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Chapter 19: Problem 38

How does the entropy of the system change when (a) the temperature of the system increases, (b) the volume of a gas increases, \((c)\) equal volumes of ethanol and water are mixed to form a solution?

Short Answer

Expert verified
(a) When the temperature of a system increases, the entropy generally increases, as particles gain kinetic energy and move more randomly, leading to higher disorder. (b) The entropy of a system increases when the volume of a gas increases, as the increased volume allows for more possible arrangements and disorder among gas particles. (c) The entropy of a system increases when equal volumes of ethanol and water are mixed, as the mixing creates a greater number of molecular configurations, leading to higher disorder.

Step by step solution

01

(a) Temperature Increase

When the temperature of a system increases, the entropy of the system generally increases. Entropy is the measure of the degree of disorder/randomness in a system. As the temperature increases, the particles in the system gain kinetic energy and start moving more rapidly, leading to a higher degree of disorder. Consequently, the entropy increases due to increasing temperature.
02

(b) Volume Increase of a Gas

When the volume available to a gas increases, the gas particles have more space to disperse throughout. The increased volume allows for more possible arrangements of gas particles, leading to a higher degree of disorder in the system. As the disorder increases, so does the entropy of the system. Thus, when the volume of a gas increases, the entropy of the system also increases.
03

(c) Mixing Ethanol and Water

When equal volumes of ethanol and water are mixed together to form a solution, the entropy of the resulting solution is greater compared to the entropy of the individual components (ethanol and water) when separated. This is because mixing the two liquids creates a greater number of possible configurations for the molecules in the system, leading to a higher level of disorder. Consequently, the entropy of the system increases when ethanol and water are mixed together to form a solution.

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Key Concepts

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

Temperature effects on entropy
An increase in temperature usually leads to an increase in entropy. This happens because entropy is related to the disorder or randomness of a system.
When temperature rises, particles move faster because they gain kinetic energy.
Faster particle movement results in greater disorder. More disorder means higher entropy.
  • Temperature increases particle motion.
  • Faster particles equal more disorder.
  • More disorder increases entropy.
Think of it like shaking a box of mixed candies. The faster you shake, the more mixed the candies become, increasing the disorder inside the box.
Volume changes and entropy
When a gas expands to fill a larger volume, its entropy increases. Why? Because entropy is about possible arrangements of particles.
With more space, gas particles can spread out in countless ways, increasing possible arrangements.
That means there's more disorder.
  • More volume allows particles to spread out.
  • Spreading out means more particle arrangements.
  • More arrangements lead to more disorder and higher entropy.
Imagine opening a previously closed door in a crowded room. Suddenly, people have more space to move and can arrange themselves in numerous new ways, increasing the room's "disorder".
Mixing substances and entropy changes
Mixing two substances like ethanol and water increases the entropy of the system. This occurs because mixing leads to more possible molecular arrangements.
More arrangements translate to higher disorder.
The higher the disorder, the more the system's entropy increases.
  • Mixing creates new molecular arrangements.
  • New arrangements lead to higher disorder.
  • Higher disorder results in increased entropy.
Imagine pouring two different colored sands into one jar. The mixed sand has many more arrangements and patterns, increasing disorder and thus, entropy.

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Most popular questions from this chapter

As shown here, one type of computer keyboard cleaner contains liquefied 1,1 -difluoroethane \(\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{~F}_{2}\right),\) which is a gas at atmospheric pressure. When the nozzle is squeezed, the 1,1 -difluoroethane vaporizes out of the nozzle at high pressure, blowing dust out of objects. (a) Based on your experience, is the vaporization a spontaneous process at room temperature? (b) Defining the 1,1 -difluoroethane as the system, do you expect \(q_{\mathrm{sys}}\) for the process to be positive or negative? Explain. (c) Predict whether \(\Delta S\) is positive or negative for this process. (d) Given your answers to (a), (b), and (c), do you think the operation of this product depends more on heat flow or more on entropy change?

(a) For a process that occurs at constant temperature, express the change in Gibbs free energy in terms of changes in the enthalpy and entropy of the system. (b) For a certain process that occurs at constant \(T\) and \(P,\) the value of \(\Delta G\) is positive. What can you conclude? (c) What is the relationship between \(\Delta G\) for a process and the rate at which it occurs?

(a) How can we calculate \(\Delta S\) for an isothermal process? (b) Does \(\Delta S\) for a process depend on the path taken from the initial state to the final state of the system? Explain.

Indicate whether each of the following statements is true or false. If it is false, correct it. (a) The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends entirely on the value of \(\Delta H\) for the process \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) .\) (b) The re- action of \(\mathrm{Na}(s)\) with \(\mathrm{Cl}_{2}(g)\) to form \(\mathrm{NaCl}(s)\) is a spontaneous process. (c) A spontaneous process can in principle be conducted reversibly. (d) Spontaneous processes in general require that work be done to force them to proceed. (e) Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system.

Consider the following equilibrium: $$ \mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) $$ Thermodynamic data on these gases are given in Appendix C. You may assume that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not vary with temperature. (a) At what temperature will an equilibrium mixture contain equal amounts of the two gases? (b) At what temperature will an equilibrium mixture of 1 atm total pressure contain twice as much \(\mathrm{NO}_{2}\) as \(\mathrm{N}_{2} \mathrm{O}_{4} ?\) (c) At what temperature will an equilibrium mixture of 10 atm total pressure contain twice as much \(\mathrm{NO}_{2}\) as \(\mathrm{N}_{2} \mathrm{O}_{4} ?\) (d) Rationalize the results from parts (b) and (c) by using Le Ch芒telier's principle. [Section 15.7]
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