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Physical Chemistry Test (A) Dalian University of Technology Name Course: Physical Chemistry Date: Jan 16, 2009 No. Department Standard Score Test: Total page: 8 (A) Type: close book I II III IV V VI VII VIII Total 10 16 18 10 12 10 16 8 100 Scoring Grade: Fundamental Constants: Avogadro constant: L= 6.022 1023mol-1; Class: The mass of electron I. Plank constant h=6.626 10-34J s m = 9.109×10-28g True or False (10 points ) Direction: Write “T” in the bracket before the sentence, which you think to be correct, and “F” to be wrong. [ ] 1. Surfactants lower the surface tension of liquids in which they are dissolved. [ ] 2. All the particles have the characteristics classically ascribed to waves. [ ] 3. Milk is a water -in- oil emulsion of water in butterfat. [ ] 4. A saddle point is not maximum point on the potential energy surface. [ ] 5. The Born-Oppenheimer Approximation treats atoms as having fixed nuclei. [ ] 6. In quantum mechanics, the orbital is a mathematical expression, describing the probability of finding an electron at some point near the nucleus. [ ] 7. General speaking, the energies of particles cannot be varied continuously. [ ] 8. When the labels of any two identical fermions are exchanged, the total wavefunction changes sign. [ ] 9. Due to surface tension, liquids try to have the minimum surface. [ ] 10. It is impossible to specify simultaneously, with arbitrary precision, both the momentum and the position of a quantum particle. 1 Physical Chemistry Test (A) II. Selection (16 points) Direction: Choose the best answer for each question and write the letter of your selection in the corresponding brackets. [ ] 1. The equation for the "electronic" Hamiltonian neglects which term in the original equation? (A) the term to calculate the kinetic energy of the electrons (B) the term for kinetic energy for nuclei (C) the term to describe the repulsive force of an electron on another electron (D) the term to calculate the repulsive force of a nucleus on another nucleus [ ] 2. A silver iodide sol was prepared by mixing KI and Ag NO3 solution with the KI in slight excess, the silver iodide sol particle is [ (A) Positively charged (B) negatively charged (C) electrically neutral (D) uncertainty ] 3. The PCl5 molecule consists of the elements( multi-choice): (A)C3 [ (B) (C) C2 (D) i ] 4. If is the fraction of the surface occupied by adsorbate molecules at equilibrium, then, according to the Langmuir theory, the rate of adsorption is given by (A) k (1– ) (B) k (C) k p (D) k (1– ) p where k is a constant. [ ] 5. The HCN molecule belong to the point group: (A) C2v [ ] 6. (B) Td (C) C∞v The probability of locating an electron is calculated by the (A) square of the Hamiltonian (B) square of the wavefunction (C) square of the energy of the system [ ] 7. (D) D6h The Schrödinger's Equation (A) cannot be used to solve one-electron atoms (B) can be solved exactly only for one-electron atoms (C) is not used for large molecules 2 Physical Chemistry Test (A) ] 8. If a liquid of density rises in a capillary of radius r to a height h cm, and is [ the contact angle, then the surface tension of the liquid is (A) 1 rhg cos 2 (B) r gρ h 2 cos θ (C) 2 cosθ rhρh (D) 2rh g cos III Fill in the blanks (18 points) 1 Write down the Hamiltonion of a rigid rotor. 2 In a case of a particle moving in a cubic box of edge a, calculate the degeneracy corresponding to energy (E) equal to 14h2/8ma2. ( E nx , n y , nz 2 h 2 n x2 n y n z2 ( 2 2 2) ) 8m a a a 3 Write down the Hamiltonion of a harmonic oscillator. . 4 The assumptions of ab initio quantum chemistry are: , and . 5 Does the vibration of a homonuclear diatomic molecule (e.g. O2, N2, etc.) result in infrared absorption and why? . 6 Distinguish between a fermion and a boson. . 7 Identify the point groups to which the following objects belong: (a) a sphere , (b) an isosceles triangle , (c) an equilateral triangle , (d) an unsharpened cylindrical pencil . 8 The Langmuir adsorption isotherm is based on the following assumptions: (i) ; (ii) ; (iii) ; (iv) . 9 Please indicate the direction of excess pressure p of the curved surface with arrow on the following diagram: 3 Physical Chemistry Test (A) IV (10 points) The following data for the gas – phase decomposition reaction 2A (g) 2Y (g) + Z (g) were obtained. Reaction Temperature Initial pressure of A Half-life period T/K PA,0/kPa t1/2/s 950 39.4 1520 950 157.6 380 1020 7.8 1378 1020 50.7 212 The rate law can be expressed as dpA k A pAn . dt (a) Determine the reaction order n. (b) Calculate the rate coefficient kA (950K) and kA (1020K). (c) Calculate the activation energy Ea. 4 Physical Chemistry Test (A) V (12points) Answer the following questions: 1 What are the assumptions of quantum mechanics? 2 Discuss the approximations built into the Hückel method(HMO). 3 How to convert physical observables into their operators in quantum mechanics? 5 Physical Chemistry Test (A) 4 Discuss the steps involved in the calculation of the energy of a system by using the variation principle. VI (10points) Derive the rate law for the decomposition of ozone in the reaction, 2O3(g) → 3O2(g), on the basis of the following proposed mechanism: 6 Physical Chemistry Test (A) VII (16 points) (1)Calculate the following partition function of 1mole N2 at 25℃ and 100 kPa. For N2, the moment of inertia I=1.394 10 frequency v = 7.705 10 –13 s –1 (a) translational partition function qt; (b) rotational partition function qr; (c) vibrational partition function qv. 7 –46 kg m2, the vibration Physical Chemistry Test (A) (2) Write down the Schrödinger equation of He, calculate the orbital energy, the angle between the orbital angular momentum and z axis, and the angle between the spin angular momentum and z axis of 4,3,1,1/2 (He+). VIII (8 points) List the symmetry elements of NO2 molecule, construct the group multiplication table, name the point group to which it belongs, point out the normal subgoups and check up the table by multiplication table rule. 8