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12.19 The transition

Sn(s, gray) Sn(s, white)

is in equilibrium at 18 0C and 1 atm pressure. IfS = 8.8 J/K mol for the transition at

18 0C and if the densities are 5.75 g/cm3 for gray tin and 7.28 g/cm3 for white tin,

calculate the transition temperature under 100 atm pressure.

12.20 For the transition, rhombic sulfur monoclinic sulfur, the value of S is positive.

The transition temperature increases with increase in pressure. Which is denser, the

rhombic or themonoclinic form? Prove your answer mathematically.

12.21 Liquid water under an air pressure of 1 atm at 25 0C has a larger vapor pressure than it

would in the absence of air pressure. Calculate the increase in vapor pressure

produced by the pressure of the atmosphere on the water. The density of water= 1

g/cm3 ; the vapor pressure (in the absence of the air pressure)= 3167.2 Pa.

13.12 For CCl4 Kb= 5.03 K kg/mol and Kf= 31.8 K kg/mol. If 3.00g of a substance in 100g

CCl4 raises the boiling point by 0.60 K, calculate the freezing-point depression, the

relative vapor pressure lowering, the osmotic pressure at 25 C, and the molar mass of

the substance. The density of CCl4 is 1.59 g/cm3 and the molar mass is 153.823

g/mol.

13.13 Calculate the boiling-point elevation constant for each of the following substances.

Substance tb/0C Hvap/(J/g)

Acetone, (CH3)2CO 56. 1 520.9

Benzene, C6H6 80.2 394.6

Chloroform, CHCl3 61.5 247

Methane, CH4 -159 577

Ethyl acetate, CH3C02C2H5 77.2 426.8

Plot the values of Kb versus the product MTb .

13.14 Once the boiling point of the liquid depends on the pressure, Kb is a function of

pressure. Calculate the value of Kb for water at 750 mmHg and at 740 mmHg

pressure. Use the data in the text. Assume Hvap is constant.

14.5 A gaseous mixture of two substances under a total pressure of 0.8 atm is in equilibrium

with an ideal liquid solution. The mole fraction of substance A is 0.5 in the vapor

phase and 0.2 in the liquid phase. What are the vapor pressures of the two pure

liquids?

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14.6 The composition of the vapor over a binary ideal solution is determined by the

composition of the liquid. If x1 and yl are the mole fractions of 1 in the liquid and

vapor, respectively, find the value of x1 for which yl - x1 has a maximum. What is the

value of the pressure at this composition?

14.7 Suppose that the vapor over an ideal solution contains nl mol of 1 and n2 mol of 2 and

occupies a volume Vunder the pressure p = p1 + p2 . If we define = RT/

and =

RT/ , show that Raoult's law implies V = nl

+ n2 .

14.8 Show that, while the vapor pressure in a binary ideal solution is a linear function of

the mole fraction of either component in the liquid, the reciprocal of the pressure is a

linear function of. the mole fraction of either component in the vapor.

14.9 Given the vapor pressures of the pure liquids, and the overall composition of thesystem, what are the upper and lower limits of pressure between which liquid and

vapor coexist in equilibrium?

14.10 a. The boiling points of pure benzene and pure toluene are 80.1 C and 110.6 C under1 atm. Assuming the entropies of vaporization at the boiling points are the same, 90

J/K mol, by applying the Clausius-Clapeyron equation to each, derive an implicit

expression for the boiling point of a mixture of the two liquids as a function of the

mole fraction of benzene, xb .

b. What is the composition of the liquid that boils at 95 C ?

16.1 The apparent value of K I in sucrose (C1 2H2201 1) solutions of various

concentrations

m/(mol/kg) 0.10 0.20 0.50 1.00 1. 50 2.00

Kf/(K kg/mol) 1.88 1.90 1.96 2.06 2.17 2.30

a) Calculate the activity of water in each solution.

b) Calculate the activity coefficient of water in each solution.

c) Plot the values of a and y against the mole fraction of water in the solution.

d) Calculate the activity and the activity coefficient of sucrose in a 1 molal solution.

16.2 The Henry's law constant for chloroform in acetone at 35.17 C is 0.199 if the vapor

pressure is in atm, and concentration of chloroform is in mole fraction. The partial

pressure of chloroform at several values of mole fraction is :

XCHCl3 0.059 0.123 0.185

PCHCl3,/mmHg 9.2 20.4 31.9

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If = x, and 1 as x0, calculate the values of a and l' for chloroform in the three

solutions.

16.3 At the same concentrations as in Problem 1 6.2, the partial pressures of acetone are-

323.2, 299.3, and 275.4 mmHg, respectively. The vapor pressure of pure acetone is

344.5 mmHg. Calculate the activities of acetone and the activity coefficients in these

three solutions ( = x; 1 as x0).

17.23 Write the cell reaction and calculate the potential of the following cells without

transference.

a) Pt(s) | H2(g, p= 1 atm) | HCI(aq, a) | H2(g, p = 0.5 atm) | Pt(s)

b) Zn(s) | Zn2+ (aq, a= 0.01) :: Zn2+ (aq, a = O.l) | Zn(s).

17.24 At 25 C the potential of the cell with transference,

Pt(s) | H2(g, f=1) | HCI(aq, a = 0.009048) : HCI(aq, a = 0.0175 1) | H2(g, f= l) | Pt(s),

is 0.02802 V. The corresponding cell without transference has a potential of 0.01696

V. Calculate the transference number of H+ ion and the value of the junction

potential.

17.25 Consider the reaction

Sn + Sn4+ 2 Sn2+ .

If metallic tin is in equilibrium with a solution of Sn 2+ in which a Sn2+= 0.100, what is

the equilibrium activity of Sn4+ ion ? Use data in Table 17.1 .

17.26 Consider a Daniell cell that has 100 cm3 o f 1.00 mol/L CuSO4 solution in the positive

electrode compartment and 100 cm3 of 1.00 mol/L ZnSO4 in the negative electrode

compartment. The zinc electrode is sufficiently large that it does not limit the reaction.

a) Calculate the cell potential after 0 %, 50 %, 90 %, 99 %, 99.9 %, and 99.99 % of

the available copper sulfate has been consumed.

b) What is the total electrical energy that can be drawn from the cell ? Note:Gtotal =

c) Plot the cell potential as a function of the fraction of the total energy that has been

delivered,

17.27 A platinum electrode is immersed in 100 mL of a solution in which the sum of the

concentrations of the Fe2+ and Fe3+ ions is 0,100 mol/L.

a) Sketch the fraction of the ions that are present as Fe3+ as a function of the potential

of the electrode.

b) If Sn2+ is added to the solution, the reaction 2 Fe3+ + Sn2+ 2 Fe2+ + Sn4+ occurs.

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Assume that initially all the iron is present as Fe3+ . Plot the potential of the platinum

after the addition of 40 mL, 49.0 mL, 49.9 mL, 49.99 mL, 50.0 mL, 50.01 mL, 50. l0

mL, 51.0 mL, and 60 mL of 0.100 mol/L Sn2+ solution.