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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 increases when the temperature increases, as particles gain kinetic energy and move more randomly. (b) The entropy of the system increases when the volume of a gas increases, as there are more possible positions for the gas particles, increasing disorder. (c) The entropy of the system increases when equal volumes of ethanol and water are mixed to form a solution, as the dispersion of molecules increases disorder due to the larger volume and more possible arrangements.

Step by step solution

01

(a) Effect of increasing temperature on entropy

As the temperature of a system increases, the particles within the system gain kinetic energy. This increase in kinetic energy causes the particles to move faster and more randomly. Since entropy is a measure of disorder, the entropy of the system increases when the temperature increases.
02

(b) Effect of increasing volume of a gas on entropy

When the volume of a gas increases, the number of possible positions for the gas particles also increases. The increase in the number of possible positions means that there is a higher degree of disorder or randomness in the system. Thus, the entropy of the system increases when the volume of a gas increases.
03

(c) Effect of mixing equal volumes of ethanol and water on entropy

When we mix equal volumes of ethanol and water to form a solution, both the molecules of ethanol and water are dispersed within each other. This dispersion of the ethanol and water molecules increases the disorder of the system. This is because there is now a larger volume for the particles to move, and more possible arrangements for the particles relative to each other. As a result, the entropy of the system increases when we mix equal volumes of ethanol and water to form a solution.

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Most popular questions from this chapter

Consider the reaction $\mathrm{CH}_{4}(\mathrm{~g})+4 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)+$ \(4 \mathrm{HCl}(g) .\). (a) Using data from Appendix C, calculate $\Delta G^{\circ}\( at \)298 \mathrm{~K} .(\mathbf{b})\( Calculate \)\Delta G\( at \)298 \mathrm{~K}\( if the reaction mixture consists of \)50.7 \mathrm{kPa}$ of \(\mathrm{CH}_{4}(g), 25.3 \mathrm{kPa}\) of $\mathrm{Cl}_{2}(g), 10.13 \mathrm{kPa}$ of \(\mathrm{CCl}_{4}(\mathrm{~g})\) and \(15.2 \mathrm{kPa}\) of \(\mathrm{HCl}(\mathrm{g})\)

The oxidation of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\( in body tissue produces \)\mathrm{CO}_{2}$ and \(\mathrm{H}_{2} \mathrm{O} .\) In contrast, anaerobic decomposition, which occurs during fermentation, produces ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\( and \)\mathrm{CO}_{2}$. (a) Using data given in Appendix \(\mathrm{C}\), compare the equilibrium constants for the following reactions: $$ \begin{array}{r} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \rightleftharpoons 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \\ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \rightleftharpoons 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(I)+2 \mathrm{CO}_{2}(g) \end{array} $$ (b) Compare the maximum work that can be obtained from these processes under standard conditions.

(a) Using data in Appendix \(C\), estimate the temperature at which the free- energy change for the transformation from \(\mathrm{I}_{2}(s)\) to \(\mathrm{I}_{2}(g)\) is zero. (b) Use a reference source, such as Web Elements (www.webelements.com), to find the experimental melting and boiling points of \(I_{2}\). (c) Which of the values in part (b) is closer to the value you obtained in part (a)?

(a) What sign for \(\Delta S\) do you expect when the volume of 0.200 mol of an ideal gas at \(27^{\circ} \mathrm{C}\) is increased isothermally from an initial volume of \(10.0 \mathrm{~L} ?\) (b) If the final volume is \(18.5 \mathrm{~L},\) calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?

Indicate whether \(\Delta G\) increases, decreases, or stays the same for each of the following reactions as the partial pressure of \(\mathrm{O}_{2}\) is increased: (a) \(\mathrm{HgO}(s) \longrightarrow \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\) (b) $2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)$ (c)
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