Question

Without using Appendix B, predict the sign of \(\Delta S^{\circ}\) for (a) \(\mathrm{H}_{2} \mathrm{~S}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \frac{1}{8} \mathrm{~S}_{8}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) (b) \(\mathrm{HCl}(a q)+\mathrm{NaOH}(a q) \longrightarrow \mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) (c) \(2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)\)

Short answer

For all reactions, \(\text{\textdelta S^{\textup{o}}}\) is expected to be negative.

Step-by-step solution

Predict the Sign of \(\u2206 S^{\textup{o}}\) for Reaction (a)

In reaction (a), the reactants are two gases, \(\text{H}_{2} \text{S}(g)\) and \(\frac{1}{2} \text{O}_{2}(g)\), and the products are a solid \(\frac{1}{8} \text{S}_{8}(s)\) and a gas \(\text{H}_{2} \text{O}(g)\). When gases react to form a solid, the entropy decreases because solids have lower entropy than gases. Therefore, \(\u2206 S^{\textup{o}}\) is expected to be negative.

Predict the Sign of \(\u2206 S^{\textup{o}}\) for Reaction (b)

For reaction (b), the reactants are aqueous solutions, \(\text{HCl}(aq)\) and \(\text{NaOH}(aq)\), which react to form another aqueous solution \(\text{NaCl}(aq)\) and a liquid, \(\text{H}_{2} \text{O}(l)\). The formation of liquid water from aqueous ions generally results in a decrease in entropy, meaning \(\text{\textdelta S^{\textup{o}}}\) is expected to be negative.

Predict the Sign of \(\text{\textdelta S^{\textup{o}}}\) for Reaction (c)

In reaction (c), two gas molecules \(\text{NO}_{2}(g)\) combine to form one gas molecule \(\text{N}_{2} \text{O}_{4}(g)\). Combining gas molecules reduces the number of gas particles, which generally leads to a decrease in entropy. Therefore, \(\text{\textdelta S^{\textup{o}}}\) is expected to be negative.

Key concepts

Entropy

Entropy is a measure of the randomness or disorder of a system. Essentially, it tells us how much energy in a system is dispersed or spread out. The more disordered a system, the higher its entropy.

• Gases have high entropy because their molecules move freely and occupy a lot of space.
• Solids, on the other hand, have low entropy since their particles are tightly packed and orderly.
• Liquids fall somewhere in between.

When predicting changes in entropy for a chemical reaction, keep in mind the physical states of the reactants and products. For example, the formation of a solid from gases will decrease entropy, while a solid dissolving into ions in solution will increase entropy.

Chemical Reactions

In chemical reactions, the rearrangement of atoms and molecules can lead to changes in entropy.

Let's look at the reactions from the exercise to understand this better:

• Reaction (a): \[\text{H}_{2} \text{S}(g) + \frac{1}{2} \text{O}_{2}(g) \rightarrow \frac{1}{8} \text{S}_{8}(s) + \text{H}_{2} \text{O}(g)\] Here, we start with two gas molecules and end with a solid and a gas. Solids are more ordered than gases, indicating that the entropy (∆S) of the system decreases.
• Reaction (b): \[\text{HCl}(aq) + \text{NaOH}(aq) \rightarrow \text{NaCl}(aq) + \text{H}_{2} \text{O}(l)\] Starting with aqueous ions and ending with a liquid means that the ions, which are usually free to move in solution, become part of a more ordered liquid structure, decreasing the system's overall entropy.
• Reaction (c): \[\text{2NO}_2(g) \rightarrow \text{N}_2 \text{O}_4 (g)\] Combining two gas molecules into one gas molecule reduces the number of particles, resulting in lower entropy (∆S is negative).

By understanding these reactions, we can see how the types of reactants and products determine the change in entropy.

Thermodynamics

Thermodynamics is the study of energy transformations in chemical and physical processes. Entropy plays a crucial role in the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time.

This law also means that natural processes tend to move towards a state of maximum entropy (or disorder). Here are some key points:

• In any reaction, some energy is always lost as waste heat, increasing the universe's overall entropy.
• When predicting the spontaneity of a reaction, both changes in entropy (∆S) and enthalpy (∆H) are essential considerations. The Gibbs free energy equation \[ \text{ΔG} = \text{ΔH} - T\text{ΔS} \] combines these quantities to determine if a reaction is spontaneous (\text{ΔG} < 0) or not.

By understanding these principles, students can better predict and explain the behavior of various chemical reactions.