Question

Indicate whether the entropy of the system would increase or decrease in each of the following reactions. If you cannot be certain simply by inspecting the equation, explain why. (a) \(\mathrm{CCl}_{4}(1) \longrightarrow \mathrm{CCl}_{4}(\mathrm{g})\) (b) \(\mathrm{CuSO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow\) \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) (c) \(\mathrm{SO}_{3}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (d) \(\mathrm{H}_{2} \mathrm{S}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{SO}_{2}(\mathrm{g})\) (not balanced)

Short answer

a) Increases, b) Decreases, c) Uncertain from the equation alone, d) Uncertain due to unbalanced equation.

Step-by-step solution

Analyze Reaction (a)

In the reaction \(\mathrm{CCl}_{4}(1) \longrightarrow \(\mathrm{CCl}_{4}(\mathrm{g})\), the carbon tetrachloride transitions from liquid to gaseous state. For all spontaneous physical and chemical changes, the system always tends toward greater randomness. Since gases have higher entropy than liquids, the entropy increases in this reaction.

Analyze Reaction (b)

In the reaction \(\mathrm{CuSO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\), the number of gaseous molecules decreases (we go from 2 moles to 0 moles of gas). The reaction is forming an ordered solid, in which the molecules have less freedom to move around. This decrease in randomness translates to a decrease in entropy.

Analyze Reaction (c)

The reaction \(\mathrm{SO}_{3}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) includes two moles of gas on the left of the equation and two moles of gas on the right of the equation. No change in the number of gas molecules or the phase, so we may not be able to determine this reaction's change in entropy just by looking at the reaction.

Analyze Reaction (d)

In this final unbalanced reaction, \(\mathrm{H}_{2} \mathrm{S}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{SO}_{2}(\mathrm{g})\), it's difficult to analyze the entropy change just through the equation due to imbalance. It's recommended to balance the equation first. However, an initial analysis suggests that both reactants and products are in gaseous state, thus it's uncertain whether entropy increases or decreases without further detailed balance and calculations.

Key concepts

Phase Changes

Phase changes are intriguing because they involve the transformation of a substance from one state of matter to another, such as from liquid to gas. This transformation is closely related to changes in entropy, the measure of disorder or randomness in a system.
When substances undergo phase changes, particularly from liquid to gas, there is an increase in entropy. This is because gas particles move more freely and occupy a larger volume compared to when they are in a liquid state.
For example, in the reaction \(\mathrm{CCl}_4(1) \rightarrow \mathrm{CCl}_4(\mathrm{g})\), carbon tetrachloride changes from a liquid to a gas. This transition naturally leads to an increase in randomness, hence, the system's entropy increases.
Understanding phase changes can help predict whether a reaction will be spontaneous. A spontaneous process is one that occurs without continuous input of energy from outside the system. For most chemical reactions, entropy tends to increase as substances move from more ordered (solid) to less ordered phases (liquid or gas).
This concept is evident in everyday life, such as when water boils and turns into steam, demonstrating how phase changes affect molecular movement and entropy.

Molecular Order and Disorder

Molecular order and disorder are fundamental concepts in understanding entropy. Entropy is dependent on how particles are arranged and their freedom of motion.
Generally, solids have more ordered structures compared to liquids and gases. Therefore, transitions involving solidification result in a decrease in entropy because the molecules become more ordered.
In Reaction (b), \(\mathrm{CuSO}_4 \cdot 3 \mathrm{H}_2 \mathrm{O}(\mathrm{s})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}(\mathrm{s})\), there is a transition from gaseous water molecules to solidified, more orderly water molecules within a hydrated crystal. This indicates a decrease in entropy, as the disorder of gas molecules becomes the order of a solid state.
Understanding molecular ordering helps in predicting the entropy change of reactions. Reactions resulting in more structured, solid products from gaseous reactants involve a reduction in randomness. Conversely, reactions that lead to gaseous products from solid or liquid reactants increase disorder, reflecting an entropy increase.
These principles are applied in real-world contexts, such as in crystal formation or even in understanding biochemical pathways where ordered structures are essential for cellular function.

Balancing Chemical Equations

Balancing chemical equations is crucial to accurately predicting the direction of entropy change and understanding the stoichiometry of chemical reactions.
A balanced chemical equation has the same number of each type of atom on both sides of the equation, respecting the Law of Conservation of Mass. This is essential when analyzing complex reactions involving changes in entropy.
In Reaction (d), \(\mathrm{H}_2 \mathrm{S}(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g})+\mathrm{SO}_2(\mathrm{g})\)\(\text{ (not balanced)}\), balancing the equation would first require ensuring equal numbers of each type of atom are present in both reactants and products. Only then can we properly assess the change in entropy.
Balancing the reaction allows us to clearly see the relationship between reactant and product molecules, ultimately providing better insights into how the disorder in the system shifts.
Therefore, writing and balancing equations precisely enables chemists to calculate entropy changes accurately and predict whether a reaction is exothermic or endothermic, crucial for both academic and industrial applications.