课程名称︰普通化学一 课程性质︰化学系必修 课程教师︰郑原忠 开课学院：理学院 开课系所︰化学系 考试日期（年月日）︰101年1月11日 考试时限（分钟）：120分钟 (助教延长到130分钟) 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : General Chemistry (I) Final Exam Date: 1/10/2012 100 pts + 20 pts bonus ; (总分最高计算至100分) ┌────────────────────┐ │c = 3.0*10^8 m/s │ │mass of electron = 9.1*10^(-31) kg │ │h = 6.626*10^(-34) Js │ │1 eV = 1.60*10^(-19) J │ │Ry = -13.6 eV │ │k_B = 1.38*10^(-23) J/K │ │R = 0.082 L-atm/K-mol │ └────────────────────┘ 1.(15%) Considr the LCAO-MO model for the hydrogen molecular ion with hydrogen 1s and 2s AOs as the basis functions. (a)(5%) Give the LCAO molecular orbitals. You should give the normalization constants in terms of the overlap integrals. (b)(5%) Draw a qualitative MO correlation diagram to denote the energy lev- els of atomic and molecular orbitals. Denote the allowed electronic transition on the diagram. (c)(5%) If a molecule of H2(+) absorbs a photon and is excited to the low- est electronic excited state, predict what happens to the molecule. 2.(20%) Consider thermal equilibrium at a temperature of 450 K, estimate the following ratios: (a)(5%) The number of hydrogen atoms in the first electronic excited state to the number in the electronic ground state. [老师提示请大家特别注意 degeneracy] (b)(5%) The number of molecules in the first excited vicrational state of the molecule N2 to the number in the ground state. The vibrational frequency of N2 is 7.07*10^(13) s^(-1). (c)(5%) The number of molecules in the first excited rotational state of the molecule CO (C-12, O-16) to the number in the ground state.The first absorption line in the pure ratational spectrum of gaseous CO has the frequency 1.15*10^(11) s^(-1). (d)(5%) The number of protons in the spin α state (parallel to the magne- tic field) to the number in the β state of a TMS solution sample placed inside a 300 MHz NMR machine. 3.(30%) Consider the following chemical reaction at 300 K and 1 atm (unbal- anced): PbO2 (s) + HNO3 (aq) → Pb(NO3)2 (aq) + H2O (l) + O2 (g) (a)(5%) Balance the chemical equation. (b)(5%) Give the oxidation number of each atom that chamges oxidation state in the course of the reaction. Which species is oxidized and which is reduced? (c)(3%) Which species is acid and which is base? (d)(2%) Rewrite the equation as a net ionic equation. (e)(5%) What volume of a 3 M solution of nitric acid is just sufficient to react with 11.95 g of lead(IV) oxide? (atomic masses: Pb: 207, N: 14, O: 16) (f)(5%) Following (e), estimate the volume of oxygen released when the re- action is completed. (g)(5%) Following (e), estimate the boiling point of the remaining solution The boiling-point elevation constant of water is Kb = 0.512 degC-kg/mol. 4.(10%) Consider gaseous CO2: (a)(2%) Give the Lewis structure and predict the equilibrium structure of CO2 using VSEPR. (b)(2%) How many vibrational modes does CO2 have? Explain your answer. (c)(3%) Sketch the stretching vibrational modes of CO2. Denote the IR acti- vity of each mode. (d)(3%) Sketch the bending vibrational modes of CO2. Denote the IR activity and degeneracy. 5.(10%) The P-T phase diagram of nitrogen is shown on the right. 10^3┌──────────┬───────────────────────┐ │ 　　／￣ │ 10^2├ 　／ │ │ ／ │ 10├ │ │ │ │ ─˙ │ 1├ │ ／ │ │ │ / │ 10^-1├ │ / ˙ │ │ │/ │ 10^-2├ ˙ │ │ / │ 10^-3├ / │ │ / │ 10^-4├ / │ │ / │ 10^-5└─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴┘ 0 100 200 300 纵轴: pressure (MPa) 横轴: temperature (K) (a) Sketch the same graph on your answer sheet and label the zones and points indicated on the diagram. Specifically label the name and (P,T) coordinates of the three points denoted by the black dots. (b) Some nitrogen starts out at room temperature and 1 atm. It is compre- ssed to reach the pressure of 1000 MPa at constant temperature, and then cooled down to 80K at constant pressure. Next it is decompressed at 80K back to 1 atm and finally heated to room temperature at constant pressure. Describe the phases and state transitions during the whole cycle. 6.(15%) The Maxwell-Boltzmann velocity distribution is → → f( v ) = (m/2πk T)^(3/2) * exp[-m|v|^2 / 2k T] B B (a) Give the Maxwell-Boltzmann speed distribution (no need to carry out in- tegration.) What is its physical meaning? Give the definition of the variables and constants in your expression. (b) Calculate the most probable speed of a gaseous molecule described by the Maxwell-Boltzmann speed distribution. (c) Calculate the average speed of a gaseous molecule described by the Max- well-Boltzmann speed distribution. ∞ (∫ x^(2n+1) * exp[-ax^2] dx = n!/[2a^(n+1)] , a>0; n positive integer) 0 7.(Bonus,10%) When sulfuric acid (boiling point = 290 degC) is mixed with water at 98% weight, an azeotrope with a boiling point of 338 degC is formed. (a) Sketch a diagram of the dependence of boiling temperature on mole frac- tion of sulfuric acid in the mixture to explain why distilling a 1 M solution of sulfuric acid does not give you pure sulfuric acid? (atomic masses: S: 32, O: 16) (b) Is sulfuric acid-water mixture a maximum-boiling azeotrope or a minimum -boiling azeotrope? Does the mixture deviate positively or negatively from the Raoult's law? Rationalize the results based on a consideration of inter-molecular interactions. 8.(Bonus,10%) Consider a harmonic oscillator with vibrational frequency ν_0 that is in cintact with a heat bath at thermal equilibrium of temperature T. Is the rate as the oscillator is excited from n=0 to n=1 level greater than the rate for the reverse process? What is the ratio of the rate constants? [Hint: think of the dynamical equilibrium between the two states] --

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