111年 - [非官方正解]111 國立中山大學_碩士班暨碩士在職專班招生考試_化學系：物理化學及分析化學#126341

1. Before doing the Joule experiment, which of following statement is NOT correct?
(A) We need to know Cv (B) Design a dU = 0 experiment (C) We need to know µ_J first (D) Create an adiabatic free expansion process.

2. In an isothermal reversible expansion process for an ideal gas, which of following statement is NOT correct?
(A) ∆U=0 (B) AT=0 (C) dq ≠0 (D)

3. At 300K, which gas has a negative Joule-Thomson coefficient?
(A) He (B) Ar (C) CO₂ (D) N₂

4. What is the correct relationship between Cp and S? (A)(B) as dP=0, dS = dT (C) as dP=0, dS = C_pdT (D) dV=0, dS = dP

5. If we mix 0.3 mole of pure benzene with 0.7 mole of pure toluene at temperature T. Assume this mixture is an ideal solution. What is △Gmix? (A) 0.7Rln0.3 + 0.3Rln0.7 (B) 0.7RTln0.3 + 0.3RTln0.7 (C) 0.3Rln0.3 + 0.7Rln0.7 (D) 0.7RTln0.7 +0.3RTln0.3

6. Please estimate the molecular density for 1 mole ideal gas per cm³ at 1 torr and 300 K?
(A)~3.2×10¹⁴ (B) ~3.2×10¹⁵ (C)~3.2×10¹⁶ (D) ~3.2×10¹⁷

7. In terms of energy, 3 GHz is identical to X wavenumber (cm¯¹), What is X?
(A) 1 (B) 0.5 (C) 30 (D) 0.1

8. What is the boundary condition for a "particle on a ring" model?
(A) ψ(0) = ψ(2π) (B) ψ(0) = ψ(π) (C) ψ(0) = ψ
(D) ψ(0) = 0, ψ(2π) = 0

9. The lowest eigenvalue for a H atom is -13.6 eV. Calculate the energy uncertainty if the lifetime in the given state is 1.0 nanosecond? (A) 4.74 μεν (B) 38.1 μεV (C) 0.33 μεV (D) 1.35 μεν

10. The (θ, Φ) is an eigenfunction of, so what is the eigenvalue?
(A) 2ħ (B) 2ħ² (C) 6ħ² (D) 4ħ²

11. What kind of symmetry operation is for determination of the minus sign of ³Σg^-?
(A)σ_υ (B) C_∞v (C) S(φ) (D) C₂

12. The rate constant for the reaction 2I→ I₂ is 7.0x10⁶ m³mol^-1s^-¹ at
296 K and 7.7×10⁶ m³mol^-1s^-¹ at 303 K. What is E_a (kJ/mol)?
(A) 16.5 (B) 35.5 (C) 10.2 (D) 185

13. If the population decay channels of the excited state decay include three channels, such as fluorescence channel (kF = 10⁹ s¯¹), internal conversion channel (k_ıc = 10¹² s¯¹), and intersystem crossing channel (k_Isc = 10³ s¯¹), what is the observed fluorescence lifetime TF? (A) 1 psec (B) 1msec (C) 1 nsec (D) 1 µsec

14. If we want to acquire a Raman spectrum with a 785 nm laser for exciting a C-H stretching at 3000 cm-¹, what Stokes peak in nanometer (nm) will be appeared in the Raman spectrometer? (A) 985 (B) 1064 (C) 1027 (D) 633

15. At room temperature, which kind of molecular motion has least contribution to the entropy for CH₄?
(A) Rotation (B) Vibration (C) Translation (D) Electronic

1. The equation of state of a van der Waals gas is given as (P+) (V – b) = RT, where a, b, and R are constants. Derive the critical temperature Tc. (10%)

2. Find ＜P_x＞, ＜P_x²＞ for n=1 state of a particle in a 1D box with a length L. (10%)

3. What is the difference between the end point and equivalence point in a volumetric titration? (5%)
How do you correct this "difference" in an acid-base titration? (5%)

(a) increasing ionic strength
(3%);

(b) increasing ionic charge (3%);

(c) decreasing hydrated radius (3%). Which statements are true?

5. The concentration of the alkane C₂₀H₄₂ (molecular weight: 282.55) in a particular sample of rainwater is 0.2 ppb. Assume that the density of rainwater is close to 1.00 g/mL and find the molar concentration of C₂₀H₄₂. (10%)

6. A 0.0450 M solution of benzoic acid has a pH of 2.78. Calculate pKa for this acid. (10%)

7. Calculate the pH of 5.0 × 10^-8 M HClO₄.(7%) What fraction of the total H⁺ in this solution is derivedfrom the dissociation of water? (4%)