1.55 write ionic half-equations representing the reactions at the electrodes during electrolysis

Positive ions gain electrons at the negative electrode, so we write the electrons on the left hand side of the equation.  This is a reduction reaction.  Examples are below:

2H+(aq) + 2e- ® H2(g)               forming hydrogen gas

Cu2+(aq) + 2e- ® Cu(s)             forming copper metal

Negative ions have their extra electrons removed at the positive electrode, so we write the electrons on the right hand side of the equation to show that they have been lost.  This is an oxidation reaction.

2Cl-(aq) ® Cl2(g)  + 2e-                 forming chlorine gas

Where oxygen is formed in electrolysis of solutions, it comes from hydroxide ions in the water:

4OH-(aq) ® O2(g) + 2H2O(l)  + 4e-