課程名稱︰物理化學二 課程性質︰必修 課程教師︰戴子安 開課學院：工學院 開課系所︰化工系 考試日期（年月日）︰101/4/2 考試時限（分鐘）：130 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Table 1.Chemical thermodynamic properties at 298.15K and 1bar. ╔═════╦═════╦═════╦═════╗ ║substance ║ Δ Hﾟ ║ Δ Gﾟ ║ _ ║ ║ ║ f ║ f ║ S ﾟ ║ ╠═════╬═════╬═════╬═════╣ ║ H (g) ║ 0 ║ 0 ║ 130.684 ║ ║　 2 ║ ║ ║　 　　　║ ╠═════╬═════╬═════╬═════╣ ║　 +　 ║ 0 ║ 0 ║ 0 ║ ║　 H (ao) ║ ║ ║ ║ ╠═════╬═════╬═════╬═════╣ ║　 -　 ║ -229.994 ║ -157.244 ║ -20.75 ║ ║　 OH (ao)║ ║ ║ ║ ╠═════╬═════╬═════╬═════╣ ║　 Cl (g) ║ 0 ║ 0 ║ 223.066 ║ ║　 2　 ║ ║ ║ ║ ╠═════╬═════╬═════╬═════╣ ║　 -　 ║ -167.159 ║ -131.228 ║ 56.5　 ║ ║　 Cl (ao)║ ║ ║ ║ ╠═════╬═════╬═════╬═════╣ ║ Ag(s) ║ 0 ║ 0 ║ 42.55 ║ ╠═════╬═════╬═════╬═════╣ ║　AgCl(s) ║ -127.068 ║ -109.789 ║ 96.2 ║ ╚═════╩═════╩═════╩═════╝ (kJ/mol) (kJ/mol) (J/K˙mol) 1.(30%) Explain the following terms. Using graph if necessary. (a) Describe how the EMF of a galvanic cell is measured by using a potentiometer. (b) Ionic atmosphere. + (c) Plot how typically the mean ionic activity coefficient of an ion, γ( ) - changes with increasing ionic strength, I from low I<0.01, to 0.01<I<0.1, and to high I>0.1. 1 + - (d) For the formation reaction of an hydrogen ion ---H (g) ---> H (ao) + e 2 2 _ - , what is the standard molar entropy for the electron, Sﾟ(e )? (e) Based on the lecture note, explain how a pH meter works. ^ (f) For an operator, A, what is its corresponding eigenfunction and eigenvalue. (g) The tunneling effect for a quantum mechanical particle in a finite depth box. (h) Explain why the zero point energy for a quantum mechanical harmonic oscillator is not zero. (i) Why is only one quantum number needed to characterize the eigenfunctions for rotation in two dimensions, whereas two quantum numbers are needed to characterize the eigenfunctions for rotation in three dimensions? (j) Why does the energy of a rotating molecule depend on l, but not on m ? l 2.(10%) For the galvanic cell H (1bar)∣HCl(ai)｜Cl (1bar), 2 2 δE the standard electromotive force at 298K is 1.3604V and (------) = -1.247E-3. δT P (a) for the cell reaction, what are the values of Δ Gﾟ,Δ Hﾟ,Δ Sﾟ? r r r - _ (b) For Cl (ao), what are the values of Δ Gﾟ,Δ Hﾟ,and Sﾟ? f f _ _ (Sﾟ(H )=130 J/K‧mol and Sﾟ(Cl )=130 J/K‧mol) 2 2 3.(25%) Consider the cell, Zn(s)∣ZnCl (0.005 m/kg)｜Hg Cl (s), Hg(l), for 2 2 2 - 2+ which the cell reaction is Hg Cl (s)+Zn(s) ---> 2Hg(l)+2Cl (aq)+Zn (aq). 2 2 2+ Given that Eﾟ(Zn ,Zn)=-0.7628V, Eﾟ(Hg Cl ,Hg)=0.2676V, and that the emf is 2 2 1.2272V. (a) wrie the Nernst equation for the cell. Determine: (b) the standard emf _ (c) Δ Gﾟ,Δ Gﾟand K r r (d) the mean ionic activity and the activity coefficient of ZnCl from the 2 measured emf (e) the mean ionic activity coefficient ZnCl from the Debye-Huckel limiting law. 4.(10%) Based on Planck's treatment, derive the expression of the total energy, E, for an N-atoms black body with the same vibrational frequency, ν at an absolute temperature of T. 5.(10%) Derive the energy and the normalized wave function for a quantum mechanical particle in a 1-D infinite-depth box from its corresponding Schrodinger equation. 6.(10%) The term "Space Quantization" is often used to describe how the plane of an orbiting electron, in an atom, can only have a certain numbers of orientations. For example, for l=2, where l is the angular momentum quantum number, plot the possible orientation for the angular momentum vectors, L and L and write down their corresponding magnitude. z 7.(5%) Calculate the degeneracies of the first three levels for a particle in a cubical box. 12 16 8.(10%) The C O molecule which rotates around its center of mass has an equilibrium bond displace of 112.8pm (1pm=1E-12m). Calculate (a) the reduced mass (b) the moment of inertia (c) the wavelength of the photon emitted when the molecule makes the transition from l=1 to l=0.(h=6.626E-34J) 9.(5%) Plot the space quantization for the two spin states of an electron. --

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