Potential Difference and EMF of a Cell

Introduction

A galvanic or 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, the potential difference of a cell is defined 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. EMF can also be defined as the potential difference across the terminal of a cell in the absence of electric current in the circuit.

Electrochemical cells

Electrochemical cells generate electrical energy from chemical reactions or use electrical energy to cause a chemical reaction. Electrochemical cells can be two types: Galvanic or Voltaic cells and Electrolytic cells.

Galvanic cell

A Galvanic cell or a voltaic cell is an electrochemical cell made of two metallic conductors of different metals immersed in their own ionic solutions. A galvanic or voltaic cell gets energy from a spontaneous redox reaction. In a Galvanic cell, the Gibbs energy from a spontaneous redox reaction is converted into electrical energy to run a motor or other electronic device. The reduction occurs at the cathode end of the Galvanic cell, and the oxidation occurs at the anode end. The anode, the source of electrons, is the negative terminal of the Galvanic cell.

Daniell Cell

This is an implementation of a Galvanic cell created by copper electrodes being immersed in copper sulfate solution and zinc electrodes being immersed in a zinc sulfate solution. A salt bridge connects the two half cells. Salt bridge contains inert electrolytes that diffuse into each of the half cells to balance the charges of the electrolyte.

Potential Difference and EMF of a cell

The potential difference between Galvanic cell electrodes is termed the cell potential. It is defined as the difference between the reduction potentials of the anode and cathode of the cell. This difference is measured in volts.

When no current is drawn from the cells, then the potential difference of the cells is termed the EMF. The EMF of a cell is positive and measured as the difference between the potential of the half cell on the right and the half cell on the left.

The EMF Formula:

Ecell = Eright – Eleft   ….. (eq1)

Cell reaction:

Copper electrode is the anode of the cell and silver electrode is the cathode.

Cu (s) + 2Ag+ (aq) → Cu2+ (aq) + 2 Ag (s)   ……. (eq2)

Here, (s) represents the electrode in solid form and (aq) represents it to be dissolved in water.

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.

The half-cell reaction of the above cell reaction can be given as:

Cathode reduction of the silver electrode

2Ag+ (aq) + 2e– → 2Ag(s)  ……. (eq3)

Anode oxidation of the copper electrode

 Cu(s) → Cu2+ (aq) +2e–    ……..(eq4)

The summation of eq3 and eq4 results in the overall cell reaction from eq2. 

Eq1 can be represented in terms of the silver and copper electrode as:

Ecell = EAg+|Ag – ECu2+|Cu

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

The 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 EMF calculated of the cell when no current is drawn from the cell is always more than the terminal potential of the cell while the cell is discharging. When the terminal potential of the cell is calculated during charging of the cell, then the value is greater than the EMF of the cell. Charging of the cell indicates when the positive electrode of the cell or cathode is connected to the positive end of the charger, and the negative electrode of the cell or the anode is connected to the negative end of the charger. When the cell is discharging, the current moves from the cathode to the anode inside the cell, and during charging, the movement of current in the cell is from anode to the cathode of the cell.

I = E/(r+R), 

Where I is the current in the circuit;

E is the potential difference or EMF;

r is the internal resistance; and 

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

The potential difference of a cell is defined as the difference in reduction potential of the two electrodes of the cell, i.e. the cathode and the anode. The cathode is considered the positive end of the cell, and the anode is the negative end of the cell, as it releases electrons during the oxidation process. Electromotive Force or EMF of a cell can be defined as 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 calculated will be lesser than the terminal potential, and during discharging, it will be revered; that is, the EMF of the cell will be greater than the terminal potential difference of a cell.