Problem 44 - Chemistry Matter and Change

Question

Predict the sign of \(\Delta S_{\text { system }}\) for each of the following changes. \(\begin{array}{ll}{\text { a. } \mathrm{ClF}(\mathrm{g})+\mathrm{F}_{2}(\mathrm{g}) \rightarrow \mathrm{ClF}_{3}(\mathrm{g})} & {\text { c. } \mathrm{CH}_{3} \mathrm{OH}(1) \rightarrow \mathrm{CH}_{3} \mathrm{OH}(\mathrm{aq})} \\ {\text { b. } \mathrm{NH}_{3}(\mathrm{g}) \rightarrow \mathrm{NH}_{3}(\mathrm{aq})} & {\text { d. } \mathrm{C}_{10} \mathrm{H}_{8}(\mathrm{l}) \rightarrow \mathrm{C}_{10} \mathrm{H}_{8}(\mathrm{s})}\end{array}\)

Step-by-Step Solution

Answer

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

Step 1: Analyze Reaction a

Reaction: \( \text{ClF}(\text{g}) + \text{F}_2(\text{g}) \rightarrow \text{ClF}_3(\text{g}) \)In this reaction, two gas molecules combine to form one gas molecule. The number of gas molecules is decreasing, which typically signifies a decrease in disorder. Therefore, \( \Delta S_{\text{system}} \) is predicted to be negative.

Step 2: Analyze Reaction b

Reaction: \( \text{NH}_3(\text{g}) \rightarrow \text{NH}_3(\text{aq}) \)The conversion from a gas to an aqueous solution involves a decrease in entropy because gases have higher disorder than solutes in solution. Therefore, \( \Delta S_{\text{system}} \) is predicted to be negative.

Step 3: Analyze Reaction c

Reaction: \( \text{CH}_3\text{OH}(l) \rightarrow \text{CH}_3\text{OH}(\text{aq}) \)The transition from a liquid to an aqueous state typically results in an increase in disorder due to the solute molecules being dispersed. Therefore, \( \Delta S_{\text{system}} \) is predicted to be positive.

Step 4: Analyze Reaction d

Reaction: \( \text{C}_{10}\text{H}_8(l) \rightarrow \text{C}_{10}\text{H}_8(s) \)The change from a liquid to a solid represents a decrease in entropy since solids have more ordered structures than liquids. Therefore, \( \Delta S_{\text{system}} \) is predicted to be negative.

Key Concepts

Entropy Prediction

Entropy is a measure of the disorder or randomness in a system. When predicting changes in entropy, or \( \Delta S_{\text{system}} \), it is important to consider the nature of the initial and final states. A simple rule of thumb is that systems tend to move towards greater disorder or higher entropy. However, specific scenarios, like the nature of the substances involved, can affect this. Key points to remember:

• When a reaction results in more complex molecules breaking down into simpler ones, entropy increases.
• Reactions where simpler molecules combine to form more complex ones usually decrease entropy.
• The physical state change, such as moving from solid to liquid or gas, typically increases disorder, hence increasing entropy.

Overall, understanding the arrangement and potential movement of particles helps in predicting whether entropy will increase or decrease.

Gaseous Reactions

In the realm of chemistry, gaseous reactions are particularly interesting due to the vast freedom gas particles possess. Gases are less constrained by intermolecular forces compared to solids and liquids. This gives them a high degree of entropy, or disorder.

When involving reactions that include gases, observe the number of gaseous molecules before and after the reaction:

• If the total number of gas molecules decreases, it often indicates that entropy decreases. For example, in a reaction where two gas molecules form one, \( \Delta S_{\text{system}} \) is likely negative.
• If the number increases, as in the case where one gas forms two or more molecules, entropy should increase.

A careful count of gas molecules can simplify predictions of entropy changes in gaseous reactions.

Aqueous Solution

Aqueous solutions involve substances dissolved in water. In chemistries of solutions, the interaction between solute and solvent can impact entropy.A key aspect is whether the system becomes more ordered or disordered:

• Gas to Aqueous: Transforming a gaseous substance into an aqueous solution tends to decrease entropy because gases are more disorganized compared to liquids. Thus, \( \Delta S_{\text{system}} \) is usually negative.
• Liquid to Aqueous: When a liquid becomes aqueous, such as a solute being dispersed, entropy increases since the particles are more spread and gain mobility.

Aqueous solutions are pivotal in understanding entropy as they demonstrate how solvation affects molecular arrangements and movements.

Phase Transition

A phase transition refers to the change of a substance from one state of matter (solid, liquid, gas) to another. These changes significantly influence the entropy of the system.Some basic principles for predicting changes in entropy during phase transitions include:

• Solid to Liquid: When solids melt into liquids, entropy increases because the orderly structure of solids becomes more relaxed and disordered. \( \Delta S_{\text{system}} \) is positive.
• Liquid to Solid: Conversely, when liquids freeze into solids, entropy decreases as the particles become tightly packed and ordered, resulting in a negative \( \Delta S_{\text{system}} \).
• Liquid to Gas: Evaporation or boiling increases entropy as particles gain freedom of movement.
• Gas to Liquid or Gas to Solid: These reduce entropy due to the decrease in particle movement and corresponding disorder.

Understanding phase transitions is crucial in forecasting entropy changes, offering insights into the arrangements and behavior of molecules across states.