7: 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

States of Matter

(01) Solids have definite shape and definite volume. Liquids have indefinite shape and definite volume. Gases have indefinite shape and indefinite volume.

(02) Potential energy because the energy from the sun has been stored.

(03)

1. Kinetic energy
2. Kinetic energy
3. Kinetic energy
4. Potential energy
5. Potential energy

(04)

1. A car traveling at 75 mph
2. A match burning at 110 degrees Celsuis
3. Digesting a a 300 Calorie snack
4. An engine burning a 20 gallon tank
5. A 20-lb lead weight falling from a cliff

(05) KE s < l < g and PE g < l < s

(06) KE ice < Hg < N₂

(07) 77°F and 37°C

(08) 77°C and 171°F

(09) No, water is an important and interesting exception. For most substances, the solid state has greater density than the liquid state.

Changes of State

(10) Yes, as the substance is heated from a solid to liquid, the kinetic energy starts to overcome and disrupt the cohesive intermolecular forces allowing more movement between molecules in a liquid compared to a solid.

(11) melting: solid + heat → liquid

boiling: liquid + heat → gas

condensing: gas → liquid + heat

freezing: liquid → solid + heat

(12) Steam causes more damage because in addition to the heat from the steam causing damage. The water vapor releases additional heat as it condenses to a liquid causing further damage.

(13) 1-Propanol can form H-bonds which increase the potential energy of the intermolecular forces and create a higher boiling point.

Pressure

(14) Any three of the following five pressure units: 1 atm = 760 mmHg = 760 torr = 14.70 psi = 1.013 x 10⁵ Pa

(15)

1. 6200 torr
2. 6.1 x 10⁵ Pa
3. 3.7 atm

(16) ​ vapor pressure: isopropyl alcohol < formaldehyde < butane

boiling points: butane < formaldyde < isopropyl alcohol

Gases

(17) 13 atm

(18) 1.2 atm

(19) a) ​False

b) True

c) True

(20) partial pressure of Ar is 15 mmHg

(21) total pressure is 3890 mmHg; 39% Cl₂; 17% Br₂; 21% F₂; 23% I₂