4: Homework Solutions

Sacramento City College
CHEM 309: General, Organic and Biochemistry
Prof. Dianne Bennett

Agenda (Fall)  •   Agenda (Spring)  •  Homework Problems

1. Chapter 2: The Classical Wave Equation
2. 2.1: The One-Dimensional Wave Equation
3. 2.2: The Method of Separation of Variables
4. 2.3: Oscillatory Solutions to Differential Equations
5. 2.4: The General Solution is a Superposition of Normal Modes
6. 2.5: A Vibrating Membrane
7. 2.E: The Classical Wave Equation (Exercises)

 •  Homework Solutions

1. Chapter 11: Computational Quantum Chemistry
2. 11.1: Gaussian Basis Sets
3. 11.2: Extended Basis Sets
4. 11.3: Orbital Polarization Terms in Basis Sets
5. 11.4: The Ground-State Energy of H2H2
6. 11.5: Quantum Calculations
7. 11.E: Computational Quantum Chemistry (Exercises)

Chapters

1. Chapter 12: Group Theory: The Exploitation of Symmetry
2. 12.1: The Exploitation of Symmetry
3. 12.2: Symmetry Elements
4. 12.3: Symmetry Operations Define Groups
5. 12.4: Symmetry Operations as Matrices
6. 12.5: The C3VC3V Point Group
7. 12.6: Character Tables
8. 12.7: Characters of Irreducible Representations
9. 12.8: Using Symmetry to Solve Secular Determinants
10. 12.9: Generating Operators
11. 12.E: Group Theory: The Exploitation of Symmetry (Exercises)

  •  Video Tutorials

1. Chapter 13: Molecular Spectroscopy
2. 13.1: The Electromagnetic Spectrum
3. 13.2: Rotations Accompany Vibrational Transitions
4. 13.3: Unequal Spacings in Vibration-Rotation Spectra
5. 13.4: Unequal Spacings in Pure Rotational Spectra
6. 13.5: Vibrational Overtones
7. 13.6: Electronic Spectra Contain Electronic, Vibrational, and Rotational Information
8. 13.7: The Franck-Condon Principle
9. 13.8: Rotational Spectra of Polyatomic Molecules
10. 13.9: Normal Modes in Polyatomic Molecules
11. 13.10: Irreducible Representation of Point Groups
12. 13.11: Time-Dependent Perturbation Theory
13. 13.12: The Selection Rule for the Rigid Rotator
14. 13.13: The Harmonic Oscillator Selection Rule
15. 13.14: Group Theory Determines Infrared Activity
16. 13.E: Molecular Spectroscopy (Exercises)

 •  Basic Knowledge Practice Quizzes

Ionic Bonding and Simple Ionic Compounds

1. salt

2. lose; cations

3. gain; anions

4. H⁺ for hydrogen ion; H^- for hydride ion

5. Complete the table below.

Element	Number of Valence Electrons	Ion Formed by this Element	Report the number of electrons lost or gained
\(K\)	1	K+	1 electron lost
\(Br\)	7	Br^-	1 electron gained
\(Ca\)	2	Ca^2^+	2 electrons lost
\(O\)	6	O^2-	2 electrons gained
\(Al\)	3	Al^3^+	3 electrons lost

6. Determine the number of protons and electrons in each of the following elements.

   1. 11 protons; 10 electrons

   2. 16 protons; 18 electrons

   3. 56 protons; 54 electrons

   4. 29 protons; 27 electrons

   5. 17 protons; 18 electrons

Ionic Compounds

(7) a) attract

b) repel

c) repel

d) attract

e) repel

(8) ​ a) ​peroxide

b) sulfate

c) crbonate

d) hydroxide

e) hypochlorite

Compounds Containing Polyatomic Ions

(9) ​a) ​bicarbonate; acetate

b) sulfite; sulfate

c) cyanide; hydroxide

d) nitrite; nitrate

e) phosphate; biphosphate; dihydrogen hosphate

(10) ​a) ​HPO₄^2-

b) NH₄⁺

c) HCO₃^-

d) ClO^-

e) HSO₄^-

(11) ​a) ​ClO^-; Cl^-

b) PO₄^3-; HPO₄^2-

c) CO₃^2-; HCO₃^-

d) SO₄^2-; HSO₄-

e) OH^-; H^-

(12) Some polyatomic ions can change formula and charge by bonding with hydrogen ions. Using this knowledge, answer the following questions about the phosphate ion:

​a) ​PO₄^3-

b) 5 atoms bond to form one ion

c) HPO₄^2-; H₂PO₄^-

d) Na₃PO₄; Na₂HPO₄; NaH₂PO₄

(13) ​a) ​NaOCl

b) KOH

c) NH₄NO₃

d) Al₂(SO₃)₃

e) Fe(CN)₃

Writing Formula Units and Naming Compounds

(14) Complete the table below.

Cation	Anion	Formula Unit
\(Zn^{2+}\)	\(Br^-\)	ZnBr2
\(K^+\)	\(CO_3^{2-}\)	K2CO3
\(Al^{3+}\)	\(HCO_3^{-}\)	Al(HCO3)3
\(Fe^{2+}\)	\(OH^-\)	Fe(OH)2
\(Cu^+\)	\(NO_3^-\)	CuNO3

(15) Complete the table below.

Ionic Compound	Cation Symbol and Name	Anion Symbol and Name
\(NaC_2H_3O_2\)	Na^+; sodium	C2H3O2^-; acetate
\(Cr(NO_3)_3\)	Cr^3^+; chromium(III)	NO3^-; nitrate
\(PbCl_2\)	Pb^2^+; lead(II)	Cl^-; chloride
\(Hg_3(PO_4)_2\)	Hg^2^+; mercury(II)	PO4^3^-; phosphate
\(Ca(HCO_3)_2\)	Ca^2^+; calcium	HCO3^-; bicarbonate

(16) ​a) ​ 1 aluminum ion & 3 hydroxide ions

b) 3 lithium ions & 1 phosphate ion

c) 1 potassium ion & 1 chloride ion

d) 1 zinc ion & 2 fluoride ions

e) 2 sodium ions and 1 oxide ions

(17) a) Na₂S

b) BaI₂

c) Fe₂O₃

d) AlBr₃

e) Li₃N

(18) a) silver oxide

b) zinc chloride

c) gold(III) nitrate

d) potassium hydroxide

e) barium bromide

(19) a) mercury(I) sulfide

b) chromium(III) oxide

c) potassium sulfae

d) iorn(III) carbonate

e) zinc hypochlorite

(20) a) covalent

b) ionic

c) ionic

d) covalent

e) covalent

(21) a) gold(III) nitride

b) tin(IV) oxide

c) copper(I) sulfide

d) lead(IV) bromide

e) iron(II) iodide

(22)

Formula Unit	Chemical Name
\(MgS\)	magnesium sulfide
Al2O3	aluminum oxide
\(Fe(OH)_3\)	iron(III) hydroxide
CuCl2	copper(II) chloride
\(Pb(CO_3)_2\)	lead(IV) carbonate
Zn(HCO3)2	zinc bicarbonate
\(CaSO_4\)	calcium sulfate
NaC2H3O2	sodium acetate
\(BaBr_2\)	barium bromide
NH4NO3	ammonium nitrate

Additional Exercises

(23) a) Ba(C₂H₃O₂)₂ barium acetate

b) (NH₄)₂SO₄ ammonium sulfate

c) Zn(ClO)₂ zinc hypochlorite

d) Al(OH)₃ aluminum hydroxide

e) Na₂CO₃ sodium carbonate

(24) a) CaO

b) NaOH

c) AlBr₃

d) correct

e) Sr₃N₂

(25) HgO and Hg₂O

(26) UO₂(NO₃)₂ and (UO₂)₃(PO₄)₂