Question

Predict the algebraic sign of the entropy change for the following reactions. (a) \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{PCl}_{5}(g)\) (b) \(\mathrm{SO}_{2}(g)+\mathrm{CaO}(s) \longrightarrow \mathrm{CaSO}_{3}(s)\) (c) \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{CO}_{3}(a q)\) (d) \(\mathrm{Ni}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{NiCl}_{2}(a q)\)

Short answer

The entropy change is predicted to be negative for reactions (a), (b), and (c), and positive for reaction (d).

Step-by-step solution

Understanding Entropy Changes

Entropy is a measure of the disorder or randomness in a system. An increase in entropy (positive change) occurs when a system becomes more disordered. A decrease in entropy (negative change) is associated with a system becoming more ordered. Entropy generally increases when gases are produced, when substances are mixed, or when the number of moles of gaseous products is greater than that of gaseous reactants.

Analyzing Reaction (a)

In reaction (a), the number of gas molecules decreases as one molecule of PCl3 and one molecule of Cl2 combine to form one molecule of PCl5. There is a decrease in disorder because there are fewer gas molecules in the product than in the reactants. Consequently, we predict a negative change in entropy.

Analyzing Reaction (b)

In reaction (b), one gas molecule and one solid combine to form one solid product. The disorder decreases since gases have higher entropy than solids. As a result, the change in entropy is negative.

Analyzing Reaction (c)

Reaction (c) involves one gas and one liquid reacting to form an aqueous solution. The number of gaseous molecules decreases and a solution is formed, which can increase disorder to some extent due to solvation. However, the transition from gas to aqueous typically indicates a decrease in entropy, suggesting a negative entropy change.

Analyzing Reaction (d)

In reaction (d), a solid and an aqueous solution react to produce a gas and another aqueous solution. There is an increase in the number of gas molecules, which indicates an increase in disorder. Thus, the change in entropy is positive.

Key concepts

Thermodynamics

In the simplest terms, thermodynamics is the study of energy, its transformations, and its relation to matter. One of the foundational concepts within this field is the first law of thermodynamics, which asserts that energy cannot be created or destroyed, only transformed from one form to another.

This law is akin to a cosmic accounting system for energy, ensuring that the balance sheet of the universe always tallies. A closely related concept is the second law of thermodynamics, which introduces the idea of entropy as a measure of a system's thermal energy per unit temperature that is not available for doing work.

Understanding these laws helps us grasp why certain processes are spontaneous, such as heat flowing from a hot object to a cooler one, and why some reactions require input energy to proceed.

Chemical Reactions

Chemical reactions are transformations where the chemical identities of substances change. Reactions can absorb energy (endothermic) or release energy (exothermic), and they can also be categorized based on their impact on the entropy of a system.

Understanding the types of chemical reactions, such as synthesis, decomposition, single replacement, and double replacement, is fundamental when we consider the entropy changes they might produce. Every change—be it breaking bonds, forming new bonds, or changing the state of matter—will have an entropy implication.

Entropy in Chemistry

Entropy in chemistry is often likened to the level of disorder or randomness within a system. In the microscopic context, it's a measure of how many ways the components (like atoms or molecules) can be arranged while maintaining the same energy state.

An increase in entropy typically leads to a more stable and spontaneous system. For instance, when a solid melts into a liquid, there’s an increase in entropy because the molecules have more freedom to move. Entropy changes also help us understand molecular behavior during reactions, such as the dispersal of gas molecules or the mixing and dissolution in solutions.

Predicting Entropy Change

Predicting the entropy change of a chemical reaction involves considering the states of the reactants and products, as well as the complexity and number of particles before and after the reaction. Here are a few quick guidelines:

• If a reaction produces more gas molecules from fewer, or from solids or liquids, the entropy likely increases.
• When a reaction results in fewer gas molecules, or creates a more ordered phase, like a solid from a gas, the entropy likely decreases.
• Dissolution can lead to an increase in entropy, but if it results in a compound that has less mobility than the reactant molecules, entropy may not increase significantly.

Through these principles, one can often predict the sign of the entropy change for various chemical reactions and understand the driving forces behind their spontaneity or non-spontaneity.