Since the amount of substance (n) and volume (V) are constant, wouldn't the Ideal Gas Law be a more complicated way of stating the relationship. Gay-Lussac's Law still states the same relationship between temperature and pressure (direct), but in a simpler way. Gay-Lussac's Law can also explain the change from start to finish in this reaction, the Ideal Gas Law would only be able to explain one of those stages in the demonstration. For example, if I wanted to find the volume of the balloon after it has warmed up again, knowing the volume and temperature before the it was submerged and the temperature after it was submerged, I would use Gay-Lussac's Law. You wouldn't be able to do that with the Ideal Gas Law.