Question

Without doing any calculations, determine the sign of \(\Delta S_{\text { ys }}\) for each chemical reaction. a. \(\mathrm{Mg}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{MgCl}_{2}(s)\) b. \(2 \mathrm{H}_{2} \mathrm{S}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{SO}_{2}(g)\) c. \(2 \mathrm{O}_{3}(g) \longrightarrow 3 \mathrm{O}_{2}(g)\) d. \(\mathrm{HCl}(g)+\mathrm{NH}_{3}(g) \stackrel{(g)}{\longrightarrow} \mathrm{NH}_{4} \mathrm{Cl}(s)\)

Short answer

a. \(\Delta S_{\text{ys}} < 0\), b. Likely \(\Delta S_{\text{ys}} < 0\), c. \(\Delta S_{\text{ys}} > 0\), d. \(\Delta S_{\text{ys}} < 0\)

Step-by-step solution

- Understanding Entropy Change

The sign of the entropy change \(\Delta S_{\text { ys }}\) in a chemical reaction depends on the disorder of the system. An increase in disorder corresponds to a positive entropy change, while a decrease corresponds to a negative entropy change.

- Analyzing Reaction a

For the reaction \(\mathrm{Mg}(s) + \mathrm{Cl}_2(g) \longrightarrow \mathrm{MgCl}_2(s)\), there is a transition from one solid and one gas to one solid. This reduces the number of moles of gas and thus decreases the disorder. Therefore, \(\Delta S_{\text{ys}} < 0\).

- Analyzing Reaction b

For the reaction \(2 \mathrm{H}_2 \mathrm{S}(g) + 3 \mathrm{O}_2(g) \longrightarrow 2 \mathrm{H}_2 \mathrm{O}(g) + 2 \mathrm{SO}_2(g)\), the number of moles of gas is the same on both sides of the equation (5 moles of gas produce 4 moles of gas). This does not give a clear change in disorder; however, oxygen gas which contributes to higher disorder is being consumed and the products are likely more structured than the reactants, suggesting a slight decrease in disorder. This implies a likely but not definite \(\Delta S_{\text{ys}} < 0\).

- Analyzing Reaction c

For the reaction \(2 \mathrm{O}_3(g) \longrightarrow 3 \mathrm{O}_2(g)\), the number of gaseous molecules is increasing (2 moles of ozone produce 3 moles of oxygen). This increases the disorder in the system. Hence, \(\Delta S_{\text{ys}} > 0\).

- Analyzing Reaction d

The reaction \(\mathrm{HCl}(g) + \mathrm{NH}_3(g) \stackrel{(g)}{\longrightarrow} \mathrm{NH}_4 \mathrm{Cl}(s)\) starts with two gases and produces a solid. This greatly reduces the disorder as gases have higher entropy than solids. Therefore, \(\Delta S_{\text{ys}} < 0\).

Key concepts

Chemical Thermodynamics

Chemical thermodynamics deals with the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. It provides us with a powerful set of tools for predicting whether a process will occur spontaneously at a given temperature.

The key concept here is the Gibbs free energy, denoted by the symbol G, which combines enthalpy, entropy, and temperature to give a criterion for spontaneity. A reaction is spontaneous if it leads to a decrease in the free energy, or more simply, if \( \Delta G < 0 \). The change in Gibbs free energy, \( \Delta G \), can be found using the equation \( \Delta G = \Delta H - T \Delta S \), where \( \Delta H \), \( T \), and \( \Delta S \) represent the change in enthalpy, temperature, and entropy, respectively.

Entropy and Disorder

Entropy, symbolized by S, is a measure of the amount of disorder or randomness in a system. A highly ordered system, with particles neatly arranged, has low entropy, while a disordered system, in which particles are randomly scattered, has high entropy.

In terms of chemical reactions, the change in entropy \( \Delta S \) often dictates the direction and spontaneity of the reaction. For example, when a substance melts, it goes from a more ordered solid state to a less ordered liquid state, increasing the entropy. The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. As a result, the universe overall is always moving towards a state of increased disorder or maximal entropy.

Relating Entropy to Phase Changes

The state of matter—whether gas, liquid, or solid—greatly affects a substance's entropy. Typically, gases have the highest entropy, followed by liquids, and then solids. This order is due to the different degrees of freedom and the spaces between particles in each phase. For instance, during a phase transition from a gas to a solid, there is a significant loss of entropy since the molecules in a solid are typically held in a fixed, orderly pattern compared to the freely moving molecules in a gas. This concept helps to predict whether the entropy change in a reaction is positive or negative without requiring complex calculations.

Gaseous to Solid Phase Transitions

A phase transition from the gaseous to the solid state represents one of the most dramatic decreases in entropy a substance can undergo. Gases are characterized by considerable freedom of motion of the molecules, leading to high entropy. When a gas transforms directly into a solid—a process known as deposition—the molecules arrange into a highly structured and rigid lattice, significantly reducing their freedom of motion.

This phenomenon can be observed in the formation of frost from water vapor in the air during cold weather, where the vapor transitions directly to ice without becoming liquid first. In the context of chemical reactions, when a reaction results in the formation of a solid from gaseous reactants, as seen in exercise examples a and d, we expect a large negative change in entropy, indicating a substantial decrease in disorder. This transformation's difference in entropy is a crucial factor when considering the energy balance and spontaneity of such reactions.