Problem Set #10 Assigned November 8, 2013 Due Friday, November 15, 2013 Please show all work for credit To Hand in

Size: px

Start display at page:

Download "Problem Set #10 Assigned November 8, 2013 Due Friday, November 15, 2013 Please show all work for credit To Hand in"

Leslie Cunningham
6 years ago
Views:

1 Problem Set #10 Assigned November 8, 2013 Due Friday, November 15, 2013 Please show all work for credit To Hand in

3. 4. The vapor pressure of an unknown solid is approximately given by ln(p/torr) = 22.

2 3. 4. The vapor pressure of an unknown solid is approximately given by ln(p/torr) = (K/T), and the vapor pressure of the liquid phase of the same substance is approximately given by ln(p/torr) = (K/T). a. Calculate H vaporization and H sublimation. b. Calculate H fusion. 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) Absorbance (260 nm) For the formation of a self-complementary duplex DNA from single strands H = kj mol 1, and T m = 311 K for strand concentrations of 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? 2

8. 1.053 g of beef heart myoglobin dissolved in 50.

to support a column of solution of height d.

9. Calculate the change in the freezing point of water if 0.

3 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 g of a protein with molecular weight g mol 1 is dissolved in 100. ml of water

4 13. 4

5 Extra practice for exam, do not hand in Phase equilibrium 1. Use the vapor pressures for C 2 N 2 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 Solid Liquid Liquid Use the vapor pressures of Cl 2 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) 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 K, H fusion = 6010 J mol 1, the density of ice is 920 kg m 3, and the density of liquid water is 997 kg m 3. 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 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? 5

6 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 H transition = 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 T m = 335 K. At T = 315 K, UV absorbance determines that the fraction of native protein is f N = At T = 345. K, f N = 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, C A,0 = C B,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 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 The vapour pressure of 2-propanol is kpa at C, but it fell to 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 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. 6

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.

A and B form an ideal solution. At a total pressure of 0.900 bar, y A = 0.450 and x A = 0.650.

7 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 ) h/cm a Calculate the molar mass of the enzyme. 7. a 8. a 9. A and B form an ideal solution. At a total pressure of bar, y A = and x A = Using this information, calculate the vapor pressure of pure A and of pure B. 10. The heat of fusion of water is J mol 1 at its normal melting point of K. Calculate the freezing point depression constant K f. 7

Problem Set #10 Assigned November 8, 2013 Due Friday, November 15, 2013 Please show all work for credit. To Hand in

Problem Set #10 Assigned November 8, 013 Due Friday, November 15, 013 Please show all work or credit To Hand in 1. 1 . A least squares it o ln P versus 1/T gives the result 3. Hvaporization = 5.8 kj mol