KClO3 (aq) will have greater molar entropy than KClO3 (s) because molar entropy increases with increase in temperature.
As the temperature rises, the standard molar entropy of any substance rises. Entropy and a Single Substance's Temperature ” Entropy increases significantly when a solid turns into a liquid and when a liquid turns into a gas. The entropy of the liquid is lower than that of the gas. As a result, entropy rises in reactions that produce gaseous byproducts from solid or liquid reactants. When solid reactants produce liquid products, entropy also rises.
The full solution can be found in the image attached. Graham's law was applied to the problem. The rate of diffusion of a gas is inversely proportional to its molar mass or vapour density. Molar mass= 2vapour density