Final answer:
Dissolving solid borax in water increases the standard entropy of the system, with the sign of ΔS being positive due to a greater dispersal of matter and increased randomness.
Step-by-step explanation:
When solid borax is dissolved in water, we expect the standard entropy of the system to increase. This occurs because the solid state, which is more ordered, transitions to an aqueous state where its ions are freely mobile in solution. This results in a greater dispersal of matter and increases the randomness of the system. Consequently, the sign of ΔS, which represents the entropy change, will be positive.
For example, dissolving NaCl in water gives an increase of mobile ions in solution, leading to a positive sign for entropy change due to the increased disorder. Similarly, when NaNO3(s) dissolves to form Na+ (aq) and NO3- (aq), there is a positive entropy change. However, processes such as the freezing of liquid water or the formation of a solid precipitate lead to a negative entropy change because the system becomes more ordered.