Potassium Bromide and its Reaction
Potassium bromide (KBr) is an ionic compound that is highly soluble in water. When it is dissolved in water, it dissociates into potassium ions (K+) and bromide ions (Br-).

Reactions with Various Substances
When potassium bromide solution is treated with different substances, different reactions occur. Let's examine the reactions with each of the given substances:

a) Hydrogen Iodide (HI)
When potassium bromide is treated with hydrogen iodide, a redox reaction takes place. Hydrogen iodide is a stronger reducing agent than bromide ions, so it can displace bromine from potassium bromide.

The reaction can be represented as follows:
2 KBr + 2 HI → 2 KI + Br2 + H2

This reaction liberates bromine (Br2) as a product. Bromine is a reddish-brown volatile liquid that can be easily identified by its color and odor.

b) Sulphur Dioxide (SO2)
Sulphur dioxide does not react with potassium bromide to liberate bromine. Therefore, it is not the correct answer.

c) Chlorine (Cl2)
Chlorine is a highly reactive and powerful oxidizing agent. When chlorine gas is passed through potassium bromide solution, a displacement reaction occurs. Chlorine displaces bromine from potassium bromide and forms potassium chloride.

The reaction can be represented as follows:
2 KBr + Cl2 → 2 KCl + Br2

This reaction liberates bromine (Br2) as a product. However, in this case, chlorine is the reagent that causes the displacement reaction, not the liberated bromine.

d) Iodine (I2)
Iodine does not react with potassium bromide to liberate bromine. Therefore, it is not the correct answer.

Conclusion
Among the given options, only hydrogen iodide (HI) can react with potassium bromide to liberate bromine. The redox reaction between potassium bromide and hydrogen iodide results in the formation of potassium iodide (KI) and bromine (Br2).