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Chapter 18: Problem 26

Predict the sign of the entropy change for each of the following processes. a.A drop of food coloring diffuses throughout a glass of water. b.A tree leafs out in the spring. c.Flowers wilt and stems decompose in the fall. d.A lake freezes over in the winter. e.Rainwater on the pavement evaporates.

Short Answer

Expert verified
Entropy increases in a, c, and e, decreases in b and d.

Step by step solution

01

Understanding Entropy

Entropy is a measure of disorder or randomness in a system. In natural processes, entropy tends to increase as systems move towards equilibrium and greater disorder.
02

Reasoning for Diffusion

For process (a), a drop of food coloring diffusing in water, the entropy change is positive. This is because the system goes from a state of order (coloring concentrated in one place) to disorder (color spread throughout the water).
03

Reasoning for Leafing

For process (b), a tree leafs out in the spring, the entropy change is negative. This process involves organizing energy and materials into structured, complex leaves, decreasing disorder.
04

Reasoning for Decomposition

For process (c), flowers wilting and stems decomposing in the fall, the entropy change is positive. This is because complex structures break down into simpler molecules, increasing disorder.
05

Reasoning for Freezing

For process (d), a lake freezing over in the winter, the entropy change is negative. Freezing transforms disordered liquid water molecules into an ordered crystalline solid, thus decreasing disorder.
06

Reasoning for Evaporation

For process (e), rainwater evaporating from the pavement, the entropy change is positive. Liquid water molecules gain energy and become vapor, increasing randomness as they disperse into the air.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Positive Entropy
In the context of thermodynamics, positive entropy is when a system moves towards greater disorder. This happens during processes like diffusion or evaporation, where molecules spread out and mix freely.
For example:
  • In diffusion, such as a drop of food coloring dispersing in water, the molecules become more dispersed. The initial ordered state, where the dye is concentrated, transforms into a state of disorder as the molecules spread throughout the liquid.
  • During evaporation, water molecules transition from a relatively ordered liquid state to a disordered gaseous state. As the molecules evaporate from a surface, they gain energy, move more randomly, and spread out into the air.
In both scenarios, there is an increase in entropy, reflecting the natural tendency for systems to move into states of higher disorder.
Negative Entropy
Negative entropy occurs when a system's disorder decreases. In nature, this is observed when disordered systems become more organized and structured.
Consider these examples:
  • When a tree forms leaves in spring, it's transforming less organized energy and nutrients into complex structures. The process organizes materials into intricate leaf shapes, reducing entropy.
  • As a lake freezes, the water molecules in the liquid state arrange into a crystalline solid form. This transition results in a lower state of disorder, causing entropy to decrease.
Such processes defy the general trend of increasing disorder, showcasing nature鈥檚 ability to organize even amidst overall entropy increase.
Entropy and Disorder
Entropy is closely linked to disorder within any system. The more disordered or random a system is, the higher its entropy.
This idea is intrinsic to many natural processes:
  • In decomposition, like flowers wilting and breaking down, cohesive and complex structures disassemble into simpler substances. This breakdown increases randomness and disorder thus leading to increased entropy.
  • Living organisms defy this rule locally by creating highly ordered systems, like the building of cells or tissues, a process that decreases local entropy even as overall entropy may increase globally.
Therefore, while entropy often suggests disorder and chaos, it can work in fascinating ways to allow order to emerge in specific conditions.
Entropy in Natural Processes
In natural processes, entropy often plays an essential role in driving change and transformation. The second law of thermodynamics famously states that the entropy of an isolated system will not decrease over time, suggesting a natural inclination towards disorder.
Examples in real-world scenarios include:
  • The evaporation of water, increasing entropy as molecules spread apart and mix with air.
  • The freezing of lakes, where even though local entropy decreases as water becomes ordered into ice, the surrounding environment's entropy typically compensates by increasing.
These principles underscore the dynamic balance of order and chaos found in nature, influenced largely by entropy changes in various processes.

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Most popular questions from this chapter

Tetrachloromethane (carbon tetrachloride), \(\mathrm{CCl}_{4}\), has a normal boiling point of \(76.7^{\circ} \mathrm{C}\) and an enthalpy of vaporization, \(\Delta H_{v a p}\), of \(29.82 \mathrm{~kJ} / \mathrm{mol}\). Estimate the entropy of vaporization, \(\Delta S_{v a p} \circ\). Estimate the free energy of vaporization, \(\Delta G_{\text {van }}^{\circ}\), at \(25^{\circ} \mathrm{C}\).

Consider a reaction in which \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are positive. Suppose the reaction is nonspontaneous at room temperature. How would you estimate the temperature at which the reaction becomes spontaneous?

18.15 Discuss the different sign combinations of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) that are possible for a process carried out at constant temperature and pressure. For each combination, state whether the process must be spontaneous or not, or whether both situations are possible. Explain.

Predict the sign of \(\Delta S^{\circ}\), if possible, for each of the following reactions. If you cannot predict the sign for any reaction, state why. a. \(\mathrm{HCl}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)\) b. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) c. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) d. \(\mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\)

18.122 Coal is used as a fuel in some electric-generating plants. Coal is a complex material, but for simplicity we may consider it to be a form of carbon. The energy that can be derived from a fuel is sometimes compared with the enthalpy of the combustion reaction: $$ \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) $$ Calculate the standard enthalpy change for this reaction at \(25^{\circ} \mathrm{C}\). Actually, only a fraction of the heat from this reaction is available to produce electric energy. In electric generating plants, this reaction is used to generate heat for a steam engine, which turns the generator. Basically the steam engine is a type of heat engine in which steam enters the engine at high temperature \(\left(T_{h}\right),\) work is done, and the steam then exits at a lower temperature \(\left(T_{l}\right)\). The maximum fraction, \(f,\) of heat available to produce useful energy depends on the difference between these temperatures (expressed in kelvins), \(f=\left(T_{h}-T_{l}\right) / T_{h} .\) What is the maximum heat energy available for useful work from the combustion of \(1.00 \mathrm{~mol}\) of \(\mathrm{C}(s)\) to \(\mathrm{CO}_{2}(g)\) ? (Assume the value of \(\Delta H^{\circ}\) calculated at \(25^{\circ} \mathrm{C}\) for the heat obtained in the generator.) It is possible to consider more efficient ways to obtain useful energy from a fuel. For example, methane can be burned in a fuel cell to generate electricity directly. The maximum useful energy obtained in these cases is the maximum work, which equals the free-energy change. Calculate the standard free-energy change for the combustion of \(1.00 \mathrm{~mol}\) of \(\mathrm{C}(s)\) to \(\mathrm{CO}_{2}(g)\). Compare this value with the maximum obtained with the heat engine described here.
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