The half equation for the electrolysis of dilute potassium bromide (KBr) using a graphite electrode can be described as follows:
At the anode (positive electrode): 2Br⁻ (aq) → Br₂ (g) + 2e⁻
At the cathode (negative electrode): 2H₂O (l) + 2e⁻ → H₂ (g) + 2OH⁻ (aq)
Overall, the balanced equation for the electrolysis of dilute potassium bromide is:
2Br⁻ (aq) + 2H₂O (l) → Br₂ (g) + 2OH⁻ (aq) + H₂ (g)
Please note that this reaction occurs in an aqueous solution, and the presence of water allows for the formation of hydrogen gas at the cathode.