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Ch.19 - Chemical Thermodynamics
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.19 - Chemical ThermodynamicsProblem 47
Chapter 19, Problem 47

Predict which member of each of the following pairs has the greater standard entropy at 25°C: (a) Sc(s) or Sc(g). Use Appendix C to find the standard entropy of each substance. (b) NH3(g) or NH3(aq). Use Appendix C to find the standard entropy of each substance. (c) O2(g) or O3(g). Use Appendix C to find the standard entropy of each substance. (d) C(graphite) or C(diamond). Use Appendix C to find the standard entropy of each substance.

Verified step by step guidance
1
Step 1: Understand the concept of standard entropy. Standard entropy is a measure of the amount of disorder or randomness in a system. Generally, gases have higher entropy than liquids, and liquids have higher entropy than solids due to the increased freedom of movement of particles.
Step 2: For part (a), compare Sc(s) and Sc(g). Recognize that the gaseous state (Sc(g)) typically has a higher entropy than the solid state (Sc(s)) because gas particles are more disordered and have more freedom of movement.
Step 3: For part (b), compare NH3(g) and NH3(aq). Consider that gases usually have higher entropy than aqueous solutions because gas molecules are more dispersed and have more freedom to move compared to when they are dissolved in water.
Step 4: For part (c), compare O2(g) and O3(g). Note that molecules with more atoms generally have higher entropy due to the increased number of ways they can arrange themselves. Therefore, O3(g) might have a higher entropy than O2(g) because it has more atoms.
Step 5: For part (d), compare C(graphite) and C(diamond). Recognize that graphite has a layered structure allowing more freedom of movement compared to the rigid, tightly bonded structure of diamond, suggesting that C(graphite) has a higher entropy than C(diamond).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Standard Entropy

Standard entropy is a measure of the disorder or randomness in a system at a specified temperature, typically 25°C. It is denoted as S° and is expressed in units of J/(mol·K). Higher entropy values indicate greater disorder, which often correlates with the number of microstates available to a substance. Understanding standard entropy is crucial for predicting the spontaneity of processes and the stability of different phases of matter.
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Phase Changes and Entropy

The phase of a substance significantly affects its entropy. Gases generally have higher entropy than liquids, which in turn have higher entropy than solids due to the increased freedom of movement and greater number of microstates in gases. For example, comparing solid and gaseous states of the same element, the gas will have a greater standard entropy due to its higher disorder and molecular motion.
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Comparative Entropy of Solutions

When comparing the standard entropy of a solute in different states, such as gas versus aqueous solution, the solute in solution typically has a lower entropy than its gaseous form. This is because solvation restricts the movement of solute particles, leading to a more ordered arrangement. Thus, understanding how solvation affects entropy is essential for predicting which state will have a greater standard entropy.
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Related Practice
Textbook Question

Cyclopropane and propylene are isomers that both have the formula C3H6. Based on the molecular structures shown, which of these isomers would you expect to have the higher standard molar entropy at 25 °C?

Textbook Question

Predict the sign of ΔSsys for each of the following processes: (d) Calcium phosphate precipitates upon mixing Ca(NO3)2(aq) and (NH4)3PO4(aq).

Textbook Question
Three of the forms of elemental carbon are graphite, diamond,and buckminsterfullerene. The entropies at 298 Kfor graphite and diamond are listed in Appendix C.(b) What would you expect for the S° value of buckminsterfullerene(Figure 12.49, p. 509) relative to the valuesfor graphite and diamond? Explain.
Textbook Question
The standard entropies at 298 K for certain group 4A elements are: C(s, diamond) = 2.43 J>mol@K, Si1s2 = 18.81 J>mol@K, Ge1s2 = 31.09 J>mol@K, and Sn1s2 = 51.818 J>mol@K. All but Sn have the same (diamond) structure. How do you account for the trend in the S° values?