3.23.4.00 L of Ar and 2.50 L of He, each at 298 K and
1.50 atm, were mixed isothermically and isobarically. The mix-
ture was then expanded to a final volume of 20.0 L at 298 K.
Write chemical reactions for each step, and determine the
change in entropy for the complete process.
3.24.Dentists might use a mixture of 40% N 2 O and 60% O 2
as an initial anesthetic of nitrous oxide (although the exact
proportions may vary). Determine the entropy of mixing for
1 mole of such a mixture. Assume ideal gas conditions.
3.25.A 5.33-g piece of Cu metal is heated to 99.7°C in boil-
ing water, then dropped into a calorimeter containing 99.53 g
of H 2 O at 22.6°C. The calorimeter is sealed to the outside en-
vironment, and temperature equalizes. Cp[Cu (s)] 0.385 J/gK,
Cp[H 2 O] 4.18 J/gK. (a)Discuss the process that occurs in-
side the calorimeter in terms of the zeroth and first laws of
thermodynamics. (b)What is the final temperature inside
the system? (c)What is the entropy change of the Cu (s)?
(d)What is the entropy change of the H 2 O ()? (e)What is
the total entropy change in the system? (f)Discuss the
process that occurs inside the calorimeter in terms of the
second law of thermodynamics. Do you expect it to be spon-
taneous?
3.26.In the last exercise, neither Cu nor H 2 O is an ideal gas.
Comment on the expected reliability of your answers for S
for parts c, d, and e. (Hint:consider the derivation of the equa-
tion you used to calculate S.)
3.27.The first law of thermodynamics is sometimes stated
“You can’t win” and the second law is stated similarly as “You
can’t even break even.” Explain how these two statements can
be considered apt (though incomplete) viewpoints for the first
and second laws of thermodynamics.
3.28.Trouton’s rule states that the entropy of boiling at the
normal point is 85 J/molK. (a)Does the data from Example
3.2 support Trouton’s rule? (b)H 2 O has a heat of vaporization
of 40.7 kJ/mol. Does the vapSfor H 2 O at its normal boiling
point support Trouton’s rule? Can you explain any deviation?
(c)Predict the boiling point of cyclohexane, C 6 H 12 , if its vapH
is 30.1 kJ/mol. Compare your answer to the measured normal
boiling point of 80.7°C.
3.6 Order and the Third Law
of Thermodynamics
3.29.Argue from Boltzmann’s definition for entropy that S
can never have a negative value. (Hint:see equation 3.24.)
3.30.Calculate the value of Boltzmann’s constant in units of
(a)Latm/K and (b)(cm^3 mmHg)/K.
3.31.Which system has the higher entropy? (a)A clean
kitchen or a dirty kitchen? (b)A blackboard with writing on
it or a completely erased blackboard? (c)1 g of ice at 0°C or
10 g of ice at 0°C? (d)1 g of ice at 0 K or 10 g of ice at 0 K?
(e)10 g of ethyl alcohol, C 2 H 5 OH, at 22°C (roughly room
temperature) or 10 g of ethyl alcohol at 2°C (the approximate
temperature of a cold drink)?
3.32.Which system has the higher entropy? (a)1 g of solid
Au at 1064 K or 1 g of liquid Au at 1064 K? (b)1 mole of CO
at STP or 1 mole of CO 2 at STP? (c)1 mole of Ar at a pres-
sure of 1 atm or 1 mole of Ar at a pressure of 0.01 atm?
3.33.The element helium is thought to remain a liquid at
absolute zero. (Solid helium can be made only by exerting
a pressure of about 26 atm on a liquid sample.) Is the en-
tropy of liquid helium at absolute zero exactly zero? Why or
why not?
3.34.Order the following substances in order of increasing
entropy: NaCl (solid), C (graphite), C (diamond), BaSO 4 (solid),
Si (crystal), Fe (solid).3.7 Entropies of Chemical Reactions
3.35.Why isn’t the entropy of elements in their standard
pressure at normal (that is, room) temperatures equal to zero?
3.36.Determine the entropy of formation, fS, of the follow-
ing compounds. Assume 25°C. (a)H 2 O () (b)H 2 O (g)
(c)Fe 2 (SO 4 ) 3 (d)Al 2 O 3 (e)C (diamond)
3.37.The thermite reaction has solid aluminum powder re-
acting with iron(III) oxide to make aluminum oxide and iron.
The reaction is so exothermic that the iron product is usually
molten initially. Write the balanced chemical reaction for the
thermite reaction and determine the rxnSfor the process.
Assume standard conditions.
3.38.In place of iron(III) oxide in the thermite reaction in the
previous problem, chromium(III) oxide can be used in its place,
generating chromium metal and aluminum oxide as products.
Calculate rxnHand rxnSfor this thermite-type reaction.
Assume standard conditions.
3.39.Determine the differences in the rxnSunder standard
conditions for the two following reactions:
H 2 (g) + ^12 O 2 (g) →H 2 O ()
H 2 (g) + ^12 O 2 (g) →H 2 O (g)
and justify the difference.
3.40.What is the change in entropy when 2.22 mol of water
is heated from 25.0°C to 100°C? Assume that the heat capac-
ity is constant at 4.18 J/gK.
3.41.Estimate the entropy change of an 800-lb engine (1 lb
2.2 kg) that goes from normal environmental temperature,
about 20°C, to an average operational temperature of 650°C.
The heat capacity of iron (the major component of most en-
gines) is 0.45 J/gK.
3.42.Calculate the molar entropy change of the gas that ac-
companies the bursting of a balloon if the initial pressure is
2.55 atm and the external pressure is 0.97 atm.
3.43.A normal breath is about 1 L in volume. Assume you
take a breath at sea level, where the pressure is 760 mmHg.
Then you instantly (this is a thought experiment, after all) go
to Los Alamos, New Mexico, located in the mountains where
the normal atmospheric pressure is 590 mmHg, and you ex-Exercises for Chapter 3 87