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This is because the reaction taking place is a displacement reaction, meaning that one element is being displaced by another.
So what is being displaced?:
If you look at the periodic table, chlorine is more reactive than bromine and is therefore going to want to react more aggressively than bromine. Due to this, the chlorine is stronger and can take the place of bromine in the potassium bromide solution and now becomes potassium chloride solution. Since the bromine ions now float freely in the solution, there is a visible colour change to orange due to the natural orange/brown colour of bromine.see more