Chemistry 452/ August 2012

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1 Chemistry 45/456 7 August 0 End- of-term Examination Professor G. Drobny Enter your answers into a blue or green Composition Book. Perform only the number of problems required. Answers must be given in energy mass units of kilograms (kg), distance as meters (m), energy units of Joules (J), pressure units of Pascals (Pa), time units of seconds. Useful Constants and Conversions Universal Gas Constant= R = 8.3 J / mole K = 0.08 L atm / mole K Faraday s Constant= I= 96,458 Coulombs / mole gravitational constant=g=9.8m/s Avagadro s Number=N A =6.0x0 3 molecules/mole atm=0,35 Nt/m =760 torr bar=0 5 N/m = atm= torr N/m =Pascal (=Pa) torr= mmhg Joule= N m= kg m s - =0 7 ergs= Coulomb-Volt erg= g cm s - = dyne cm 000L=m 3 Part (8 points) Give 3 out of 6 definitions/explanations..) Cooperativity. Define the term as it is used in ligand binding. Sketch the binding isotherms (i.e. ν vs. c L ) for cooperative and non-cooperative binding..) Give three examples of phenomena that you experience in everyday life that are produced by the surface tension of water or by the surface tension of water solutions. Explain..3) State the assumptions of the Debye-Huckel theory of electrolyte solutions. Give the Debye-Huckel limiting law for the mean activity coefficient. When is this expression valid?.4) When deep sea divers return too quickly to the ocean surface they suffer a sometimes fatal condition called decompression sickness or the bends. Explain the origin of decompression sickness using Henry s Law..5) Consider a solution produced by mixing equimolar amounts of benzene (C 6 H 6 ) and carbon tetrachloride (CCl 4 ). For this solution HMIX = 09Jmol at T=98K. In addition, when the mole fractions of the components are varied, the vapor pressure for each component is a non-linear function of mole fraction. Write a plausible equation of state for this solution that for each component relates vapor pressure to solution composition. Explain your answer.

2 .6) Compare HMIX,, SMIX, GMIX for the ideal and regular solution models. Explain the differences and similarities. Part : (0 points total) Topics for discussion/derivation. Answer out of the 4 questions..) Here you will do a derivation that shows how to measure an activity coefficient and Z ε + ε the regular solution parameter w = ε from a colligative property. RT Suppose solvent forms a dilute regular solution with solute, i.e. χ <<. The solvent H fusion activity a = γχ is related to the freezing point depression T by ln a = T RTf where T f is the freezing point of the pure solvent. Using this equation and the χ approximation ln ( χ) χ obtain an expression for w in terms of T, H fusion, T f, and χ..) Osmotic pressure measurements have been used to determine the molecular weight of polymers using the van Hoff osmotic equation π = crt where π is the osmotic pressure and c is the polymer concentration. This approach works well if the polymer is uncharged but many biological polymers are charged in solution and possess counter ions like Na +. In the experiment shown in figure a above, we have in the left solution a protein P with charge z and initial concentration c, and counter-ion Na +, separated by a semipermeable membrane from a NaCl solution with initial ion concentrations b. The membrane is permeable to Na + and Cl - but not to the protein. In figure b the system has reached equilibrium and the osmotic pressure is zc + cb + z c found to be π = RT. Explain (i.e. no derivation necessary) what has zc + b happened and explain how you could perform this experiment to recover the simple van t Hoff osmotic equation..3) In the two graphs below, the vapor pressure of a solvent above a polymer solution is shown as a solid line. The corresponding solvent vapor pressure above an ideal solution is shown as a dashed line. Explain the difference in the solvent vapor pressure above these two types of solutions. In particular, explain why the solvent vapor pressures above ideal and polymer solutions deviate less when plotted as functions of solvent volume

$fraction. You may use expression derived from Flory-Huggins theory to illustrate your points.$ to be ineffective. A schematic diagram of a time-release capsule is shown at the right. Explain how it works, thermodynamically. Part 3: (30 points total) Short Calculations.

to be ineffective. A schematic diagram of a time-release capsule is shown at the right. Explain how it works, thermodynamically. Part 3: (30 points total) Short Calculations.

3 fraction. You may use expression derived from Flory-Huggins theory to illustrate your points...4) Time release drugs have the advantage of releasing the drug to the body at a constant rate so that the drug concentration at any time is not high enough to have harmful side effects or so low as to be ineffective. A schematic diagram of a time-release capsule is shown at the right. Explain how it works, thermodynamically. Part 3: (30 points total) Short Calculations. Perform out of the 4 calculations. 3.)The enzyme tetrahydrofolate synthetase has four identical and independent binding sites for its substrate ATP. At T=93K (i.e. 0 o C) the equilibrium binding constant is K=.00x0 4. Scatchard plots of ATP binding to tetrahydrofolate synthetase are shown at the right for T=93K and 30K (i.e. 37 o C). Calculate K at T=30K, H o and S o for ATP binding to tetrahydrofolate synthetase. Assume both H o and S o are constant between 73K and 30K. 3.) An electrochemical cell has the half reactions: AgCl ( s) + e Ag ( s) + Cl + H ( g) H + e For this cell the standard EMF is ψ 0 = 0.5V at t=98k. For a cell with composition c c M + = = the EMF is found to be ψ = V for P H Cl H = atm. Calculate the mean activity coefficient for the resulting HCl solution. Assume the

4 reference concentration for all ionic species is M. Assume the reference pressure for all gaseous species is atm. Assume all gases behave ideally. 3.3) Methanol and acetone are mixed together at T=333K to form a non-ideal solution. At equilibrium the solution has a mole fraction for acetone equal to x acetone = while the vapor has a mole fraction for acetone equal to y acetone = If the total vapor pressure above the solution is P T =035 Pa, calculate the activities and activity coefficients for acetone and methanol. At T=333K, the vapor pressures for pure acetone and methanol Pacetone = 0479Pa and Pmethanol = 7346Pa. Assume the vapor behaves ideally. Assuming methanol and acetone form a regular solution, calculate w. 3.4) The surface tension of dilute aqueous solutions of propionic acid C H 5 COOH is given by γ = γ * bc where γ * = 0.07Nm is the surface tension of pure water, C is the 3 concentration of propionic acid and b = Nm mol. Calculate the surface tension γ for a 0.0M aqueous solution of proprionic acid, the surface adsorption Γ, and determine the surface area occupied by a single proprionic acid molecule. Assume T=300K. Part 4 (3 points total ) Perform one of the two multi-step problems. 4.) According to chemiosmotic theory the synthesis of ATP ADP + Pi ATP + H O, G = 3kJmol is driven by the pumping of protons across the inner mitochondrial membrane. The ph gradient across the membrane is ph = phin phout =.5 and the proton concentration inside the membrane is in 7 C + =.0 0 M. The concentration of Cl - out outside the membrane is C = 0.05M. The H Cl steady state trans-membrane potential is ψ = ψout ψin = 0.40V Assume the activity coefficients for the ions inside and outside the membrane are about equal. Assume also T=98K. a) Assuming the inner mitochondrial membrane is passively permeable to chloride ions, calculate the concentration of chloride ion inside the membrane. b) Suppose inside the membrane CATP = M, CADP = M, CP i = 0.005M. Calculate the work (i.e. G) required to produce one mole of ATP. c) Calculate the difference between the electrochemical potentials of H + inside and outside the membrane. d) Suppose 50% of the free energy produced by the transport of protons from inside the membrane to the outside of the membrane can be used to synthesize ATP. How many protons must be transported across the inner mitochondrial membrane to phosphorylate a ADP molecule?

5 4.) Assume compounds A and B form a regular solution. For A/B solutions assume a coordination number Z=6 and assume the exchange energy is ε AA + ε BB ε = εab = 00Jmol a) Calculate w at T=98K. b) For a 9: mixture of A and B (i.e. χ A = 0.9 and χ B = 0.) calculate U MIX, SMIX, and AMIX. Do A and B mix in these proportions at T=98K? At what temperature do A and B separate? c) Suppose a 9: regular solution of A and B at T=98K is separated by a semi-permeable membrane from pure A. Assume the membrane is permeable to A but not to B. Calculate the activity coefficient of A and calculate the osmotic pressure produced across the membrane. Assume the partial molar volume of A is x0-5 m 3 mol -. Compare this result to the osmotic pressure developed if the solution were ideal.

Part 1 (18 points) Define three out of six terms, given below.

Part 1 (18 points) Define three out of six terms, given below. Chemistry 45/456 3 August End-of-term Examination Professor G. Drobny Useful Constants and Conversions Universal Gas Constant= R = 8.31 J / mole K =.81 L atm / mole K Faraday s Constant= I= 96,458 Coulombs