Problem 42 - Chemistry: The Central Science in SI Units, Global Edition

Question

Predict the sign of \(\Delta S_{s y s}\) for each of the following processes: (a) Gaseous \(\mathrm{H}_{2}\) reacts with liquid palmitoleic acid \(\left(\mathrm{C}_{16} \mathrm{H}_{30} \mathrm{O}_{2},\right.\) unsaturated fatty acid) to form liquid palmitic acid \(\left(\mathrm{C}_{16} \mathrm{H}_{32} \mathrm{O}_{2}\right.\) saturated fatty acid). (b) Liquid palmitic acid solidifies at \(1^{\circ} \mathrm{C}\) to solid palmitic acid. (c) Silver chloride precipitates upon mixing \(\mathrm{AgNO}_{3}(a q)\) and \(\mathrm{NaCl}(a q) .\) (d) Gaseous \(\mathrm{H}_{2}\) dissociates in an electric arc to form gaseous H atoms (used in atomic hydrogen welding).

Step-by-Step Solution

Answer

(a) \(\Delta S_{sys}<0\) (b) \(\Delta S_{sys}<0\) (c) \(\Delta S_{sys}<0\) (d) \(\Delta S_{sys}>0\)

Step 1: Identify the phases of the reactants and products

The reactants include gaseous \(\mathrm{H}_{2}\) and liquid palmitoleic acid, while the product is liquid palmitic acid.

Step 2: Determine the change in disorder

In this reaction, a gaseous molecule reacts with liquid to form a liquid. The loss of a gaseous molecule means that the system becomes more ordered.

Step 3: Predict the sign of \(\Delta S_{sys}\)

Since the system becomes more ordered, the entropy change will be negative: \(\Delta S_{sys}<0\). (b) Liquid palmitic acid solidifies at \(1^{\circ} \mathrm{C}\) to solid palmitic acid.

Step 4: Identify the phase change

The process involves the transition from a liquid to a solid.

Step 5: Determine the change in disorder

Going from a liquid to a solid means that the molecules become more ordered and less randomly distributed.

Step 6: Predict the sign of \(\Delta S_{sys}\)

Since the system becomes more ordered, the entropy change will be negative: \(\Delta S_{sys}<0\). (c) Silver chloride precipitates upon mixing \(\mathrm{AgNO}_{3}(a q)\) and \(\mathrm{NaCl}(a q)\).

Step 7: Identify the process

The process involves the formation of a solid precipitate (silver chloride) from two aqueous solutions.

Step 8: Determine the change in disorder

The formation of a solid precipitate means that the system becomes more ordered.

Step 9: Predict the sign of \(\Delta S_{sys}\)

Since the system becomes more ordered, the entropy change will be negative: \(\Delta S_{sys}<0\). (d) Gaseous \(\mathrm{H}_{2}\) dissociates in an electric arc to form gaseous H atoms (used in atomic hydrogen welding).

Step 10: Identify the process

The process involves the dissociation of a gaseous molecule into single gaseous atoms.

Step 11: Determine the change in disorder

During the dissociation, one gaseous molecule is converted into two individual gaseous atoms, leading to an increase in the number of particles and disorder.

Step 12: Predict the sign of \(\Delta S_{sys}\)

Since the system becomes more disordered, the entropy change will be positive: \(\Delta S_{sys}>0\).

Key Concepts

Entropy Change

Entropy is a measure of disorder or randomness in a system. In chemical processes, entropy change, denoted as \( \Delta S \), helps predict how the disorder of a system changes. An increase in disorder is often associated with a positive entropy change, while a decrease suggests negative entropy change. For example, when gaseous \( \mathrm{H}_{2}\) reacts with liquid palmitoleic acid to form liquid palmitic acid, the system transitions from having both gaseous and liquid phases to just one liquid phase. This reduction in randomness indicates a negative entropy change \( \Delta S < 0 \).

• Increased disorder ≈ positive \( \Delta S \)
• Decreased disorder ≈ negative \( \Delta S \)
• More phases typically mean higher entropy

By understanding these principles, predicting the sign of entropy change becomes more intuitive.

Phase Transitions

Phase transitions involve changes between physical states, like solid, liquid, and gas. During these transitions, the arrangement and movement of particles change significantly. When liquid palmitic acid solidifies, for instance, it undergoes a transformation from the liquid to solid state.

• Liquid to Solid: Particles become more orderly, leading to a negative \( \Delta S \)
• Solid to Liquid or Liquid to Gas: Particles become less orderly, resulting in a positive \( \Delta S \)

Understanding phase transitions and the associated entropy change is crucial, especially in predicting the behavior under temperature variations. During freezing, particles in a liquid slow down and arrange themselves in a fixed, orderly pattern, thereby reducing disorder and entropy.

Chemical Reactions

Chemical reactions often involve rearranging atoms and molecules to form new substances, and they are closely linked to changes in entropy. When \( \mathrm{AgNO}_{3}(a q) \) is mixed with \( \mathrm{NaCl}(a q) \), a reaction leads to the formation of solid silver chloride, a precipitate.

• Formation of solids typically decreases randomness
• Regrouping atoms can sometimes increase entropy, if it means more products

In this example, as the aqueous ions form a solid, the lack of movement leads to a more ordered state and thus negative entropy change. Predicting entropy changes in reactions requires analyzing whether the resulting state is more ordered (typically solids) or more disordered (gases).

Gaseous Reactions

Gaseous reactions can lead to significant fluctuations in entropy due to their high energy and mobility. In the case where gaseous \( \mathrm{H}_2 \) dissociates into individual H atoms, there is an increase in randomness as one molecule splits into multiple atoms.

• Breaking bonds typically increases particle count, boosting disorder
• More particles generally mean higher entropy
• The freedom of movement in gases amplifies entropy changes

Due to these characteristics, gaseous reactions often show positive entropy changes. Dissociation specifically results in more particles, enhancing disorder and resulting in increased entropy, expressed as \( \Delta S > 0 \).