Burdge/Overby, Chemistry: Atoms First, 2e Ch14 | Page 31

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CHAPTE R 14? Entropy and Free Energy

14.46 The standard enthalpy of formation and the standard
entropy of gaseous benzene are 82.93 kJ/mol and
269.2 J/K ? mol, respectively. Calculate ?H°, ?S°, and
?G° for the given process at 25°C. Comment on your
answers.
C6H6(l)

C6H6(g)

14.47 (a) Trouton’s rule states that the ratio of the molar
heat of vaporization of a liquid (?Hvap) to its boiling
point in kelvins is approximately 90 J/K ? mol. Use the
following data to show that this is the case and explain
why Trouton’s rule holds true:
Tbp (°C)

Benzene 80.1
Hexane 68.7
Mercury 357
Toluene 110.6

?Hvap(kJ/mol)
31.0
30.8
59.0
35.2

(b) Use the values in Table 12.5 to calculate the same
ratio for ethanol and water. Explain why Trouton’s rule
does not apply to these two substances as well as it
does to other liquids.
14.48 Referring to Problem 14.47, explain why the ratio is
considerably smaller than 90 J/K ? mol for liquid HF.
14.49 Predict whether the entropy change is positive or
negative for each of these reactions:
(a) Zn(s) + 2HCl(aq)
ZnCl2(aq) + H2(g)
(b) O(g) + O(g)
O2(g)
(c) NH4NO3(s)
N2O(g) + 2H2O(g)
(d) 2H2O2(l)
2H2O(l) + O2(g)
14.50 A certain reaction is spontaneous at 72°C. If the
enthalpy change for the reaction is 19 kJ/mol, what is
the minimum value of ?S (in J/K ? mol) for the reaction?
14.51 Use the following data to determine the normal boiling
point, in kelvins, of mercury. What assumptions must
you make to do the calculation?
Hg(l): ?H ° = 0 (by definition)
f
S° = 77.4 J/K ? mol
Hg(g): ?H ° = 60.78 kJ/mol
f
S° = 174.7 J/K ? mol
14.52 The reaction NH3(g) + HCl(g)
NH4Cl(s)
proceeds spontaneously at 25°C even though there is a
decrease in entropy in the system (gases are converted
to a solid). Explain.
14.53 A certain reaction is known to have a ?G° value of
–122 kJ/mol. Will the reaction necessarily occur if the
reactants are mixed together?
14.54 The molar heat of vaporization of ethanol is 39.3 kJ/mol,
and the boiling point of ethanol is 78.3°C. Calculate ?S
for the vaporization of 0.50 mole of ethanol.
14.55 As an approximation, we can assume that proteins exist
either in the native (physiologically functioning) state
or the denatured state. The standard molar enthalpy and
entropy of the denaturation of a certain protein are 512
kJ/mol and 1.60 kJ/K ? mol, respectively. Comment
on the signs and magnitudes of these quantities, and
calculate the temperature at which the denaturation
becomes spontaneous.

bur11184_ch14_570-603.indd 600

14.56 When a native protein in solution is heated to a high
enough temperature, its polypeptide chain will unfold
to become the denatured protein. The temperature at
which a large portion of the protein unfolds is called
the melting temperature. The melting temperature of
a certain protein is found to be 46°C, and the enthalpy
of denaturation is 382 kJ/mol. Estimate the entropy of
denaturation, assuming that the denaturation is a twostate process; that is, native protein
denatured
protein. The single polypeptide protein chain has 122
amino acids. Calculate the entropy of denaturation per
amino acid. Comment on your result.
14.57 A 74.6-g ice cube floats in the Arctic Sea. The pressure
and temperature of the system and surroundings are
at 1 atm and 0°C, respectively. Calculate ?Ssys, ?Ssurr,
and ?Suniv for the melting of the ice cube. What can
you conclude about the nature of the process from the
value of ?Suniv? (The molar heat of fusion of water is
6.01 kJ/mol.)
14.58 A reaction for which ?H and ?S are both negative is
(a) nonspontaneous at all temperatures.
(b) spontaneous at all temperatures.
(c) spontaneous at high temperatures.
(d) spontaneous at low temperatures.
(e) at equilibrium.
14.59 The sublimation of carbon dioxide at –78°C is given by
CO2(s)

CO2(g)?????Hsub = 25.2 kJ/mol

Calculate ?Ssub when 84.8 g of CO2 sublimes at this
temperature.
14.60 Many hydrocarbons exist as structural isomers, which
are compounds that have the same molecular formula
but different structures. For example, both butane and
isobutane have the same molecular formula of C4H10
(see Problem 7.42 on page 267). Calculate the mole
percent of these molecules in an equilibrium mixture at
25°C, given that the standard free energy of formation
of butane is –15.7 kJ/mol and that of isobutane is
–18.0 kJ/mol. Does your result support the notion that
straight-chain hydrocarbons (that is, hydrocarbons in
which the C atoms are joined along a l ine) are less
stable than branch-chain hydrocarbons?
14.61 Consider the following reaction at 298 K:
2H2(g) + O2(g)

2H2O(l)???H° = –571.6 kJ/mol

Calculate ?Ssys, ?Ssurr, and ?Suniv for the reaction.
14.62 Which of the following is not accompanied by an
increase in the entropy of the system: (a) mixing of
two gases at the same temperature and pressure,
(b) mixing of ethanol and water, (c) discharging a
battery, (d) expansion of a gas followed by compression
to its original temperature, pressure, and volume?
14.63 Which of the following are not state functions:
S, H, q, w, T?
14.64 Give a detailed example of each of the following, with
an explanation: (a) a thermodynamically spontaneous
process, (b) a process that would violate the first law
of thermodynamics, (c) a process that would violate
the second law of thermodynamics, (d) an irreversible
process, (e) an equilibrium process.

9/10/13 12:01 PM