14.0 Electromotive Force

It is the difference in the potential between two point. It is measured in volts. SI unit of emf is Volts. Electrical work done in moving a charge through a conductor is

$${\text{Electric Work}} = {\text{Charge}} \times {\text{potential difference}}$$

writing the SI units of each term, we get $${\text{Joules}} = {\text{Coulomb}} \times {\text{Volt}}$$

We know that faraday's constant is the magnitude of the charge on one mole of electron, which is equal to $96500\ C$. So in moving this quantity of charge from one electrode to another, the work done by voltaic cell is the product of faraday's constant $F$ times the potential difference between the electrodes.

So work is negative of this, because voltaic cell loses energy as it does work on the surroundings.

$$W = - F \times {\text{potential difference}}$$

In usual operation of voltaic cell, potential difference across the electrodes is less than the maximum possible voltage of the cell..

One reason for this is that it takes energy to drive the current through the cell itself. When the cell voltage decreases, current drawn reflects as the energy expenditure within the cell. So more the current, less will be the voltage.

So we can say that cell has maximum voltage when no current flows through it.

Now we can define emf as the maximum potential difference between the electrodes of a voltaic cell and denoted as ${E_{cell}}^0$.

To write down the expression for maximum work obtained from voltaic cell, let $n$ no. of electrons are involved in the cell reaction, so maximum electrical work of a voltaic cell is given as $${W_{\max }} = - nF{E_{cell}}^0$$