Final answer:
The entropy of a gas increases when it expands into a vacuum due to the additional microstates available, reflecting increased disorder. The change in entropy (ΔS) for a reaction is determined by the difference in the system's entropy before and after the reaction, and typically, reactions lead to an increase in the entropy of the system.
Step-by-step explanation:
Change in Entropy of a Chemical Reaction in Vacuum
The concept of entropy is central to understanding the spontaneous nature of chemical reactions. Specifically, when a gas expands into a vacuum, there is an increase in entropy due to the greater volume allowing for more atomic or molecular disorder. Considering an ideal gas expanding into a vacuum—where it occupies a larger volume V₂ from a previous volume V₁—the expansion results in an increase in the number of accessible microstates, and hence, a rise in entropy (ΔS > 0).
Moreover, the entropy change (ΔS) for a reaction can implicate the spontaneity of a process. The change in entropy is the difference between the entropy of the final state (Sf) and the initial state (Si). The second law of thermodynamics tells us that the total entropy change of the universe (system plus surroundings) must be positive for a spontaneous process. While entropy changes occurring in a vacuum eliminate the need to consider the surroundings explicitly, the entropy of the system can still be calculated by using the difference in the substance's absolute entropies before and after the reaction.
An example is the vaporization of water where the entropy change can be calculated from the known absolute entropies of the reactants and products. Additionally, the general principle is that chemical reactions tend to increase the total entropy, with certain molecular states of reactants and products serving as indicators for whether the entropy will increase or decrease.