109年 - 109 國立台灣大學_碩士班招生考試：物化分析#90697

選擇題 (10)

1.Given the following dataset: 7, 5, 9, 15, 11, 8, 10. Which of the following is correct? (3%) (A) Mean = 9 (B) Median = 9.3 (C)Variance (σ²) = 8.78 (D)Sample size (n) = 6 (E)Standard deviation (σ) = 4.11

2. The shaded area accounts for approximately what percentage of the total area under the curve? (3%) (A) 5.5% (B) 10.7% (C) 13.5% (D)25.4% (E) 68.2%

3. A research group at NTU had studied the effect of a potential anticancer drug X. In their randomized trial, one group of mice was given X and another group was given sugar pills (placebo). Tumor size in many mice had reduced, and they reported the p-value to be p = 0.02. Which of the following interpretation is correct? (3%) (A) There is a 98% chance drug X is an effective anticancer drug. (B)There is a 98% chance that this experiment can be reproduced by other scientists. (C) There is a 2% chance drug X is an ineffective anticancer drug. (D)There is a 2% chance to observe the tumor reduction results seen in this study even if drug X has no effect at all. (E) Ail of the above.

4.Which of the following statements about UV-Vis spectrometry is correct? (3%) (A) Absorbance （A）is defined a A = , where Po and P represent the power of the light beam that has passed through the solvent and the analyte-containing solution, respectively. (B) Absorbance（A） is the reciprocal of transmittance (T); in other words, A = 1/T. (C)The molar extinction coefficient in Beer's law in SI units is m²/mol. (D)The molar extinction coefficient is characteristic of a molecular species and independent of the solvent. (E)Beer's law accurately describes the absorption behavior of all solutions regardless of their analyte concentration.

5.Which of the following statements about a Fourier transform IR spectrometer is correct? (4%) (A) It accurately measures the spectroscopic response one wavelength at a time. (B)It needs more time to acquire a spectrum than a scanning IR spectrometer. (C)It is usually equipped with a monochromator. (D)The absorbance at all wavelengths are measured simultaneously. (E)This type of instrument was named after the American physicist Daniel J. Fourier.

6.Which of the following description about atomic X-ray spectrometry is NOT correct? (4%) (A)X-rays are electromagnetic radiation with very short wavelengths (≤ 10 nm). (B) X-ray line spectra involves electronic transitions of the innermost atomic orbitals. (C) The K series refers to X-radiation as a result of electrons moving from outer orbitals of an atom into a vacant orbital of the K shell. (D)The K_a line is the result of a vacant K orbital filled by an electron falling from the M shell. (E)The wavelength (energy) of the K_a lines for molybdenum is independent of its oxid ation state.

7. Which of the following description about various forms of light emission is NOT correct? (4%) (A) Fluorescence and phosphorescence signals are typically measured at a 90° angle to the excitation beam. (B) In fluorescence spectra, the emitted radiation usually has a longer wavelength than the excitation radiation; this difference is called the Stokes shift. (C)The average lifetime of an excited triplet state is orders of magnitude shorter than that of an excited singlet state. (D)Chemiluminescence occurs when a chemical reaction generates an electronically excited species; this excited molecular species then emits light as it relaxes to the ground state. (E)Chemiluminescence is usually measured without selecting a specific wavelength for detection.

8. All of the following are spontaneous reactions that proceed to the right. Standard reduction potentials at 259C are provided for some half-cell reactions. Based on this information, rank the relative strengths of H⁺, Ag⁺ , Cd²⁺, Cu²⁺, and Zn²⁺ as electron acceptors (oxidizing agents) at 25℃. (4%) (A) Cu²⁺＞ H⁺＞Ag⁺ ＞ Cd²⁺＞Zn²⁺ (B) Ag⁺＞ Cu²⁺＞H⁺> Cd²⁺＞Zn²⁺(C) Zn²⁺＞ Cd⁺＞Ag⁺＞ Cu²⁺＞H⁺ (D)Zn²⁺＞ Cd⁺＞ H⁺＞Ag⁺ ＞ Cu2⁺(E) There is not enough information to deduce their relative oxidative strengths.

9.Graphs shown below are data obtained by the following analytical methods (from left to right): IR, NMR, EPR, and MS. What are the correct x-axis labels and units? (4%) (A) Micrometer (um) - magnetic field (MHz) - magnetic field (G) - atomic mass unit (Da) (B) Wavenumber (1/cm) - magnetic field (MHz) - magnetic field (G) - atomic mass unit to charge ratio (Da/z) (C)Wavenumber (1/cm)- chemical shift (ppm) - magnetic field (G) - atomic mass unit to charge ratio (Da/z) (D)Micrometer (μm) - chemical shift (ppm)- Coulomb （C） - atomic mass unit (Da) (E)Wavenumber (1/cm) -chemical shift (ppm)- resistance (Ω) - atomic mass unit (Da)

複選題

10. Which of the following description is correct? (4%) (A) The solubility product constant (Ksp) of aluminum hydroxide (Al(OH)3) is 3 ×10-34; the Ksp of cadmium sulfide (CdS) is 1× 10-27. Based on this information, we know that Al(OH)3 is less soluble than CdS in pure water. (B) A glass of aqueous solution (100 mL) contains [Ca²⁺] = 2.13✖10^-4 M, [F^-] = 4.26✖ 10 ^-4 M, and 0. 781 g of insoluble Caf₂ solid. Based on this information, we can estimate the Ksp of Caf2 to be ~3.9 x 10-11 (C) Even through the same chemical can sometimes exist in more than one crystalline form, e.g., CaCO₃ can be both calcite and aragonite, they are always equally soluble. (D) The pK_a1and pK_a2 of methionine are 2.28 and 9.21. Based on this information, we know that methionine has the best buffering power (capacity) at pH 5.75 (the mid-point between the two pKa values). (E) The hydrogen cation concentration ([H⁺]) of a pH 6.5 solution is 5.0 ✖10^-7 M.

申論題 (15)

(A) A) is the mass spectrum of a 3-heptanone sample obtained under positive ion mode showing the protonated molecular species [MH]⁺ with a major peak at 114 + 1 ~ 115 (m/z). This 3-hetpanone sample is chromatographically pure with only a single peak on HPLC. Why does it have a small peak at 116 (m/z) on the mass spectrum? (4%)

(B)B) is the mass spectrum of an unknown organic molecule obtained under positive ion mode. Estimate the number of protons associated with this ion and the mono-isotopic mass of this molecule. Show your work. (3%)

(A) A) is the ¹H NMR spectrum of 3-hetanone. Hydrogens associated with each carbon are labeled in the molecular structure shown below. Assigned each group of peaks from left to right on the NMR spectrum with lower-case letters (a-f). (4%)

(B) Homonuclear decoupling is a technique where the sample to be analyzed is irradiated at a select frequency to eliminate the effect of coupling due to certain nuclei. In other words, the signal of a select nucleus can be selectively saturated, such that this nucleus can no longer couple to neighboring nuciei. This technique helps to simplify complicated peak splitting. Irradiation at which group of protons (a-f) would result in spectral simplification in the 2.3 - 2.6 ppm range as shown in B)? Use the same lower-case letter(s) notation in A). (3%)

(a) (8 pts) Integrate the first and the second laws Tds = dU + PdV - μdn, together with the above conditions (a)(b)(c), to obtain the entropy formula S(U, V,n), which is a function of U,V and n (and T, P, μ are all eliminated).

(b) (4 pts) Suppose that a slightly different gas system satisfies (a') U= nCT^δbut not (a), where the constant δ ≠1. Show that the conditions (a')(b)(C) imply that the entropy change dS is not an exact differential.

(c) (8 pts) Modify the above chemical potential expression (c) into your (c), so that (a')(b)(c') make dS an exact differential. Obtain the entropy expression S(U,V,n) from (a')(b)(c').

(a) (2 pts) Write down the rate laws for d A(t)]/dt and d[B(t)]/dt.

(b) (3 pts) Initially [A(t = 0)] = A₀, and [B(t = O) = [C(t = 0)] = 0. Apply the steady state approximation on the intermediate B, to solve the product concentration [C(t)].

(c) (5 pts) Without using the steady state approximation, solve the concentra- tion [C(t)] exactly from the rate laws. What is the condition under which the steady state approximation applies?

(a) (2 pts) Show that the hamiltonian is hermitian.

(b) (A pts) Sol've the energy eigenvalues and their eigenvectors.

(d) (6 pts) T'he tine evolution of the spin state (t) obeys the time-dependent Schrodinger equation Together with the initial condition (t = 0) given above, solve (t).

(e)6 pts) Calculate the vectorrepresents the expectation value of the operatorat the time t. Plot the three components of this vector as functions of time.

109年 - 109 國立台灣大學_碩士班招生考試：物化分析#90697

試卷資訊

選擇題 (10)

申論題 (15)