課程名稱︰物理化學一 課程性質︰系訂必修 課程教師︰李弘文 開課學院：理學院 開課系所︰化學系 考試日期（年月日）︰2011/01/11 考試時限（分鐘）：120 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Final Exam Physical Chemistry (I) Total Time: 2hours (Jan 11, 2011, 13:20-15:20) ￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣ 1. This exam has total 11 pages. There are 3 part, with total 110 points. 2. Answer diractly on this exam. Only answers shown in assigned boxes will be graded. 3. Formula sheets are given at the end of this exam. 4. No other sheets/notes are allowed. 5. You can ONLY use your own calculator. 6. Correct answers must be accompanied with the correct sign and unit. 7. You must show all the intermediate steps in how you work out the answers to the calculation/description questions to get partial credits. 8. We will not answer any question during the exam. Periodic Table of the Element (略) Section 1: 單選題 (20 points) Pick one best answer ￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣ 1. Which of the following statements about enzyme-catalyzed reactions is not TRUE? (a) At saturating levels of substrate, the rate of an enzyme-catalyzed is proportional to the enzyme concentration. (b) The rate of the reaction decreases steadity with time as substrate is depleted. (c) The activation of the catalyzed reaction is the same as for the uncatalyzed reaction, but the equilibrium constant is more favorable in the enzyme- catalyzed reaction. (d) The Michaelis-Menton constant KM equal the [S] at which V=1/2 Vmax. 2. Which of the following enzyme-substrate complex bind most tightly together? (a) Insulin recepter-insulin (KD = 10^-10 M) (b) Avidin-biotin (KD = 10^-15 M) (c) anti-HIV Immunoglobin-gp41 (KD = 4 x 10^-10 M) (d) Calmodulin-Ca^2+ (KD = 3 x 10^-6 M) 3. A protein can exist in two stable conformations, with the energy of conform- ation A higher than the conformation B by 2.785 kJ/mol. What is the equilib- rium temperature, when 25% of total protein is found in conformation A? (a) 295 K (b) 300 K (c) 305 K (d) 310 K 4. Which of the following gas has the largest molar heat capacity? (a) Ne (b) Ar (c) H2 (d) CH4 5. Which of the following parameters will alter the value of the equilibrium constant in solution? (a) Pressure (b) Temperature (c) Catalyst (d) Concentration (e) All of the above k1 k2 6. For the reaction A--> B--> C : if k1 >> k2, which of the following graph best describes the time course of the concentration profiles? (選項圖略) 7. Which is true for a spontaneous change of a process? (a) (dS)U,P > 0 (b) (dU)S,V < 0 (c) (dH)S,V < 0 (d) (dG)S,V < 0 (e) (dA)S,V < 0 8. Maxwell construction can be used to correct the van der Waals loop when T > Tc. (a) True (b) False (c) intermediate 9. If water freeze at (-10度C) , the sign of ΔSsystem should be (a) positive (b) negative (c) 0 (d) intermediate 10.The binding of oxyfen on hemoglobin is positively cooperative. What is the ratio of the observed K4/K1? (K4,K3,K2,K1 are dissociation costants) K1 K2 K3 K4 Hb + O2 <=> HbO2 + O2 <=> HbO4 + O2 <=> HbO6 + O2 <=> HbO8 (a) 0.153 (b) 16 (c) 192 Section 2: Short questions (40points, 8pts each) ￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣ Use the space below to provide a short calculation/description on the question. If possible, try to use quantitative statement (including equations) and figures to illustrate your reasoning. 1.Hydrophobic interaction is important for protein folding. It is observed that freezing protein slowly or heating protein both cause the unfolding of protein (cold and heat denaturation). Plot the temperature-dependence of ΔH , (–TΔS) and ΔG to explain why. 2.Consider a two-state system with energy levels, E1 and E2. The system has 1 mole distributed between these two energy levels, E1 and E2. kB=1.38 x 10-23J/K, E1= 0.0 J, and E2=3.0 x 10-21 J. Based on Boltzmann distribution, (i) Calculate the total energy of the system at equilibrium at the temperatu- re of 300 K. (ii)The energy of the system is now doubled with respect to the energy in part (i), and the system is allowed to reach equilibrium. Calculate the new temperature of the system in equilibrium. 3.Derive the relation between the relaxation time τ and the rate constants (k1, k-1, k'1 and k'-1) for the following mechanism: The system is subjected to a small displacement from equilibrium. It is assumed that equilibria, A <=> A', KA = [A]/[A'], and B <=> B', KB = [B]/[B'] , are adjusted very rapidly so that these steps remain in equilibrium. 4.Given the canonical partition function below. (方程式略) (a)Show that this system obey van der Wall equation of the state. (b)Calculate U 5.For each of the following process, fill in the table for each of the quantities (q, w, ΔU, ΔH, ΔSsys, ΔG) whether it is positive(+), negative(─), or zero(0): (a) An ideal gas is compressed adiabatically and reversibly. (b) A sample of gas is carried through a complete and reversible Carnot heat engine cycle. ┌───┬───┬───┬───┬───┬───┬───┐ │ │ q │ w │ ΔU │ ΔH │ΔSsys│ ΔG │ ├───┼───┼───┼───┼───┼───┼───┤ │ A │ │ │ │ │ │ │ ├───┼───┼───┼───┼───┼───┼───┤ │ B │ │ │ │ │ │ │ └───┴───┴───┴───┴───┴───┴───┘ Section 3 : Long questions (50 points) ￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣ 1.(9 points) Increased Tryptophan (Trp, one kind of amino acids) fluorescence is usually used to monitor the protein unfolding process. Below is the measu- rement of Trp fluorescence intensity (arbitrary unit) as function of tempera- ture for a pair of wild-type (WT) and mutant Pfu DNA polymerase. This basica- lly is a protein melting curve we dealt with in class. (1a). What are the melting temperatures of WT and Mutant proteins, roughly? You may assume protein at 10°C is totally folded and protein at 95°C is totally unfold. (1b). Explain how you will use the appropriate plots and steps needed to det- ermine ΔH, ΔS of unfolding these two proteins (no calculation requir- ed). (1c). Assume ΔH of the WT is 23.8 Kcal/mol, and ΔS is 78 cal/K-mol. If you want exactly 0.1% of the WT protein to be folded, what temperature do you have to choose? 2.(10 points) Consider the reversible isothermal compression of 0.45 mole of helium gas from 0.5 atm and 22 L to 1 atm at 25°C. (2a). Calculate the values of w, ΔH, ΔSsys, and ΔG for this process. (2b). Can you use the ΔG value you calculated above to predict whether this process is spontaneous or not? Explain. 3.(12 points) The gas phase reaction: 2NO + H2 ↔ N2O + H2O goes to completi- on and is known to follow the rate law of:(略) The data below is obtained:(略) (3a). Estimate the half-time for experiment 2 and 4. (3b). Calculate k at 820 °C in (mmHg)-2s-1. (3c). Calculate the molar activation energy of the reaction in kcal/mol. 4.(12 points) N distinguishable particles can only exist in one of the 3 non-degenerate energy levels of energies –ε, 0 and +ε. The system is in contact with a thermal reservoir at temperature T. (4a). What is the molecular partition function? (4b). What is the canonical partition function? (4c). What is the average energy of the system? (4d). What is the entropy of the system? (4e). Plot the temperature dependence of Cv of the system. (4f). What is the value of (略) 5.(7 points) For a non-ideal binary mixture, the vapor pressure curve for one component can be represented by empirical expressions such as Margules equat- ion (方程式略) Where α and β are empirical fit parameters for this non-ideal mixture. A plot illustrating such non-ideal mixture (solid lines) along with the ideal curves (Raoult’s law, dotted lines) is shown here. Also shown is the curve for the total vapor pressure. Given the pressure dependence of chemical potential and the Gibbs-Duhem equation below: (略) Show that the vapor pressure of component 2 is in the form of (略) 公式表略 ==================================考題結束===================================== --

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