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Problem Set #10

Assigned November 8, 2013 – Due Friday, November 15, 2013

Please show all work for credit

To Hand in

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4. The vapor pressure of an unknown solid is approximately given by ln(P/Torr) = 22.413 –

2035(K/T), and the vapor pressure of the liquid phase of the same substance is

approximately given by ln(P/Torr) = 18.352 – 1736(K/T).

a. Calculate Hvaporization and Hsublimation.

b. Calculate Hfusion.

c. Calculate the triple point temperature and pressure.

5. The UV absorbance of a solution of a double-stranded DNA is monitored at 260 nm as a

function of temperature. Data appear in the following table. From the data determine the

melting temperature.

Temperature (K) 343 348 353 355 357 359 361 365 370

Absorbance (260 nm) 0.30 0.35 0.50 0.75 1.22 1.40 1.43 1.45 1.47

6. For the formation of a self-complementary duplex DNA from single strands H° = –177.2

kJ mol–1

, and Tm = 311 K for strand concentrations of 1.00 10–4

M. Calculate the

equilibrium constant and Gibbs energy change for duplex formation at T = 335 K.

Assume the enthalpy change for duplex formation is constant between T = 311 K and T =

335 K.

7. At –47°C, the vapor pressure of ethyl bromide is 10.0Torr and that of ethyl chloride is 40.0

Torr. Assume that the solution is ideal. Assume there is only a trace of liquid present and

the mole fraction of ethyl chloride in the vapor is 0.80 and then answer these questions:

a. What is the total pressure and the mole fraction of ethyl chloride in the liquid?

b. If there are 5.00 mol of liquid and 3.00 mol of vapor present at the same pressure as in part

(a), what is the overall composition of the system?

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8. 1.053 g of beef heart myoglobin dissolved in 50.0 ml of water at T = 298 K generates

sufficient osmotic pressure to support a column of solution of height d. If the molar

mass of myoglobin is 16.9 kg per mole, calculate d.

9. Calculate the change in the freezing point of water if 0.0053 g of a protein with molecular

weight 10083 g mol–1

is dissolved in 100. mL of water.

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Extra practice for exam, do not hand in Phase equilibrium

1. Use the vapor pressures for C2N2 given in the following table to estimate the temperature

and pressure of the triple point and also the enthalpies of fusion, vaporization, and

sublimation.

Phase T (°C) P (Torr)

Solid –62.7 40.0

Solid –51.8 100.

Liquid –33.0 400.

Liquid –21.0 760.

2. Use the vapor pressures of Cl2 given in the following table to calculate the enthalpy of

vaporization using a graphical method or a least-squares fitting routine.

T (K) P (atm) T (K) P (atm)

227.6 0.585 283.15 4.934

238.7 0.982 294.3 6.807

249.8 1.566 305.4 9.173

260.9 2.388 316.5 12.105

272.0 3.483 327.6 15.676

3. It has been suggested that the surface melting of ice plays a role in enabling speed skaters

to achieve peak performance. Carry out the following calculation to test this hypothesis.

At 1 atm pressure, ice melts at 273.15 K, Hfusion = 6010 J mol–1

, the density of ice is 920

kg m–3

, and the density of liquid water is 997 kg m–3

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a. What pressure is required to lower the melting temperature by 5.0°C?

b. Assume that the width of the skate in contact with the ice has been reduced by sharpening

to 25 10–3

cm, and that the length of the contact area is 15 cm. If a skater of mass 85 kg is

balanced on one skate, what pressure is exerted at the interface of the skate and the ice?

c. What is the melting point of ice under this pressure?

d. If the temperature of the ice is –5.0°C, do you expect melting of the ice at the ice–skate

interface to occur?

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4. Consider the transition between two forms of solid tin, Sn(s, gray) Sn(s, white).

The two phases are in equilibrium at 1 bar and 18°C. The densities for gray and white tin

are 5750 and 7280 kg m–3

, respectively, and Htransition = 8.8 J K–1

mol–1

. Calculate the

temperature at which the two phases are in equilibrium at 200 bar.

5. A protein has a melting temperature of Tm = 335 K. At T = 315 K, UV absorbance

determines that the fraction of native protein is fN = 0.965. At T = 345. K, fN = 0.015.

Assuming a two-state model and assuming also that the enthalpy is constant between T =

315 and 345 K, determine the enthalpy of denaturation. Also, determine the entropy of

denaturation at T = 335 K. By DSC, the enthalpy of denaturation was determined to be

251 kJ mol–1

. Is this denaturation accurately described by the two-state model?

6. Suppose a DNA duplex is not self-complementary in the sense that the two

polynucleotide strands composing the double helix are not identical. Call these strands A

and B. Call the duplex AB. Consider the association equilibrium of A and B to form

duplex AB

A+B

Assume the total strand concentration is C and, initially, A and B have equal concentrations;

that is, CA,0 = CB,0 = C/2. Obtain an expression for the equilibrium constant at a point where

the fraction of the total strand concentration C that is duplex is defined as f. If the strand

concentration is 1.00 10–4

M, calculate the equilibrium constant at the melting temperature.

Ideal and Real Solutions

1. Predict the ideal solubility of lead in bismuth at 280°C given that its melting point is

327°C and its enthalpy of fusion is 5.2 kJ mol−1.

2. The vapour pressure of 2-propanol is 50.00 kPa at 338.8°C, but it fell to 49.62 kPa when

8.69 g of an involatile organic compound was dissolved in 250 g of 2-propanol. Calculate

the molar mass of the compound.

3. The addition of 5.00 g of a compound to 250 g of naphthalene lowered the freezing

point of the solvent by 0.780 K. Calculate the molar mass of the compound.

4. The osmotic pressure of an aqueous solution at 288 K is 99.0 kPa. Calculate the freezing

point of the solution.

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5. The molar mass of an enzyme was determined by dissolving it in water, measuring the

osmotic pressure at 20°C, and extrapolating the data to zero concentration. The

following data were obtained:

c/(mg cm−3) 3.221 4.618 5.112 6.722

h/cm 5.746 8.238 9.119 11.990

Calculate the molar mass of the enzyme.

6. a

7. a

8. a

9. A and B form an ideal solution. At a total pressure of 0.900 bar, yA = 0.450 and xA =

0.650. Using this information, calculate the vapor pressure of pure A and of pure B.

10. The heat of fusion of water is 6.008 103 J mol

–1 at its normal melting point of 273.15 K.

Calculate the freezing point depression constant Kf.

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