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PROBLEMS

Section 9.1 9.13 At 25°C and 1 atm, a solution of 72.061 g of H O and
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9.1 Give the SI units of each of these solution-composition 192.252 g of CH OH has a volume of 307.09 cm . In this solu-
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quantities: (a) c ; (b) m (molality); (c) x . tion, V H 2 O 16.488 cm /mol. Find V CH 3 OH in this solution.
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9.2 Which of the three quantities in Prob. 9.1 change if T 9.14 The density of a methanol–water solution that is 12.000
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changes? If P changes? weight percent methanol is 0.97942 g/cm at 15°C and 1 atm.
For a solution that is 13.000 weight percent methanol, the den-
9.3 Calculate the number of moles of the solute HCl in each sity is 0.97799 g/cm at this T and P. Since the change in solu-
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of the following aqueous solutions. (a) 145 mL of a solution
tion composition is small, we can estimate V A by
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with HCl molarity 0.800 mol/dm ; (b) 145 g of a 10.0 weight
percent HCl solution; (c) 145 g of a solution whose HCl molal-
ity is 4.85 mol/kg. V A 10V>0n A 2 T,P,n B 1¢V>¢n A 2 T,P,n B

V
Calculate (CH OH) for a methanol–water solution at 15°C
9.4 In an aqueous solution of CH OH that is 30.00% CH OH 3
3 3 1
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by weight, the CH OH molarity at 20°C and 1 atm is 8.911 mol/ and 1 atm that is 12 % CH OH by weight. Then calculate
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dm .(a) Find the solution’s density at 20°C and 1 atm. (b) Find V (H O) for this solution.
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the CH OH molality. (c) Find the CH OH mass concentration.
3 3 9.15 Use Fig. 9.3 to find (a) the molality at which V 0;
MgSO 4
9.5 Find the NH molality and mole fraction in an aqueous (b) the partial molar volume of MgSO (aq) in the limit of an
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solution of NH that is 0.800% NH by weight. infinitely dilute solution; (c) V of MgSO and V of H O in a
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0.05 mol/kg MgSO (aq) solution.
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9.6 When 2.296 mol of CsCl is dissolved in 450 mL of water
and the resulting solution is diluted to a volume of 1.0000 L at 9.16 At infinite dilution, the ions of an electrolyte are infi-
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20°C and 1 atm, the final solution has a density of 1.2885 g/cm . nitely far apart and do not interact with one another. Therefore,
q q
Find the CsCl molality in the final solution. V i of a strong electrolyte in solution is the sum of V values
q
for the ions. Some V i values for aqueous solutions at 25°C and
9.7 The density of a KI(aq) solution with molality 1.506 1 atm are 16.6 cm /mol for NaCl, 38.0 cm /mol for KNO , and
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mol/kg is 1.1659 g/cm at 20°C and 1 atm. Find the KI molarity. 3 q 3
27.8 cm /mol for NaNO . (a) Find V i for KCl in water at 25°C
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q
9.8 Show that in a very dilute solution of density r with sol- and 1 atm. (b) Find 10m i >0P2 T,n j for KCl in water at 25°C.
vent mole fraction close to 1, the solutes’ molar concentra-
9.17 Prove that the internal energy of a phase satisfies U
tions and molalities are c rx /M and m x /M and that
i i A i i A PV TS n m . The proof is very short.
c rm . i i i
i i
9.18 Write the defining equation for the partial molar
9.9 Show that m (1000n /n M r,A ) mol/kg, where m is Helmholtz energy of substance i in a solution and state fully
A
B
B
B
the molality of solute B and M r,A is the molecular weight (rela- what every symbol in your definition stands for.
tive molecular mass) of the solvent.
9.19 Show that H i U i P . i
V
Section 9.2 9.20 (a) Use G n m , m m° RT ln (P /P°) [Eqs. (9.23)
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9.10 True or false? (a) V i 10V i >0n i 2 T,P,n j i . (b) The volume and (6.4)] and Eq. (4.65) applied to pure gas i to show that G of
of a solution at T and P equals the sum of the volumes of its an ideal gas mixture at T is given by G G*(T, P , n ),
i i i i
pure components at T and P. (c) V i in a solution must equal where P and n are the partial pressure and number of moles of
3 i i
V* . (d) The SI units of V i are m /mol. (e) If half of a solution gas i in the mixture, and G* is the Gibbs energy of n moles of
m,i
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i
is poured down the sink, the partial molar volumes in the pure gas i at temperature T and pressure P . (This result was
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remaining solution are equal to those in the original solution. mentioned in Sec. 6.1.) (b) Use ( G/ T) S and the result
P,n i
(f) The volume of a solution cannot be less than the volume of of (a) to show that for an ideal gas mixture S S*(T, P , n ).

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the pure solvent used to prepare the solution. (g) H i (c) Use G H TS to show that for an ideal gas mixture H
. (h) m is a partial molar quantity. (i) In a solu- H*(T, n ). (d) Show that for an ideal gas mixture C
10H i >0n i 2 T,P,n j i i i i i P
tion of water plus ethanol, each of the quantities , S i ,V i and G i C* (T, n ) and U U*(T, n ). (e) Find C at 25°C and
P,i
P
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is a function of T, P, and x H 2 O and no other variables. 500 torr of a mixture of 0.100 mol of O (g) and 0.300 mol of
2
CO (g), using Appendix data. State any assumptions made.
9.11 At 25°C and 1 atm, a 0.5000-mol/kg solution of NaCl in 2

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water has V 18.63 cm /mol and V 18.062 cm /mol.
NaCl H 2 O
Find the volume at 25°C and 1 atm of a solution prepared by Section 9.3
dissolving 0.5000 mol of NaCl in 1000.0 g of water. 9.21 Verify (9.35) for ( mix G/ T) P,n j .
9.12 In an aqueous 0.1000-mol/kg NaCl solution at 25°C and

1 atm, C P,H 2 O 17.992 cal/(mol K) and C P,NaCl 17.00 Section 9.4
cal/(mol K). Find C of 1000.0 g of such a solution. Note that 9.22 Use Fig. 9.9 to calculate the volume at 20°C and 1 atm
P
this amount of solution does not contain 0.1000 mol of NaCl. of a solution formed from 20.0 g of H O and 45.0 g of C H OH.
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