Problem 74 - Chemistry The Molecular Nature of Matter

Question

Predict the algebraic sign of the entropy change for the following reactions. (a) \(\mathrm{I}_{2}(s) \longrightarrow \mathrm{I}_{2}(g)\) (b) \(\mathrm{Br}_{2}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{BrCl}_{3}(g)\) (c) \(\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)\) (d) \(\mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)\)

Step-by-Step Solution

Answer

The sign of the entropy change for the reactions: (a) positive, (b) negative, (c) negative, (d) slightly negative or neutral.

Step 1: Identify the Phase Change for Reaction (a)

For reaction (a) \(\mathrm{I}_{2}(s) \longrightarrow \mathrm{I}_{2}(g)\), solid iodine (\(\mathrm{I}_{2}(s)\)) is changing into gaseous iodine (\(\mathrm{I}_{2}(g)\)). This is a phase transition from solid to gas, typically associated with an increase in entropy.

Step 2: Predict the Sign of the Entropy Change for Reaction (a)

Since going from solid to gas results in higher randomness and disorder, the entropy change (\(\Delta S\)) for the reaction (a) will be positive.

Step 3: Analyze the Number of Gaseous Molecules for Reaction (b)

In reaction (b) \(\mathrm{Br}_{2}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{BrCl}_{3}(g)\), the number of gaseous molecules decreases as 4 initial gaseous molecules result in 2 gaseous molecules of product. A reduction in the number of gaseous molecules often leads to a decrease in entropy.

Step 4: Predict the Sign of the Entropy Change for Reaction (b)

A decrease in the number of gaseous molecules implies the system becomes more ordered. Therefore, the entropy change (\(\Delta S\)) for reaction (b) should be negative.

Step 5: Determine the Physical State Change for Reaction (c)

Reaction (c) \(\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)\) involves two gaseous reactants combining to form a solid product. Transition from gas to solid generally results in reduced entropy.

Step 6: Predict the Sign of the Entropy Change for Reaction (c)

Since the product is a solid and the reactants are gases, the entropy decreases as the randomness and disorder of the system decrease. Hence, the entropy change (\(\Delta S\)) for reaction (c) will be negative.

Step 7: Assess the Phase Change for Reaction (d)

In reaction (d) \(\mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)\), solid (\(s\)) and liquid (\(l\)) are reacting to produce a solid. This reaction does not involve a phase change as the resultant product is also a solid.

Step 8: Predict the Sign of the Entropy Change for Reaction (d)

As there's no phase change and no change in the number of particles, we expect the entropy change to be small. However, due to associations between ions in the aqueous phase before they precipitate, the entropy might slightly decrease, so the entropy change (\(\Delta S\)) for reaction (d) may be slightly negative or potentially neutral.

Key Concepts

Thermodynamics

Thermodynamics is the branch of physics that deals with heat, work, and temperature, and their relation to energy, radiation, and properties of matter. The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed in an isolated system. The second law of thermodynamics introduces the concept of entropy, a measure of the disorder or randomness in a system. Entropy predicts the feasibility of a process or reaction; in a spontaneous process, the total entropy of the system and its surroundings always increases. Understanding entropy is crucial in predicting whether a chemical reaction can occur without external energy input.

In educational settings, making thermodynamics easily graspable can involve comparing these concepts to everyday experiences such as melting ice (increasing entropy) or boiling water (energy transfer in the form of heat).

Phase Transitions

A phase transition is a transformation of a substance from one state of matter—solid, liquid, or gas—to another. As substances change phases, they absorb or release energy, and their entropy changes. During such transitions, a solid melting into a liquid or a liquid evaporating into a gas typically results in an increase in entropy, signifying a greater degree of randomness and disorder. Conversely, freezing and condensation decrease entropy as the molecules become more ordered.

With students, an analogy often used is the organization of a bedroom; a tidy room (solid) has low entropy, while a messy room (gas) has high entropy. These transitions connect to daily life, like ice melting on a hot day or steam from a kettle, making the concept of phase transitions tangible and relatable.

Chemical Kinetics

Chemical kinetics is the study of the speed or rate at which chemical reactions occur and the factors affecting these rates. The rate of a chemical reaction is influenced by several factors including temperature, concentration of reactants, surface area, presence of a catalyst, and the nature of the reactants. Kinetics is central to understanding how reactions occur over time and the pathway taken during the reaction, often described by the reaction mechanism.

Explaining chemical kinetics to students can be illustrated by comparing it to cooking times for various dishes. Some meals take longer to cook (slow reactions), while others cook quickly (fast reactions). The cook (akin to a chemist) can change the cooking conditions, such as turning up the heat or adding an ingredient, to speed up or slow down the cooking time.

Physical Chemistry

Physical chemistry combines chemistry with physics, focusing on how matter behaves on a molecular and atomic level and how chemical reactions occur. It serves as a bridge between the macroscopic world we observe and the microscopic behaviors that define chemical reactions. By understanding these behaviors, one can predict properties of new compounds and the outcomes of chemical reactions.

To make physical chemistry relatable to students, one might use the analogy of puzzle pieces. Just like puzzles, atoms and molecules have specific ways they can be arranged and react. Solving a puzzle can be likened to finding the right conditions for a chemical reaction to produce the desired product. Practical examples, like the development of new materials or medicines, can help clarify the relevance of physical chemistry to technological advances and everyday life.