Problem 42 - Chemistry The Central Science In Si Units

Question

Predict the sign of \(\Delta S_{\text {sys }}\) 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 Hatoms (used in atomic hydrogen welding).

Step-by-Step Solution

Answer

(a) Negative, (b) Negative, (c) Negative, (d) Positive

Step 1: Analyze Process (a) – Reaction of H2 with Palmitoleic Acid

For the reaction of gaseous \ \(\text{H}_2\) with liquid palmitoleic acid to form liquid palmitic acid, observe that a gas is being consumed to form a liquid. This transition from gas to liquid represents an increase in order because gases have higher entropy than liquids. Thus, the system's entropy, \(\Delta S_{\text{sys}}\), decreases, resulting in a negative sign.

Step 2: Analyze Process (b) – Solidification of Palmitic Acid

When liquid palmitic acid solidifies at \(1^\circ\text{C}\), it changes from a more ordered liquid state to a more ordered solid state. Since solids have lower entropy than liquids (are more ordered), \(\Delta S_{\text{sys}}\) also decreases, resulting in a negative sign.

Step 3: Analyze Process (c) – Precipitation of Silver Chloride

The precipitation of silver chloride from an aqueous solution means that ions come together to form a solid. Going from ions dispersed in liquid to a solid form decreases disorder, resulting in a decrease in system entropy. Thus, \(\Delta S_{\text{sys}}\) for this process is negative.

Step 4: Analyze Process (d) – Dissociation of H2

Gaseous \(\text{H}_2\) dissociating into gaseous hydrogen atoms in an electric arc involves a transition from a diatomic molecule to individual atoms. This increases the number of particles present in the system, leading to increased disorder (higher entropy). Therefore, \(\Delta S_{\text{sys}}\) is positive.

Key Concepts

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. It explores how systems convert energy from one form to another and how these processes affect the overall behavior of the system. This discipline is grounded in four laws, which lay the framework for understanding energy conservation and entropy.
Fundamentally, thermodynamics helps us understand why certain processes occur spontaneously in nature and others do not. The Second Law, for instance, states that the entropy of an isolated system will tend to increase over time. This law underpins the concept that energy tends to disperse or spread out if not interfered with.
Applications of thermodynamics span from everyday life to complex scientific processes. Questions like how much energy is required to heat water or why ice melts are all governed by thermodynamic principles.

Chemical Reactions

Chemical reactions are processes where reactants transform into products. These transformations involve the breaking and forming of chemical bonds and are crucial for a multitude of natural and industrial processes.
In the context of reactions, entropy changes often accompany the process. When determining the sign of \(\Delta S_{\text{sys}}\), it is vital to consider the phases of reactants and products. A reaction where gas is consumed typically signifies a decrease in entropy because gases have a higher degree of disorder compared to liquids or solids.

• In Process (a), gaseous \(\text{H}_2\) reacts with a liquid, resulting in a decreased system entropy.
• For Process (c), ions in a solution form a precipitate, reducing entropy as the ions become less disordered.
As seen, understanding the change in states of matter during reactions is key to predicting entropy change in chemical processes.

Phase Transitions

Phase transitions involve change from one state of matter to another, like solid to liquid, liquid to gas, or even liquid to solid. These transitions are often accompanied by changes in entropy, reflecting the degree of disorder of the molecules involved.
During a phase transition:

• A shift from solid to liquid or gas typically increases disorder, thus increasing entropy.
• Conversely, moving from gas to liquid or solid results in decreased disorder, thus reducing entropy.

In Process (b), when liquid palmitic acid solidifies, it experiences a decrease in entropy. This is because the molecules in a solid state are more ordered and occupy a definite structure. Understanding these transitions is crucial for predicting entropy changes during phase changes.

Entropy

Entropy is a central concept in thermodynamics that measures the degree of randomness or disorder in a system. A system with higher entropy is more disordered, and vice versa. Entropy is crucial for understanding the direction and spontaneity of processes.
Positive entropy change (\(\Delta S_{\text{sys}} > 0\)) implies increased disorder. This can occur when there is an increase in the number of gas molecules or when a solid dissolves, increasing randomness within the system. Conversely, negative entropy change (\(\Delta S_{\text{sys}} < 0\)) indicates a transition toward greater order, such as the formation of solids from liquids or gases.

• In Process (d), the dissociation of gaseous \(\text{H}_2\) into individual hydrogen atoms increases system entropy due to higher particle count and disorder.

Recognizing these changes helps predict the behavior of systems under various physical and chemical conditions.