115年 - [無官方正解]115 國立中山大學_碩士班考試入學招生考試試題_化學系：物理化學及分析化學#138396

1. If the reaction 2HI → H₂ + I₂ is second order in HI, which plot is linear? (A) [HI] vs t (B) ln[HI] vs t (C) 1/[HI] vs t (D) 1/ln[HI] vs t (E) [HI]² vs t

2. For a reaction at constant pressure, the standard Gibbs energies at two temperatures are: Δ_rG°(298K) = −12.0 kJ mol⁻¹, Δ_rG°(348K) = −5.0 kJ mol⁻¹. Using the Gibbs-Helmholtz equation:

what can be concluded about the sign of Δ_rH°? (assuming that ΔrH° does not depend on T) (A) Δ_rH° = 0 (B) Δ_rH° ＞ 0 (endothermic) and Δ_rH° is around +54 kJ mol⁻¹ (C) Δ_rH° ＜ 0 (exothermic) (D) Cannot be inferred from ΔrG°(T) (E) Δ_rH° ＞ 0 (endothermic) and Δ_rH° is around +5.4 kJ mol⁻¹

3. An enzyme follows Michaelis-Menten kinetics with V_max = 120 μM min⁻¹ and K_m = 30 μM. What is the initial rate v₀ when the substrate concentration is [S] = 30 μM? (A) 15 μM min⁻¹ (B) 30 μM min⁻¹ (C) 60 μM min⁻¹ (D) 90 μM min⁻¹ (E) 120 μM min⁻¹

4. A reaction proceeds by the mechanism:
Assuming the steady-state approximation for the intermediate I (i.e., d[I]/dt ≈ 0), what is the rate law for product formation r = in terms of [A] and [B]? (A) r = k₂[A][B] (B) (C) (D) r = k₁[A][B] (E) r = k₂[I][B]

5. At the same temperature, the ratio of root-mean-square speeds (urms) of helium (M = 4.0 g mol⁻¹) to nitrogen (M = 28.0 g mol⁻¹), i.e., u_rms(He) / u_rms(N2), is closest to: (A) 0.38 (B) 0.53 (C) 1.0 (D) 2.6 (E) 7.0

6. For a reversible adiabatic expansion of an ideal gas: (A) q = 0 and ΔS_sys ＞ 0. (B) q = 0 and ΔS_sys = 0. (C) q ＜ 0 and ΔU = 0. (D) q = 0 and ΔH = 0. (E) w = 0 and ΔU ＜ 0.

7. The vapor pressure of a pure liquid is P₁ = 20.0 kPa at T₁ = 300 K. Its enthalpy of vaporization is approximately constant at ΔH_vap = 40.0 kJ mol⁻¹. Using the Clausius-Clapeyron equation, what is the vapor pressure P₂ at T₂ = 330 K (closest value)? (A) 25 kPa (B) 33 kPa (C) 45 kPa (D) 60 kPa (E) 90 kPa

8. For an one-dimensional harmonic oscillator with force constant k and mass m, which statement is wrong? (A) ω =. (B) Energy levels are equally spaced. (C) Zero-point energy isℏω. (D) ⟨x⟩ = 0 for every stationary state. (E) Each vibrational energy level is doubly degenerate.

9. Which function is not acceptable as an one quantum-mechanical wavefunction on (−∞, ∞)? (A) ψ(x) = Ae^⁻|x| (B) ψ(x) = Asin(πx) e^⁻x² (C) ψ(x) = A (D) ψ(x) = Ae^+x² (E) ψ(x) = A e^⁻x²/2

10. A vibrational mode can be approximated as a harmonic oscillator with energy spacing ΔE = hν. At T = 300 K, for ΔE = 6.0 kJ mol⁻¹ and equal degeneracies, what is the ratio N_v=1/N_v=0? (A) 0.02 (B) 0.06 (C) 0.09 (D) 0.22 (E) 0.55

11. For a particle in an one-dimension box of width L with two infinite potential wells, which statement is incorrect? (A) The energy eigenvalues scale as n² (B) The ground state has nonzero energy (C) The wavefunction has n − 1 interior nodes for level n (D) If L → ∞, the energy spectrum becomes continuous (E) Shifting the box in space changes the energy eigenvalues

12. In the Born-Oppenheimer approximation as used in quantum chemistry, which statement is most accurate? (A) Nuclear and electronic motions are treated with the same Hamiltonian and solved simultaneously. (B) Nuclear motion is neglected entirely; only electrons are considered to exist. (C) The total molecular wavefunction is approximated as a product of an electronic part and a nuclear part because nuclei move much more slowly than electrons. (D) Electron-nuclear Coulomb interactions are ignored so that electrons move in a field of non-interacting nuclei. (E) The approximation is only valid for atoms but not for molecules.

13. Which of the following ground-state electron configurations is incorrect according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle? (A) O: 1s² 2s² 2p⁴ (B) Na: 1s² 2s² 2p⁶ 3s¹ (C) Cl: 1s² 2s² 2p⁶ 3s² 3p⁵ (D) Fe: [Ar] 4s² 3d⁶ (E) Cu: [Ar] 4s² 3d⁹

14. Which Maxwell relation is correct? (A) (B) (C) (D)(E)

15. A rate constant k1 increases from 1.2 × 10⁻³ s⁻¹ at 300 K to 4.8 × 10⁻³ s⁻¹ at 330 K. Assuming Arrhenius behavior, the activation energy Ea is closest to: (A) 9.5 kJ mol⁻¹ (B) 19 kJ mol⁻¹ (C) 38 kJ mol⁻¹ (D) 76 kJ mol⁻¹ (E) 150 kJ mol⁻¹

16. For the reaction A ⇌ B, the equilibrium constant is K₁ = 2.0 at T₁ = 300 K and K₂ = 8.0 at T₂ = 330 K. Assume ΔH° is temperature-independent over this range. Using the Van't Hoff equation, what is ΔH° (closest value)? (A) −20 kJ mol⁻¹ (B) −10 kJ mol⁻¹ (C) +10 kJ mol⁻¹ (D) +20 kJ mol⁻¹ (E) +40 kJ mol⁻¹

17. Which of the following statements concerning laboratory safety is INCORRECT? (A) Safety goggles should be worn at all times in the laboratory. (B) Chemical waste should be disposed of according to laboratory regulations. (C) Concentrated acids should be diluted by adding water to acid. (D) Safety data sheets (SDS) provide important information about chemical hazards. (E) Spilled chemicals should be cleaned up immediately following proper procedures.

18. Which of the following statements is INCORRECT? (A) The number 1200 has two significant figures. (B) The Q test is used to determine whether a suspected data point is an outlier in a small data set. (C) Assuming a solution density of approximately 1.0 g/mL, 200 ppb Hg²⁺ is equivalent to 1.0 μM Hg²⁺. (D) The F test is used to compare the variances of two data sets to determine whether they are significantly different. (E) 0.4 (± 0.01) + 0.2 (± 0.02) + 0.1 (± 0.01) = 0.7 (± 0.04)

19. Which of the following statements concerning the operation of laboratory glassware in analytical experiments is INCORRECT? (A) An effective desiccant maintains a low humidity environment inside the desiccator. (B) The volume of an Eppendorf pipet is set before aspirating the liquid. (C) In water, the bottom of the meniscus should be read at eye level. (D) Volumetric glassware is calibrated at a specific temperature. (E) A buret should be rinsed only with distilled water before titration.

20. Which of the following statements concerning systematic errors and random errors is INCORRECT? (A) Random errors can be reduced by increasing the number of replicate measurements. (B) Systematic errors cause measurement results to be consistently biased in one direction. (C) Systematic errors can be detected and corrected by comparing with an reliable analytical technique. (D) Carbonate formation in standardized NaOH solutions affects only the equilibrium speciation of basic species and therefore does not result in a true systematic error in acid-base titrations. (E) The balance offset is a systematic error, and taring is the calibration step used to remove it.

21. The calibration curve for the determination of nitrate (NO3⁻) in agricultural runoff water using UV-visible spectrophotometry was found to be
A = 0.025 × [NO3⁻] + 0.080
where A is the absorbance measured at 220 nm and the nitrate concentration is expressed in μM. The reagent blank produced an absorbance of 0.060 ± 0.010. Which of the following statements is INCORRECT? (A) According to the Beer-Lambert law, increasing the optical path length of the cuvette enhances absorbance sensitivity for a given analyte concentration. (B) 0.080 represents the background absorbance arising from the reagent blank and the sample matrix. (C) The coefficient of determination (R²) can be greater than 1 when the calibration data show excellent linearity. (D) The relative standard deviation of the reagent blank measurement is 16.7%. (E) The limit of detection (LOD; signal to noise = 3) estimated from the blank standard deviation is 1.2 μM.

22. Which of the following statements concerning titration is INCORRECT? (A) During the titration of a weak acid with a strong base, the pH at the half-equivalence point is equal to the pKa of the acid. (B) In complexometric titrations, the conditional formation constant of the metal-EDTA complex depends on the solution pH. (C) Iodine acts as a strong oxidizing agent in acidic, neutral, and basic media and is commonly used as a primary standard without further purification. (D) In the Mohr method, potassium chromate is used as an indicator, and the titration must be carried out under slightly alkaline conditions. (E) The addition of ammonia in the EDTA titration of Zn²⁺ is to prevent the precipitation of Zn(OH)₂.

23. Which of the following statements concerning amperometry and voltammetry is INCORRECT? (A) All working electrodes share the same oxidation and reduction potential window, which is determined solely by the electrolyte. (B) In amperometric measurements, maintaining a constant applied potential allows selective monitoring of a specific redox reaction over time. (C) Under diffusion-controlled conditions, the peak current in cyclic voltammetry is proportional to the square root of the scan rate. (D) Pulse and differential pulse voltammetric techniques are designed to minimize charging current while enhancing faradaic current. (E) Faradaic current in voltammetry is limited by mass transport via diffusion, migration, and convection.

24. Which of the following statements concerning potentiometry is INCORRECT? (A) In a pH meter, the pH is determined by measuring the absolute electrical potential of an indicator electrode (B) The pH electrode uses a thin glass membrane that allows H⁺ ions to pass through (C) Potentiometric measurements are based on a two-electrode configuration consisting of an indicator electrode and a reference electrode. (D) A high-impedance voltmeter is required to avoid drawing current during potentiometric measurements. (E) The reference electrode provides a stable and reproducible potential.

25. Which of the following statements concerning X-ray radiation is INCORRECT? (A) X-ray photoelectron spectroscopy (XPS) determines the chemical states of elements. (B) X-ray diffraction (XRD) is based on the constructive interference of monochromatic X-rays. (C) Auger Electron Spectroscopy (AES) is extremely surface sensitive, typically probing the top 1-3 nm of a material. (D) Chemical shifts observed in XPS spectra arise primarily from differences in lattice spacing and long-range crystal order. (E) In the Auger effect, an electron fills an inner-shell vacancy and the released energy ejects a second electron.

26. Mass spectrometry plays a central role in diverse areas of chemistry for the characterization of chemical species. Which of the following statements is INCORRECT? (A) Mass spectrometry measures the mass-to-charge ratio (m/z) of ions rather than their absolute mass. (B) High-resolution mass spectrometry allows the determination of elemental composition. (C) Soft ionization techniques often produce intact molecular ions with minimal fragmentation. (D) Isotopic patterns in mass spectra can be used to confirm molecular formulas. (E) Electrospray ionization produces only singly charged ions regardless of molecular size.

27. Which of the following statements related to atomic spectroscopy is INCORRECT? (A) Atomic spectroscopy relies on electronic transitions of free atoms or atomic ions in the gas phase. (B) X-ray fluorescence provides better detection limits than inductively coupled plasma mass spectrometry (ICP-MS) for trace elements. (C) At higher plasma temperatures, a larger fraction of atoms occupies higher-energy excited states according to the Boltzmann distribution. (D) Collision/reaction cell technology is used in ICP-MS to reduce spectral interferences. (E) Graphite furnace atomic absorption spectroscopy provides higher sensitivity than flame AAS due to the longer residence time of atoms in the optical path.

28. Which of the following statements concerning matrix-assisted laser desorption ionization-time of flight-mass spectrometry (MALDI-TOF-MS) is INCORRECT? (A) MALDI-TOF-MS commonly detects analytes as protonated, such as [M+H]⁺, rather than as bare molecular ions. (B) Delayed extraction in MALDI-TOF-MS improves mass resolution by compensating for initial kinetic energy dispersion of the ions. (C) MALDI-TOF-MS is well suited for the analysis of high-molecular-weight biomolecules. (D) The matrix in MALDI serves only as an inert support and does not participate in the ionization process. (E) In MALDI-TOF-MS, time-of-flight analysis separates ions based on their mass-to-charge ratio by measuring their flight times under a fixed accelerating potential.

29. Which of the following factors can enhance separation efficiency in chromatographic separations?
 (i) Use of uniform stationary phase particle sizes
(ii) Operation at a flow rate close to the Van Deemter optimum
(iii) Thin stationary-phase film thickness
(iv) Slow diffusion coefficient of analytes in the stationary phase
(v) Use of a narrow internal-diameter column
(vi) Use of small packing particle sizes
(vii) Creation of a large detector cell (detection window)
(viii) Injection of a large sample volume (A) (i), (ii), (iii), (iv) (B) (i), (ii), (v), (vi) (C) (iii), (iv), (vii), (viii) (D) (ii), (v), (vi), (vii) (E) (i), (iii), (vi), (viii)

30. Which of the following methods can be used for the separation of a mixture of Li⁺, Na⁺, and K⁺, and NH4⁺ in real-world samples?
(i) Ion-exchange chromatography
(ii) Ion-pair chromatography
(iii) Ion-exclusion chromatography
(iv) Reversed-phase high-performance liquid chromatography
(v) Normal-phase high-performance liquid chromatography
(vi) Size-exclusion chromatography
(vii) Capillary zone electrophoresis (A) i, ii, vii (B) i, iii, iv (C) ii, iv, v (D) iii, vi, vii (E) iv, v, vi

31. Which of the following statements concerning fluorescence is INCORRECT? (A) The fluorescence lifetime of small molecules is typically on the order of nanoseconds. (B) The fluorescence quantum yield is dependent of excitation power under normal experimental conditions. (C) Fluorescence occurs from the relaxation of an excited singlet state to the ground singlet state. (D) Fluorescence emission generally occurs at a longer wavelength than the excitation light due to the Stokes shift. (E) Fluorescence quenching can occur via dynamic or static mechanisms.

32. Which of the following statements concerning Raman is INCORRECT? (A) Raman scattering arises from changes in molecular polarizability during vibrational motion. (B) The Stokes signal arises from inelastic photon scattering, producing a lower-energy shift relative to the excitation light. (C) A bandpass filter is used to reject the intense Rayleigh-scattered light at the laser wavelength, allowing Raman-shifted signals to be detected. (D) Raman scattering from Raman-active analytes increases with decreasing excitation wavelength. (E) Raman scattering from Raman-active analytes is enhanced in the presence of silver nanoparticles due to surface-enhanced Raman scattering.

33. Which of the following statements concerning the advantages of Fourier transform infrared spectroscopy (FT-IR)?
(i) High signal-to-noise ratio due to the multiplex (Fellgett) advantage.
 (ii) FT-IR provides higher spectral resolution solely by using narrower slits.
(iii) High wavenumber accuracy provided by an internal laser reference.
(iv) Photomultiplier tube detectors are commonly used in FT-IR spectroscopy.
(v) A sodium chloride window is commonly used in FT-IR spectroscopy (A) (i), (iii), (v) (B) (i), (ii), (iii) (C) (ii), (iv) (D) (i), (iv), (v) (E) (iii), (iv)

34. An unknown volatile organic compound is analyzed by gas chromatography and is found to produce clear signals when detected using a thermal conductivity detector (TCD), an electron capture detector (ECD), and a nitrogen-phosphorus detector (NPD). Based on this information, which of the following elemental compositions is most likely present in the compound? (A) Carbon, Chlorine, Hydrogen (B) Carbon, Nitrogen, Bromine (C) Carbon, Chlorine, Boron (D) Carbon, Nitrogen, Chlorine (E) Carbon, Oxygen, Sulfur

35. Which of the following statements concerning activity is INCORRECT? (A) With increasing ionic strength, the activity coefficient becomes smaller. (B) An increase in the hydrodynamic radius of ions leads to a higher activity coefficient. (C) In the absence of dissolved CO2, the pH of water in 0.1 M NaCl is slightly higher than 7.0. (D) The activity is defined as the product of the molar concentration and the activity coefficient. (E) AgCl becomes more soluble in 0.1 M NaNO3.

36. Which of the following statements concerning precipitation is INCORRECT? (A) The precipitation involves two steps, including nucleation and particle growth. (B) In homogeneous precipitation, the precipitating species is produced gradually and uniformly within the bulk solution. (C) The electrical double layer is composed of a charged surface and an oppositely charged ionic layer in the surrounding solution. (D) The surface charge of the formed AgCl becomes negative when an excess amount of NaCl is added to a solution of AgNO3. (E) Large, well-formed crystals are obtained by maintaining high supersaturation.

37. Which of the following gradient techniques are most appropriately used in the respective chromatographic methods: (i) gas chromatography (GC), (ii) high-performance liquid chromatography (HPLC), and (iii) supercritical fluid chromatography (SFC)? (A) (i) Solvent composition gradient, (ii) Temperature gradient, and (iii) pH gradient (B) (i) Temperature gradient, (ii) Solvent composition gradient, and (iii) Pressure gradient (C) (i) Pressure gradient, (ii) pH gradient, and (iii) Temperature gradient (D) (i) Flow-rate gradient, (ii) Temperature gradient, and (iii) Solvent composition gradient (E) (i) Temperature gradient, (ii) Flow-rate gradient, and (iii) pH gradient

38. Which of the following statements concerning phosphorescence is INCORRECT? (A) Phosphorescence is the emission of light resulting from the spin-forbidden transition from an excited triplet state to the singlet ground state. (B) The phosphorescence quantum yield depends on the efficiency of intersystem crossing. (C) Heavy atoms enhance phosphorescence by increasing spin-orbit coupling and promoting intersystem crossing. (D) Phosphorescence emission disappears immediately when the excitation source is removed. (E) Intersystem crossing from an excited singlet state to a triplet state precedes phosphorescence.

39. Which of the following statements concerning microelectrode is INCORRECT? (A) Microelectrodes can provide high sensitivity because they have a large double-layer capacitance at the electrode-solution interface. (B) Microelectrodes have at least one dimension in the micrometer range, resulting in enhanced mass transport by radial diffusion. (C) Microelectrodes are well suited for fast cyclic voltammetry. (D) Microelectrodes allow electrochemical measurements in solutions with high resistance and minimal supporting electrolyte. (E) Microelectrodes exhibit reduced charging currents compared with conventional electrodes.

40. Which of the following statements concerning optical components is INCORRECT? (A) Lenses made of quartz are suitable for ultraviolet (UV) spectroscopy (B) The resolution of a monochromator increases with narrower slits, higher grating groove density, longer focal length, and higher diffraction order. (C) Laser operation does not require population inversion. (D) An interference filter selectively transmits a narrow wavelength band using thin-film interference. (E) Microelectrodes exhibit reduced charging currents compared with conventional electrodes.

41. Which of the following statements concerning extraction is INCORRECT? (A) The recovery of the extraction is defined as the ratio of the instrument signal after extraction to the signal before extraction. (B) Extraction can effectively alleviate matrix effects. (C) Methanol is added in supercritical fluid extraction (SFE) to facilitate the extraction of polar compounds such as ibuprofen. (D) The suitable stationary phase of a solid-phase extraction cartridge for extracting tertiary amine drugs (e.g., lidocaine) is a strong cation-exchange sorbent. (E) Lowering the pH of the solution enhances the extraction of propionic acid (pK_a = 4.0).