Final answer:
The entropy change (∆S) is positive when a solid decomposes into gaseous products, reflecting an increase in disorder and the number of microstates as the substance changes from solid to gas.
Step-by-step explanation:
The change in entropy (∆S) when a solid substance decomposes and produces gaseous products is generally positive (∆S > 0). This is because the entropy of a substance increases as it goes from the highly ordered structure of a crystalline solid to the less-ordered state of a liquid, and further increases when it changes to the still less-ordered state of a gas. In the transition from solid to gas, the number of microstates, which are the different ways in which the particles can be arranged, significantly increases because the gaseous particles have more freedom of motion and can be spread out over a larger volume than in the solid or liquid states. Therefore, the increase in the number of microstates increases entropy.