Which of the following reactions (or processes) are expected to have a negative value for \(\Delta S^{\circ} ?\) a. \(\operatorname{SiF}_{6}(a q)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{HF}(g)+\mathrm{SiF}_{4}(g)\) b. \(4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)\) c. \(\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{COCl}_{2}(g)\) d. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) e. \(\mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\)

Thermodynamics is a branch of physics that deals with the relationships between heat, work, temperature, and energy. In chemistry, it plays a crucial role in understanding how chemical reactions occur and what factors influence them.

In the context of entropy change in chemical reactions, thermodynamics tells us that systems tend to move towards a state of greater disorder or randomness, which is quantified by a property called entropy (symbolized as S). The change in entropy (ΔS) during a chemical reaction gives us insights into the degree of disorder or randomness of the system before and after the reaction.

The spontaneity of a chemical reaction can often be predicted by the sign of the entropy change (ΔS). A positive value for ΔS indicates that the disorder increases, which usually favors the spontaneity of a reaction. Conversely, a negative ΔS suggests a decrease in disorder, indicating that the reaction may not be spontaneous without some input of energy.

However, entropy alone does not determine the spontaneity of a reaction. It must be considered alongside enthalpy change and temperature to fully understand the likely behavior of a chemical process. This is where the concept of Gibbs free energy comes into play.

Gibbs free energy (G) is a thermodynamic quantity that is a very useful predictor for the spontaneity of a chemical reaction. It incorporates both the entropy (S) and enthalpy (H) of a system, as described by the equation G = H - TS, where T is the temperature in Kelvin.

A negative ΔG indicates a spontaneous process, while a positive ΔG suggests a non-spontaneous process. Essentially, for a chemical reaction to be spontaneous at constant temperature and pressure, the Gibbs free energy change must be negative. ΔG becomes more negative either by a decrease in enthalpy (ΔH < 0), an increase in entropy (ΔS > 0), or both.

The states of matter involved in chemical reactions—solid (s), liquid (l), gas (g), and aqueous (aq)—have a significant impact on the entropy change (ΔS). Typically, gases have higher entropy than liquids, which, in turn, have higher entropy than solids.

Hence, reactions in which gases are produced from liquids or solids tend to increase in entropy (ΔS > 0), indicating a more disordered system. Conversely, reactions where gases condense into liquids or solids generally result in a negative entropy change (ΔS < 0), reflecting increased order within the system. This intrinsic relationship between the states of matter and entropy guides chemists in predicting the direction in which a reaction will naturally proceed.