How to Calculate Ecell or Electro Motive Force Cell

Consider the zinc-copper cell, how can the emf of such a cell be calculated from the standard potentials, rather than by experiment? The two half-reactions are

Cu²⁺ (aq) + 2e^– → Cu (s) and Zn (s) → Zn²⁺ (aq) + 2e^–

The copper half-reaction is a reduction. Look up for E_Cu, the standard reduction potential for the following half-reaction.

Cu²⁺ (aq) + 2e^– → Cu (s)

We find that E_Cu = + 0.34V.

The zinc half-reaction is an oxidation. Please note that tables usually list reduction potentials.

If E_Zn is the reduction potential of zinc, then E_Zn = – 0.76V as per the values found in the table above. Similarly, (- E_Zn) is the oxidation potential of zinc. Therefore, (- E_Zn). +0.76 V for the following half-reaction:

Zn (s) → Zn²⁺ (aq) + 2e^–

The cell emf is the sum of the reduction potential for the copper half-cell and the oxidation potential for the zinc half-cell.

We can say that E_cell = E_Cu + (- E_Zn),

which is equal to E_cell = E_Cu – E_Zn

Therefore, E_cell = 0.34 + 0.76 = 1.1 V