A chemical change is indicated by any change that affects the composition of the substances involved. In this case, all the observations mentioned suggest a chemical change:
I. The chemicals change color from colorless to purple. (Indicates a change in chemical composition)
II. A yellow gas forms. (Indicates a new substance is produced)
III. A brown solid forms in the bottom of the beaker. (Indicates a new substance is produced - precipitate formation)
IV. The temperature of the chemicals rises 15°C. (Indicates an exothermic reaction, which is often associated with a chemical change)
Based on this analysis, the correct answer is:
C. I, II, III, and IV