why should the NaOH solution have turned clear more quickly after exercise compared to before exercise by exhaling inside of the glass with NaOH?

Exhaling into the NaOH solution releases carbon dioxide (CO2) into the solution, which reacts with the NaOH to form sodium carbonate (Na2CO3) and water. This reaction causes the solution to become clear, as the cloudiness of the NaOH solution is due to the formation of a carbonate precipitate.

During exercise, a person's metabolic rate increases, leading to a higher production of CO2. Therefore, exhaling into the NaOH solution after exercise would result in a higher concentration of CO2 being released into the solution, leading to a faster reaction and a quicker clearing of the solution compared to before exercise when the CO2 production is lower.