課程名稱︰物理化學一 課程性質︰化學系系必修 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）︰ 2009.06.19 考試時限（分鐘）： 08:10~10:10，120 是否需發放獎勵金：是 試題 : Section I: True (T) / False (F) (20 points) 1. Maximizing the multiciplicity (W) of a system while conserving the total energy leads to a exponential probability distribution. 2. The negative change in Helmholtz free energy during an isothermal process in the maximum work available from the processes 3. The rate of a process is always propotional to its free energy change. 4. The rate of the reaction with higher Ea will change more significantly with the temperature change than the reaction with lower Ea, assuming both reactions have the same frequency factor A. 5. The equilibrium constant for a reaction can be calculated from ΔG. 6. Clapeyron equation predicts that the boiling temperature at 0.5 atm is lower than that at 1 atm. 7. Joule-Thomson experiment is a constant entropy process. 8. z = exp(xy) is an exact differential function. 9. For a sample of gas carried through a complete, reversible Carnot engine cycle, the overall work is positive. 10. For water, increasing the pressure above the solid/liquid co-existance line leads to freezing. Section 2: 單選題 (20 points) Pick one best answer 1. A formic acid can form dimers in solution due to its hydrogen bonds: 2 X = X2, and the reaction occurs with 2nd order kinetics. If 50% of the monomers are gone in 10 s, how long will it take, from beginning of the reaction, to use up 75% of the monomers? (a) 30s (b) 20s (c) 15s (d) 10s 2. Which of the following system has the largest entropy? ┌─┬─┬─┬─┬─┬─┐ (a) │●│ │●│●│ │ │ └─┴─┴─┴─┴─┴─┘ ┌─┬─┬─┬─┬─┬─┬─┐ (b) │●│ │●│●│●│ │ │ └─┴─┴─┴─┴─┴─┴─┘ ┌─┬─┬─┬─┬─┐ (c) │●│ │●│●│ │ └─┴─┴─┴─┴─┘ ┌─┬─┬─┬─┐ (d) │●│●│ │●│ └─┴─┴─┴─┘ ┌─┬─┬─┐ (e) │●│●│●│ └─┴─┴─┘ 3. A process can NEVER occur spontaneously at constant temperature and pressure, if (a) ΔS >0, and ΔH >0 (b) ΔS >0, and ΔH <0 (c) ΔS <0, and ΔH >0 (d) ΔS <0, and ΔH <0 4. Binding of oxygen to hemoglobin is positively cooperative. The dissociation constants (K1, K2, K3, and K4) of each individual binding step, shown below, have been measured experimently. What is the ratio of the observed K3 / K1? K1 K2 K3 K4 Hb + O2 ==== HbO2 + O2 ==== HbO4 + O2 ==== HbO6 + O2 ==== HbO8 (a) 6 (b) 0.21 (c) 171 5. At what temperature will the average kinetic energy of SO2(g) molecules (M.W. = 64 g/mol) be the sames as that of O2(g) molecules (M.W. = 32 g/mol) at 300 K? (a) 424 K (b) 212 K (c) 300 K (d) 150K (e) 600 K 6. Which of the following Scatchard plot indicates that compound A has the same binding site with compound B, but binds to the ligand twice stronger? Y │. (交點在軸上) Y │＼　　　　　　 Y │\ A── ─ │\＼ ─ │　＼ ─ │ \ B── [L] │ \ ＼ [L] │　　＼ [L] │ \ │ \ ＼ │＼　　＼ │＼ \ │ \ ＼ │　＼　　＼ │ ＼\ │ \ ＼ │　　＼　　＼ │ .(交點在軸上) └────── └────── └────── (a) Y (b) Y (c) Y k1 k2 7. For the reaction A ─→ B ─→ C If k1>>k2, which of the following graph best describes the time course of the concentration position? conc. conc. conc. │[A] │[A] │[A] │\　 　＿＿＿ [B] │\　[B] 　＿＿ [C] │\ 　 　＿＿ [C] │ \　／　＿＿＿ [C] │ \ /\ ／ │ \　　／ │ Ｘ　／ │ X Ｘ │ ＼／ │ / Ｘ＿ │ / Ｘ ＼ │ ／＼ │.／　 　─── │/／　＼ ＼ │／──====== [B] └──────── └──────── └──────── (a) time (b) time (c) time 8. A protein can exist in two stable conformations, with the energy of conformation A higher than that of conformation B by 2.785 kJ/mol. What is the equilibrium temperature, when 25% of total protein is found in conformation A? (a) 295 K (b) 300 K (c) 305K (d) 310 K 9. A new ribonuclease (a protein) now has 6 systine residues (with -SH functional group) which forms 3 disulfide linkage (-S-S-) in the folded protein. According to Nobel winner Anfinsen's thermodynamic folding experiment, what is the percentage of enzyme activity in his control experiment (denature first, oxidize and then remove urea)? (a) ~1% (b) ~7% (c) ~15% (d) ~30% 10. What does the shaded area of the figure (right) correspond to? (a)w (b)w (c)q (d) S C│ rev irrev │　＿＿＿ │／|::::| │ |::::| └──── T T1 T2 Section 3: Short questions (20 points, 4 pts each) ※ Use the space below to provide a short calculation / description on the questions. If possible, try to use quantitative statement (including equations) and figures to illustrate your reasoning. 1. Consider a molecular system of only three energy levels in equilibrium at 300 K with Boltzmann distribution. To make your calcutation easier, use kB = 1.0 J/molecule-K. The energy levels have energy 0 J, 600 J, and 1200 J, respectively. There are total of 1000 molecules in the system. Calculate the number of molecules occupied in the energy level of 0J at equilibrium (report no decima point). 2. For a system with only two energy levels (two-level system), the heat capacity (Cv) is found to approach zero when the temperature is low (T→0) and also when the temperature is high (T→∞). Does this observation apply to systems with infinite energy levels? Explain why. 3. For a simple solution, the Gibbs free energy usually has a linear temperature dependence. However, for a process involving hydrophobic interaction, such as micelle formation and protein folding, the temperature dependence of the Gibbs energy is not linear, but reaches a maximum in the intermediate temperature. Explain which factor is contributed to this observation. k1 k2 4. For a process of A ===== B ─→ C, explain the conditions of which each of k-1 the following approximations can be used (a).equilibrium approximation and (b). steady-state approximation. 5. Benzene and toluene form ideal solution mixture. At 1.013 bar, the boiling temperatures of benzene and toluene are 80℃ and 110℃. Use the information above th sketch a plot of temperature (x-axis) molar fraction of toluene (y-axis) for this ideal mixture. Draw a bubble line (solid), a dew-poimt line (dotted), and indicate which area corresponds to the vapor phase. Section 4: Ling questions (50 points) 1. (14 points) There are several reaction pathways that drugs can be used to inhibit enzyme activity. In one of the reaction schemes (non-competitive inhibitor), the enzyme (E) has different biding sites for its normal substrate (S), and the drog (called inhibitor, I). The enzyme can adopt several forms: E, ES, EI and ESI state and the only active state of the enzyme is ES state. E + S ==== ES KM E + S ==== EI KI E + S + I ======= ESI KM*KI Where K and K are dissociation constants M I (1a). (7 points) The fraction of enzymes is ES state (YES) can be expressed by: [ES] Y = ────────────── ES [E] + [ES] + [EI] + [ESI] YES can be expressed in the standard Langmuir binding form, with [S] Y = ( Y ) ─────── ES Max K + [S] App. Derive this, and figure out the expression of Ymax, and Kapp. (1b). (7 points) Assume you can make Michelis-Menton kinetics measurement of this inhibition reaction at three different inhiditor concentrations, with [I]a > [I]b > [I]c. Make a Lineweaver-Burk plot (1/v0 v.s. 1/[S]) with three curves, each corresponds to one inhibitor concentration. Mark your curves with [I]a, [I]b, [I]c. (Hint: write out v0 using the information from part (a).) │1/v0 │ │ │ ────┴──── 1/[S] 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℃. (2a) Calculate the values of w, ΔH, ΔSsys, and ΔG for this process. (2b) Can you ues the ΔG value you calculated above to predict whether this process is spontaneous or not? Explain. 3. (14 points) For a chemical reaction of k1 A + B ===== P k-1 Using temperature-jump method, it is found that at 280K, the relaxation time th reach the new equilibrium is τ = 10 ns with equilibrium concentrations of [A] = 4 mM, [B] = 1 mM, and [P] = 0.4 mM. (3a). Calculate the equilibrium constant (2 points) and forward rate constant k1 (4 points) at 280 K. (3b). Another measurement at 300 K returns: Keq = 80, k1 = 1.24×10^10 M^-1*s^-1. Calculate the activation energy of the forward A + B → P reaction. (4 points) (3c). Calculate the standard enthalpy ΔH° of the forward reaction (A + B → P), assuming ΔH°is a constant between 280 K and 300 K. (4 points) 4. (12 points) Consider a solid consisting of N atoms, each of which has a magnetic dipole monent. When a magnetic field is applied to the solid, each dipole either points paralled to the magnetic field (with interaction energy of -μH) or antiparallel to the magnetic field (with energy of +μH). Nothing else is allowed. The system is contact with a heat reservoir which is at temperature of T. (4a). What is the partition function Q for the system consisting N distinguishable atoms? (4b). Using Q to figure out the average energy U of this N-atom system at temperature T? (4c). Based on (4b), what is the energy of this N-atom system in the limit of T→0? (4d). If the magnetic field is turned off, while the solid is at a temperature close to T = 0, the energy of the spin system will change. Based on your previous answers, calculate the change of the energy. Be careful, signs are inportant. A positive answer means the energy increases, and a negative answer means the energy decreases. (4e). As stated earlier, the system is in contact with a heat reservoir. If the heat reservoir is finite, its temperature can change if heat is added or removed, Suppose it is finite. Based on your work so far, what will happen to the temperature of the reservoir? (increase? dearease? stay the same?) --

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