課程名稱︰普通化學甲上 課程性質︰物理系、材料系合班 課程教師︰陸駿逸 開課學院：理學院 開課系所︰化學系 考試日期（年月日）︰2019/1/9 考試時限（分鐘）：120分鐘 是否發放獎勵金：是 試題 : General Chemistry (1)(24pts) Write down the chemical formulas of the following molecules： (a)Potassium tetraisothiocyanatocobaltate(II) (b)Silver hexacyanoferrate(II) (c)3-Propyl-2-hexene (d)2,3-Dimethylpentane (e)4-Ethyl-2-heptyne (f)cis-4-octene (2)(24pts) Consider the molecular orbital of HF molecule ΨMO(r)=N(CAψA(r)+CBψB(r)), where ψA(r) is the 1s of H atom, and ψB(r) is the 2pz of F atom. Suppose that HAA=-13.6eV, HBB=-17.4eV, HAB=-1eV, S≒0. (a) Express the averaged energy <E> in terms of the MO coefficients CA and CB. (b) Differentiate the averaged energy with respect to CA and CB to obtain the optimized conditions for the coefficients. (c) Solve the energies and the coefficient ratios CB/CA for the two MOs. (3)(10pts) Predict whether the nitrosyl ion (NO^+) will have a shorter or a longer bond than the nitrogen oxide molecule (NO). Will NO^+ be paramagnetic like NO or diamagnetic? (4)(20pts) The bonding of the nitrite ion (NO_2-) can be discussed either by Lewis resonance diagrams or by the molecular orbitals. (a) Predict the geometric shape of the ion using VSEPR theory. (b) Draw the possible Lewis resonance diagrams for the ion. (c) Draw qualitatively the molecular orbitals and the correlation diagram for the π system of this ion. (5)(10pts) Predict and explain the energy levels splitting of the d orbitals in the tetrahedral crystal fields. (6)(10pts) The octahedral complex ion [MnCl6]^3- has more unpaired spins than the octahedral complex ion [Mn(CN)6]^3-. How many unpaired electrons are present in each species? Explain. In each case, express the CFSE in terms of Δ_0. (7)(20pts) In the bonding of Mn^4+ and the ligands in the octahedral complexes, the π bonds with the ligands Br^- and CO have the opposite effect on the d orbital energy gap. Compare [MnBr6]^2- with [Mn(CO)6]^4+. Which one has a larger energy gap? Draw the appropriate MO correlation diagram to explain your answer. (8)(20pts) Solve the energy and the MO wave function of the π system of the linear molecule C6H8. Let α≡∫drψ1Hψ1 and β≡∫drψ1Hψ2 where H is the hamiltonian, ψ1 is the 2pz atomic orbital of one carbon atom, ψ2 is the 2pz atomic orbital of the nearest neighboring carbon atom. (9)(20pts) Suppose an electron is confined in a cubic box of length L in each side. Consider the energy levels Ψ=c_nsin(nxπ/L)sin(yπ/L)sin(zπ/L) with the corresponding energies E_n where n=1,2,3,4. The incident EM wave has the electric field in the x direction, to induce transitions from Ψ1 to the excited states. With the suitable EM wave frequency ω=2π(Em-E1)/h for m=2,3,4, which transition(s) can actually happen? Explain your answer. 備註：可以使用工程計算機 --

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