Potential Difference and Emf of a Cell

The potential difference between the two points reflects the work or energy released in the movement of a unit quantity of electricity from one point to the other. 

An electrochemical cell generates electrical energy from chemical reactions or uses electrical energy to create chemical reactions. 

The potential of a cell is the amount of work required to bring unit energy from infinity to a point within an electrical field. At the same time, we can define the potential difference of a cell as the work done to move a unit charge from one part of the cell to another in the same electrical field. 

The electromotive force or EMF of a cell is the maximum potential difference in two cell electrodes. We can also define EMF as the potential difference across the terminal of a cell in the absence of electric current in the circuit.

Potential Difference 

The potential difference measures the amount of effort required to move a unit charge from one location in an electric field to another. In other terms, the potential difference is the difference in the electric potentials of two charged substances.

When one charged body has a different electric potential than another charged body, the two bodies are said to have a potential difference. Both bodies are under stress and pressure as they strive to reach their full potential.

Volt is the unit of potential difference.

Terminal Potential Difference 

A terminal potential difference is a potential difference across a cell in a circuit. Ohm’s law states that the current flowing through a conductor is directly proportional to the voltage put across it. We may simply pick the proper choice by applying Ohm’s law correctly.

We know that EMF, denoted by E, is present in the cell. It is the energy supplied by the cell into the circuit. However, the cell’s internal resistance (r) pulls a part of this energy out of the circuit. As a result, the voltage drops somewhat. 

This voltage reduction is proportional to the reciprocal of the current in the circuit and the cell’s internal resistance. We can calculate the potential difference by subtracting this decrease from the cell’s energy.

V = E − Ir

Potential Difference and EMF of a Half-Cell

Measuring the cell’s potential can be done by measuring the difference of potential of the two half cells.

We can give the half-cell reaction of the above cell reaction as:

Cathode reduction of the silver electrode

2Ag+ (aq) + 2e- → 2Ag(s)  

Anode oxidation of the copper electrode

 Cu(s) → Cu2+ (aq) +2e-    

The sum of the above two equations summation represents the overall cell reaction. 

We can represent the cell’s overall potential as:

Ecell = EAg+|Ag – ECu2+|Cu

Relation between Internal Resistance EMF and Terminal Potential Difference of a Cell

The potential difference measured between the electrodes of a cell in a closed circuit is called the terminal potential difference of a cell. 

The cell’s EMF in the absence of internal resistance is always more than the terminal potential of the cell while it is discharging. In comparison, the terminal potential of the cell during its charging is greater than the EMF of the cell. 

Charging the cell indicates that its positive electrode or cathode is connected to the positive end of the charger, and its negative electrode or anode is linked to the negative end of the charger. 

When the cell discharges, the current moves from the cathode to the anode inside the cell. During charging, the current movement in the cell is from the anode to the cathode.

I = E/(r+R)

Where, 

I is the current in the circuit

E is the potential difference or EMF

r is the internal resistance 

R is the external resistance

When the cell is in an open circuit, the R is ∞, thus

I = E/( ∞+r) = 0. 

Therefore, V = E.

In this case, the potential difference of the cell is equal to the EMF and represents the maximum potential difference.

When a cell is in short circuit,

R = 0

I = E/(0+r) = E/r

Therefore, V = IR = 0

Thus, the current is maximum, and the potential difference of the cell is 0.

Difference between Cell Potential and EMF

Conclusion 

We can define a cell’s potential difference as the difference in reduction potential of its two electrodes, i.e. the cathode and the anode. The cathode is the cell’s positive electrode, and the anode is the negative electrode. The former gains electrons, and the latter loses electrons during an electrochemical reaction. 

Electromotive Force or EMF of a cell is the potential difference of the cell when no current is drawn from the cell, or the cell is in an open circuit. The potential difference measured between the two electrodes of a cell in a closed circuit is called the terminal potential difference of a cell. 

During charging, the EMF will be lesser than the terminal potential and vice versa during discharging.