Brine is a concentrated solution of sodium chloride (NaCl) in water. During electrolysis of brine, the ions present are Na+, Cl-, H+ (from water), and OH- (from water).
At the cathode (negative electrode), reduction takes place. The two cations competing for discharge are Na+ and H+. Because hydrogen ions are much easier to reduce than sodium ions (sodium has a very negative standard electrode potential), H+ ions are preferentially discharged:
\[2\text{H}^+(aq) + 2e^- \rightarrow \text{H}_2(g)\]
The gas produced at the cathode is therefore hydrogen.
At the anode (positive electrode), chloride ions are oxidised to produce chlorine gas. Sodium hydroxide remains in solution. Steam is not produced during electrolysis, and oxygen would only appear at the anode if a dilute solution were used instead of concentrated brine.
Exam tip: In electrolysis of brine, remember the three products: hydrogen at the cathode, chlorine at the anode, and sodium hydroxide in solution.