The color change observed when chlorine gas is bubbled into aqueous potassium bromide is due to the formation of a new chemical compound, potassium bromate. This reaction can be represented by the following chemical equation:

Br- (aq) + Cl2 (g) → BrCl (aq)

BrCl (aq) + H2O (l) → HOBr (aq) + HCl (aq)

HOBr (aq) + Br- (aq) → BrO- (aq) + HBr (aq)

The initial reaction between bromide ions (Br-) and chlorine gas (Cl2) produces bromine chloride (BrCl), which is a reddish-brown colored compound. This compound then reacts with water to form hypobromous acid (HOBr) and hydrochloric acid (HCl). The hypobromous acid then reacts with another bromide ion to form bromate ions (BrO-), which are responsible for the colorless appearance of the solution.