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Chapter 19: Problem 36

Does the entropy of the system increase, decrease, or stay the same 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) The entropy of the system will increase when the temperature increases. (b) The entropy of the system will increase when the volume of the gas increases. (c) The entropy of the system will increase when equal volumes of ethanol and water are mixed to form a solution.

Step by step solution

01

(Define entropy)

Entropy (S) is a measure of the randomness or disorder of a system. The larger the entropy of a system, the more disordered it is.
02

(Evaluate entropy)

According to the definition, when the temperature of a material increases, the molecules in the material move more chaotically and randomly, leading to an increase in entropy. So, the entropy of the system will increase when the temperature increases. #b) Effect of volume increase on the entropy of a gas#
03

(Define entropy for a gas)

Entropy of a gas is also related to the randomness of the positions and velocities of the gas particles.
04

(Evaluate entropy of the gas)

When the volume of the gas increases, the gas particles have more places to move around, thereby increasing the randomness of their positions and velocities. Consequently, the entropy of the gas increases. So, the entropy of the system will increase when the volume of the gas increases. #c) Entropy change during the mixing of ethanol and water#
05

(Define entropy for mixing of substances)

The change in entropy when two substances are mixed is related to the randomness of the particle arrangement at a microscopic level in the mixture.
06

(Evaluate entropy of the mixture)

When equal volumes of ethanol and water are mixed, the molecules of the two substances become more randomly distributed, increasing the entropy of the system. So, the entropy of the system will increase when equal volumes of ethanol and water are mixed to form a solution.

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Most popular questions from this chapter

(a) Can endothermic chemical reactions be spontaneous? (b) Can a process be spontaneous at one temperature and nonspontaneous at a different temperature? (c) Water can be decomposed to form hydrogen and oxygen, and the hydrogen and oxygen can be recombined to form water. Does this mean that the processes are thermodynamically reversible? (d) Does the amount of work that a system can do on its surroundings depend on the path of the process?

Predict the sign of the entropy change of the system for each of the following reactions: $$\begin{array}{l}{\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)} \\ {\text { (b) } \mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)} \\ {\text { (c) } 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6}(g)} \\ {\text { (d) } \mathrm{Al}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{Al}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)}\end{array}$$

Predict which member of each of the following pairs has the greater standard entropy at \(25^{\circ} \mathrm{C} :(\mathbf{a}) \operatorname{Sc}(s)\) or \(\operatorname{Sc}(g)\) (b) \(\mathrm{NH}_{3}(g)\) or \(\mathrm{NH}_{3}(a q),(\mathbf{c}) \mathrm{O}_{2}(g)\) or \(\mathrm{O}_{3}(g),(\mathbf{d}) \mathrm{C}(\mathrm{graphite})\) or \(\mathrm{C}(\) diamond). Use Appendix \(\mathrm{C}\) to find the standard entropy of each substance.

In chemical kinetics, the entropy of activation is the entropy change for the process in which the reactants reach the activated complex. Predict whether the entropy of activation for a bimolecular process is usually positive or negative.

An ice cube with a mass of 20 \(\mathrm{g}\) at \(-20^{\circ} \mathrm{C}\) (typical freezer temperature) is dropped into a cup that holds 500 \(\mathrm{mL}\) of hot water, initially at \(83^{\circ} \mathrm{C} .\) What is the final temperature in the cup? The density of liquid water is 1.00 \(\mathrm{g} / \mathrm{mL}\) ; the specific heat capacity of ice is \(2.03 \mathrm{J} / \mathrm{g}-\mathrm{C}\) ; the specific heat capacity of liquid water is \(4.184 \mathrm{J} / \mathrm{g}-\mathrm{C} ;\) the enthalpy of fusion of water is 6.01 \(\mathrm{k} \mathrm{J} / \mathrm{mol} .\)
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