114年 - [無官方正解]114 國立成功大學_碩士班招生考試試題_化學系：無機化學#139068

一、單選題：（50分，每題2.5分）
1. Which of the following is not considered a fundamental symmetry operation in molecular geometry?(A) improper rotation(B) proper rotation(C) reflection(D) glide reflection
(E) inversion

2. Determine the point group of the following cluster anion [Fe@Ge₁₀]³⁻.(A) D₅ₕ(B) D₅d(C) C₅ₕ(D) C₅ᵥ
(E) Oₕ

3. Which one of the following is the highest occupied molecular orbital for the CO molecule? Note: for clarity, the atom on the left is carbon, and the atom on the right is oxygen.(A) (圖A)(B) (圖B)(C) (圖C)(D) (圖D)
(E) (圖E)

4. Which of the following ions is classified as hard acid?(A) F⁻(B) Br⁻(C) Na⁺(D) Cs⁺
(E) S²⁻

5. Which of the following is a d² ion?(A) Mn³⁺(B) Ti⁺(C) Fe³⁺(D) Cr²⁺
(E) Ti²⁺

6. How many microstates are there for a d² free ion?(A) 2(B) 5(C) 25(D) 45
(E) 80

7. Following Question 6, according to Hund's rule, what is the lowest energy atomic state?(A) ¹G(B) ³F(C) ¹D(D) ³P
(E) ¹S

8. Which of the following statements about the complex ion [Co(en)₂Cl₂]⁺ is correct? (en = ethylenediamine)(A) It has two geometric isomers and two optical isomers.(B) Since en is a strong field ligand, the complex ion is paramagnetic.(C) It has cis and trans geometric isomers, but no optical isomers.(D) The geometric isomers of it have similar properties.
(E) The oxidation state of Co is +1.

9. Below is a new coordination complex reported in 2024, what is the electron count of the metal center?
（圖：含Co-N配位結構）(A) 9(B) 10(C) 11(D) 12
(E) 13

10. Following Question 9, what is the possible spin state (S) of the complex?(A) ¹/₂ and ³/₂(B) 0 and 1(C) 1 and ³/₂(D) ¹/₂ and ⁵/₂
(E) 1 and 2

11. In a transition metal complex having Oₕ symmetry, which configurations in the following can be classified as E?(A) t₂g⁵eg²(B) t₂g³eg³(C) t₂g⁵eg⁰(D) t₂g⁴eg²
(E) t₂g³eg⁰

12. Arrange the acidity in water for ( A ) HCo(CO)₄, ( B ) HCo(CO)₃{P(OPh)₃}, and ( C ) HCo(CO)₃(PPh₃).(A) A ＞ B ＞ C(B) A ＞ C ＞ B(C) B ＞ C ＞ A(D) C ＞ B ＞ A
(E) B ＞ A ＞ C

13. Arrange the acidity in acetonitrile for ( A ) H₂Fe(CO)₄, ( B ) H₂Ru(CO)₄, and ( C ) H₂Os(CO)₄.(A) A ＞ B ＞ C(B) A ＞ C ＞ B(C) B ＞ C ＞ A(D) C ＞ B ＞ A
(E) B ＞ A ＞ C

14. Predict the number of radial nodes and angular nodes for a 4d orbital.(A) 3, 1(B) 2, 1(C) 1, 2(D) 0, 3
(E) 1, 3

15. The following is a stable nitrene molecule isolated by Beckmann and coworkers in 2024. What is the oxidation state of N?
（圖：含N的有機結構）(A) +1(B) −1(C) +2(D) −3
(E) +3

16. Which of the following molecules is paramagnetic?(A) N₂(B) B₂(C) He₂(D) C₂
(E) F₂

17. An element crystallizes in a face-centered cubic structure. What is the relationship between the radius of that atom (r) and the length of an edge of the unit cell (l)?(A) r = 2l(B) r = l/√8(C) r = √8l(D) r = (√3/4)l
(E) r = l/2

二、問答題：（50分）
21. (13 points) Consider the NO molecule:
(A) (3 points) Draw the most stable Lewis structure of this molecule. What are the oxidation states and formal charges of each element?
(B) (5 points) Construct the molecular orbital diagram of NO. Use the following orbital potential energies to construct the MO diagram: N 2s: −25.56 eV, 2p: −13.18 eV. O 2s: −32.38 eV, 2p: −15.85 eV.
(C) (2 points) Predict the bond order and the number of unpaired electrons of NO from your results of (A) and (B).
(D) (3 points) Both NO⁺ and NO⁻ are well-known in inorganic chemistry. Based on the molecular orbital diagram results in (B), what are the bond orders of these two ions? Which one of these three would have the shortest N−O bond distance? Briefly explain.

22. (9 points) Fe(CO)₄Cl₂ has two isomers (A) and (B), determine the number of IR- and Raman-active C−O stretching vibrations for both. Is IR or Raman spectroscopy able to distinguish them? Show your work clearly to receive points.
（圖A：cis-Fe(CO)₄Cl₂，圖B：trans-Fe(CO)₄Cl₂）

23. (12 points, 4 points each) Using the angular overlap model, draw the d-orbital energy splitting diagrams and determine the energy differences between the d orbitals of the metal for the following geometries for monodentate σ-donor (L) ligands.
(A) Octahedral ML₆ complex.
(B) Trigonal planar ML₃ complex.
(C) Square pyramidal ML₅ complex.

24. (6 points) The following molecule is a monoatomic B(0) molecule reported in 2024 by Pranckevicius and coworkers. The authors draw the following Lewis structure that has a partial double bond between boron and carbon and a radical on boron. List at least three experimental techniques that could be used to support their proposed structure and briefly explain your reasoning.
（圖：含B-N有機結構）

25. (10 points) The salt LiBr has a Li−Br distance of 275 pm (1 pm = 10⁻¹² m) and has the NaCl structure.
(A) (3 points) Draw the unit cell of the molecule.
(B) (2 points) How many atoms of Li and Br are there in a unit cell?
(C) (2 points) Calculate the mass of a unit cell.
(D) (3 points) What is the density of LiBr?