Chemistry $^{3}$ : Introducing inorganic, organic and physical chemistry

Andrew Burrows, John Holman, Andrew Parsons

Chapter 14 Entropy and Gibbs energy - all with Video Answers

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Chapter Questions

Problem 1

(a) Explain the meaning of the term 'spontaneous' as applied to a chemical or physical change.
(b) Explain why some reactions which appear to be spontaneous from thermodynamic data do not in fact take place. Illustrate your answer by referring to the following changes:
(i) $\mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightarrow \mathrm{H}_{2} \mathrm{O}(0)$
(ii) Oxidation of aluminium in air. (Section 14.1)

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Problem 2

Predict the sign of the change in entropy in the system for the following processes (Section 14.1)
(a) Steam condensing on a cold window
(b) A cloud forming in the atmosphere
(c) Inflating a bicycle tyre with air
(d) Dissolving sugar in hot coffee
(e) $\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{PCl}_{5}(\mathrm{~g})$
(f) $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CaSO}_{4}(\mathrm{~s}) \rightarrow \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}(\mathrm{s})$
(g) $\mathrm{SO}_{3}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{O}) \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}$ (aq)
(h) $2 \mathrm{KCl}(\mathrm{s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{l}) \rightarrow \mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{~s})+2 \mathrm{HCl}(\mathrm{g})$
(i) $\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})$

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Problem 3

An apparatus consists of two bulbs of the same volume connected by a tap. Initially, the tap is closed with one bulb containing nitrogen gas and the other oxygen gas. Both bulbs are at the same temperature and pressure. (Section 14.2)
(a) What happens when the tap is opened? What will be the equilibrium state of the system?
(b) What are the signs of $\Delta H, \Delta S$, and $\Delta G$ for the process in (a)?
(c) Is this consistent with the Second Law of thermodynamics?

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Problem 4

Estimate the change in entropy when $1.00 \mathrm{~mol}$ of argon is heated from $300 \mathrm{~K}$ to $1200 \mathrm{~K}$. What assumptions have you made and how could you make your estimate more accurate? (Section 14.2)
(The heat capacity, $C_{p}$, of argon gas is $20.8 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ )

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Problem 5

For each of the following reactions, suggest whether the entropy change in the system would be: (i) near zero; (ii) positive; or (iii) negative. Explain your answers. (Section 14.4)
(a) $\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{~g})$
(b) $\mathrm{Zn}(\mathrm{s})+\mathrm{Cu}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{Cu}(\mathrm{s})$
(c) $3 \mathrm{Mg}(\mathrm{s})+2 \mathrm{Fe}^{3+}(\mathrm{aq}) \rightarrow 3 \mathrm{Mg}^{2+}(\mathrm{aq})+2 \mathrm{~F} \theta(\mathrm{s})$
(d) $\mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$
(e) $\mathrm{C}$ (diamond) $\rightarrow$ C (graphite)

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Problem 6

Dissolving solid potassium iodide in water results in a lowering of the temperature. Explain why this endothermic process can be spontaneous. (Section 14.2)

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Problem 7

Calculate the entropy change when 1 mol of water is heated from $250 \mathrm{~K}$ to $300 \mathrm{~K}$.
The enthalpy change of fusion for water is at $0^{\circ} \mathrm{C}$ is $+6.01 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and the heat capacities are $C_{p}=75.3 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ and $37.2 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ for water and ice, respectively. (Section 14.3)

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Problem 8

$100.0 \mathrm{~g}$ of water at $30^{\circ} \mathrm{C}$ were placed in a refrigerator at $4^{\circ} \mathrm{C}$. When the water cools down, what is the entropy change of (a) the water and (b) the refrigerator? What is the overall entropy change? Comment on the results. (Section 14.3)

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Problem 9

Given that the normal melting and boiling points of $\mathrm{CO}$ are $74 \mathrm{~K}$ and $82 \mathrm{~K}$, respectively, sketch a plot to show how the entropy of CO varies with temperature between $0 \mathrm{~K}$ and $273 \mathrm{~K}$. (Section $14.3)$

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00:55

Problem 10

What are the signs of the values of $\Delta H, \Delta S$, and $\Delta G$ for the process of a vapour condensing to form a liquid?
(Section 14.4)

Lizabeth T.

Numerade Educator

Problem 11

An ice cube of mass $18 \mathrm{~g}$ is added to a large glass of water just above $0^{\circ} \mathrm{C}$. Calculate the change of entropy for the ice and for the water (without the ice). (Section 14.4) (The enthalpy change of fusion for water is $+6.01 \mathrm{~kJ} \mathrm{~mol}^{-1}$.)

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Problem 12

Calculate the change in entropy when $100 \mathrm{~g}$ of water at $90^{\circ} \mathrm{C}$ are added to an insulated flask containing $100 \mathrm{~g}$ of water at $10^{\circ} \mathrm{C}$. (Section 14.2)

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Problem 13

Calculate the standard entropy change at $298 \mathrm{~K}$ for the reactions (Section 14.4):
(a) $\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{~g})$
(b) $\mathrm{Hg}(\mathrm{t})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{HgCl}_{2}(\mathrm{~s})$
(c) $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s})+6 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 6 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$

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Problem 14

Calculate the entropy changes for the system and surroundings when $1.00$ mol of $\mathrm{NaCl}$ melts at $1100 \mathrm{~K}$. Calculate $\Delta_{\text {fus }} \mathrm{G}$ and estimate the melting point of $\mathrm{NaCl}$. (Section 14.5)
(For the melting of sodium chloride $(\mathrm{NaCl}), \Delta_{4 u s} H=+30.2 \mathrm{kJmol}^{-1}$ and $\Delta_{\text {fus }} \mathrm{S}=+28.1 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ )

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Problem 15

Calcium carbonate $\left(\mathrm{CaCO}_{3}\right)$ decomposes to form $\mathrm{CaO}$ and $\mathrm{CO}_{2}$ with $\Delta_{\mathrm{r}} \mathrm{H}_{29 \mathrm{~g}}=+178 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta_{\mathrm{r}} \mathrm{S}_{296}=+161 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$. Estimate the temperature at which the decomposition becomes spontaneous. (Section 14.6)

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Problem 16

You expend about $100 \mathrm{~kJ}$ ) a day keeping your heart beating. What is the minimum mass of glucose you must oxidize per day in order to produce this much energy? (Section 14.5)
$$
\begin{array}{r}
\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s})+6 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 6 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(0) \\
\Delta G^{\Theta}=-2872 \mathrm{k} \mathrm{J} \mathrm{mol}^{-1}
\end{array}
$$

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Problem 17

For the reaction
$$
\begin{array}{r}
\mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(0) \\
\Delta_{\mathrm{c}} H_{29 \mathrm{e}}^{\theta}=-890 \mathrm{~kJ} \mathrm{~mol}^{-1}
\end{array}
$$
(a) Calculate $\Delta_{0} G_{299}^{\theta}$ for the combustion of methane.
(b) How much of the heat produced by buming $1.00 \mathrm{~mol}$ of methane cannot be used to do work?
(c) A heat engine uses methane as a fuel. What height could a $1.00 \mathrm{~kg}$ mass be raised to by burning $1.00 \mathrm{dm}^{3}$ of methane? (Section $14.5)$

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Problem 18

Ethanoic acid can be produced by a number of methods, including:
(a) the reaction of methanol with carbon monoxide
$$
\mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{l})
$$
(b) the oxidation of ethanol with oxygen gas
$$
\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{t})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{t})+\mathrm{H}_{2} \mathrm{O}(\mathrm{f})
$$
(c) the reaction of carbon dioxide with methane
$$
\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{CH}_{4}(\mathrm{~g}) \rightarrow \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{l})
$$
Calculate the standard Gibbs energy change for each of these reactions at (i) $298 \mathrm{~K}$ and (ii) $773 \mathrm{~K}$. (Section 14.5)

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Problem 19

The reaction of methanol $\left(\mathrm{CH}_{3} \mathrm{OH}(D)\right.$ with oxygen can be used in a fuel cell. Calculate the enthalpy change for the reaction at $298 \mathrm{~K}$ and the maximum work that can be produced by the oxidation of $1.00$ mol of methanol. (Section 14.5)

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Problem 20

Calculate the normal boiling point of ethanol given that $\Delta_{\text {vap }} H=+42.6 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta_{\mathrm{vap}} \mathrm{S}=+122.0 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} .$ (Section 14.5)

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Problem 21

$^{*}$ 'Synthesis gas' is a mixture of hydrogen and carbon monoxide, prepared by reacting water or steam with a source of carbon such as coal. The reaction can be represented as:
$$
\mathrm{C}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{~g})
$$
Estimate the temperature at which the reaction becomes thermodynamically spontaneous. (Section 14.5)

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Problem 22

Use the mean heat capacities and standard entropies listed in Appendix 7 to estimate the Gibbs energy change for the decomposition of water vapour into hydrogen and oxygen at $2000^{\circ} \mathrm{C}$ and 1 bar pressure. (Section $14.6$ )
(The standard enthalpy change of formation of water vapour is $-241.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$ )

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Problem 23

The standard Gibbs energy for a reaction is $-332.9 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $298 \mathrm{~K}$ and - $339.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $500 \mathrm{~K}$. Estimate the standard entropy change for the reaction. (Section 14.6)

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Problem 24

Find the changes in enthalpy, entropy, and Gibbs energy for, the freezing of water at $-10^{\circ} \mathrm{C}$ at 1 bar pressure. (The enthalpy change of fusion for water at $0^{\circ} \mathrm{C}$ is $+6.01 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and the heat capacities are $C_{p}=75.3 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ and $37.2 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ for water and ice, respectively.) (Several sections)

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Problem 25

Use data from Appendix 7 to consider the following reaction: $2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{~g})$
(a) Calculate the changes in enthalpy, entropy and Gibbs energy at $298 \mathrm{~K}$.
(b) Is the reaction spontaneous at $25^{\circ} \mathrm{C}$ and 1 bar? Explain the signs of $\Delta_{1} H$ and $\triangle_{\top} S$.

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Problem 26

Impure nickel metal is purified using the Mond process where it is first reacted at $80^{\circ} \mathrm{C}$ with carbon monoxide to form $\mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{~g})$
$$
\mathrm{Ni}(\mathrm{s})+4 \mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{~g})
$$
followed by heating to $200^{\circ} \mathrm{C}$ when the reverse reaction occurs. Use the following thermodynamic data to show that this approach is thermodynamically feasible.
$\begin{array}{llll} & \mathrm{Ni}(\mathrm{s}) & \mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{~g}) & \mathrm{CO}(\mathrm{g}) \\ \Delta_{1} \mathrm{G}_{2 \mathrm{~g}} / \mathrm{kJ} \mathrm{mol}^{-1}: & 0 & -601.6 & -110.5 \\ \mathrm{~S}_{299}^{\ominus} / \mathrm{JK}^{-1} \mathrm{~mol}^{-1}: & 29.9 & 415.5 & 197.6\end{array}$

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Problem 27

Determine the standard Gibbs energy change for the acid-base neutralization reaction
$$
\begin{gathered}
\left.\mathrm{NaOH}(\mathrm{aq})+\mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{NaCl}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O} 0\right) \\
\Delta_{\mathrm{f}} \mathrm{G}_{29 \mathrm{e}}^{\mathrm{O}} / \mathrm{kJ} \mathrm{mol}^{-1}: \mathrm{OH}^{-}(\mathrm{aq})-157.3 ; \mathrm{H}^{+}(\mathrm{aq}) 0 ; \mathrm{H}_{2} \mathrm{O}(\mathrm{l})-237.1
\end{gathered}
$$

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Problem 28

Two chemists were discussing the possibility of using the waste methane from an oil field to produce useful chemicals. The first suggested it could be reacted with atmospheric $\mathrm{CO}_{2}(\mathrm{~g})$ to produce ethanoic acid.
$$
\mathrm{CH}_{4}(\mathrm{~g})+\mathrm{CO}_{2}(\mathrm{~g}) \rightarrow \mathrm{CH}_{3} \mathrm{COOH}(\mathrm{l})
$$
The other chemist suggested that the methane should be converted to ethanol by reacting with water.
$$
2 \mathrm{CH}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{I})+2 \mathrm{H}_{2}(\mathrm{~g})
$$
Use Gibbs energy of formation data in Appendix 7 to examine the thermodynamic feasibility of these reactions around room temperature.

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Problem 29

Nitrogen and oxygen have very similar electronegativities. Estimate the entropy of NO at $0 \mathrm{~K}$ (the 'zero-point entropy').

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