Ag⁺]²[Cu] = [Cu²⁺] / [Ag⁺]

Q = 1 / 0.1 = 10

Cell Potential can be calculated using the Nernst equation,

E_cell = E°_cell – (RT/nF)lnQ

E_cell = -0.50 V – (0.0257 V/K)(298 K/2)(ln10)

E_cell = -0.50 V – 0.059 V

E_cell = -0.559 V

Example 3: Consider the following redox reaction, 2 Fe³⁺(aq) + 2 I^–(aq) → 2 Fe²⁺(aq) + I₂(s). Calculate the cell potential.

Solution:

To calculate the cell potential, we need to find the reduction potentials for each half-reaction and then subtract the reduction potential of the anode from the reduction potential of the cathode.

Half-reactions for the given reaction are,

Fe³⁺(aq) + e^– → Fe²⁺(aq)               E° = +0.77 V

I₂(s) + 2 e^– → 2 I^–(aq)                     E° = +0.54 V

Reduction Potential of the anode is the reduction potential of the species being oxidized, which is Fe³⁺ in this case. So, the reduction potential of the anode is +0.77 V.

The reduction potential of the cathode is the reduction potential of the species being reduced, which is I₂ in this case. So, the reduction potential of the cathode is +0.54 V.

The cell potential (E_cell) is the difference between the reduction potentials of the cathode and anode:

E_cell = E_cathode – E_anode
E_cell = +0.54 V – (+0.77 V)
E_cell = -0.23 V

Therefore, the cell potential for this reaction is -0.23 V. This means that the reaction is not spontaneous and the electrons will not flow from the anode to the cathode without an external energy source.

FAQs on Cell Potential

Q1: What is Cell Potential?

Answer:

The cell potential is the measure of the potential difference between the two half-cells of an electrochemical cell.

Q2: How is Cell Potential calculated?

Answer:

Cell potential is calculated by subtracting the reduction potential of the anode from the reduction potential of the cathode.

Q3: What is the standard reduction potential?

Answer:

The standard reduction potential is the potential of a half-reaction under standard conditions (1 M concentration, 1 atm pressure, 25°C temperature, and electrodes at a standard hydrogen electrode (SHE) potential of 0 V).

Q4: What is the difference between standard potential and actual potential?

Answer:

Standard potential is the potential under standard conditions, whereas actual potential depends on the concentrations of the reactants and products and the conditions of the cell.

Q5: What is the significance of cell potential?

Answer: 

Cell potential helps to determine whether a redox reaction is spontaneous or non-spontaneous and to predict the direction of electron flow in an electrochemical cell.

Q6: What is a positive and negative cell potential?

Answer:

A positive cell potential indicates that the reaction is spontaneous and that electrons flow from the anode to the cathode. A negative cell potential indicates that the reaction is non-spontaneous and that electrons do not flow without an external energy source.

Q7: What factors affect cell potential?

Answer:

The factors that affect cell potential include the nature of the reactants and products, their concentrations, temperature, pressure, and the presence of catalysts or inhibitors.

Q8: What is the Cell Potential formula?

Answer:

The cell potential formula is,

E_cell = E_cathode – E_anode

where,

E_cell is the overall potential of the electrochemical cell, 
E_cathode is the reduction potential of the cathode half-cell (the half-cell where reduction occurs) 
E_anode is the oxidation potential of the anode half-cell (the half-cell where oxidation occurs).