Final answer:
The water/bromothymol blue solution changes color after an exerciser blows into it because the carbon dioxide from the breath forms carbonic acid, turning the solution from blue to green or yellow.
Step-by-step explanation:
The color of the water/bromothymol blue solution changes after the exerciser blows into it due to the introduction of carbon dioxide (CO₂). When CO₂ dissolves in water, upon reaction on certain conditions it forms carbonic acid (H₂CO₃), which is a weak acid. Bromothymol blue is an indicator that changes color to indicate the presence of acid: it turns yellow in acidic conditions. Therefore, after an exerciser exhales into the bromothymol blue solution, the increased acidity causes the solution to change color from blue to yellow or green, depending on the amount of CO₂ exhaled.