Final answer:
Of the processes listed, none directly indicate a negative entropy change (ΔS). Standard principles of entropy suggest a transition from a more erratic to a more ordered state, such as condensation or freezing, would lead to a negative ΔS.
Step-by-step explanation:
In the context of entropy changes (ΔS), we must identify which process would result in a negative change in entropy, indicating a decrease in disorder. When we consider the four options provided:
Melting ice into water would cause an increase in disorder as the structured solid becomes a more erratic liquid, hence ΔS would be positive.
Water evaporating into vapor would similarly increase disorder by changing into a state where particles move freely, making ΔS positive.
A gas expanding to fill a larger volume also increases disorder as the gas particles spread out more, resulting in a positive ΔS.
However, mixing two substances together does not necessarily imply an increase or decrease in entropy, but typically mixing leads to increased disorder. Yet, without additional context about the substances and the nature of the mixing, it is not clear whether ΔS would be negative or positive.
Given the information from the associated content and standard principles of entropy in Chemistry, the most likely answer from the provided options, which would lead to a decrease in entropy or a negative ΔS, is not expressly listed. Nonetheless, we can infer from the principles that a process such as freezing or condensation, where a state changes from more erratic to more structured (gas to liquid, liquid to solid), would typically result in a negative entropy change.