1: Measurement of Matter and Energy

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

Matter and Measurement

(01) Rank the following items in order from smallest to largest size:

1. A peanut
2. Oxygen gas molecule
3. Carbon atom
4. A baseball
5. Grain of table salt

(02) Arrange the given units in order of magnitude from least to greatest and identity to which power of 10 they correspond to:

1. Mega
2. micro
3. centi
4. kilo
5. nano

(03) In each of the following pairs, indicate which the greater value is:

1. 10 cm or 1000 mm
2. 1 g or .01 kg
3. 100 mL or 1L
4. 10 mm or 100,000 micrometers
5. 1 Gm or 1000 km

(04) A graduated cylinder has a small amount of sand poured into the bottom. The cylinder then has exactly 10 mL of water added to it. The sand does not dissolve and the volume of the meniscus of the cylinder reads 11.7 mL. How much of the final volume is the sand?

(05) In comparing the following pairs, which has the greatest value?

1. 1.0x10³ and 10,000
2. 0.0001 and 1.0x10^-5
3. 5.47 and 4.2x10³
4. 3.89x10-6 and 0.000000345
5. 600,001 and 6x10⁶

(06) Of the below pairings, which represents the lesser quantity?

1. 100 mL or 100 dL
2. 1 mcg or 1 ng
3. 20 cm or 20 mm
4. 100 km or 100 Mm
5. 1000 pm or 1000 nm

(07) Convert each number into scientific notation and identify the number of significant figures.

1. 100,000,000,000,000,000
2. 60,200,000
3. 30.01
4. 0.000000004970
5. 0.000601

(08) Expand these numbers from scientific notation to conventional numbers.

1. 6.02x10³
2. 3.14x10^-7
3. 4.44x10⁴
4. 2.87x10¹²
5. 9.87x10^-2

(09) Define the following statements as being true or false.

1. Bad results are only the result of poor experimental performance
2. The definition of accuracy in an experiment is the ability to produce consistently similar results with repeated experiments
3. If an experiment’s results vary greatly between repeated performances, the results are always considered to be inaccurate
4. Measuring devices must be calibrated to give accurate results
5. You should always use the same measuring device throughout an experiment

(10) Identify the correct number of significant figure in the following numbers:

1. 6.02x10²³
2. 140000
3. 100.1
4. 0.000001000
5. 0.0000071

(11) Calculate the indicated operations and report the correct number of significant figures.

1. 5.83 + 3.09 + 7.41
2. 4.3 x 2.9 x 1.6
3. 8.13 – 2.28 – 1.99
4. 3.14 / 2.22
5. 5.01 x 4.23 / 3.97

(12) Identify which quantities are exact numbers, which have an infinite number of significant figures, and which are inexact and have a finite number of significant figures, and report how many there are when possible.

1. 1 yard = 3 feet
2. A speed of 65 miles per hour
3. Fifty dollars
4. 1 Liter = 1000 milliliters
5. A density of 1.01 grams per milliliter

(13) Convert the following metric quantities into the indicated units. Identify the number of significant figures in each answer.

1. 1000 g into mg
2. 6981 nm into cm
3. 15 dL into mcL
4. 50 km into mm
5. 150,000 pg into cg

(14) Perform the indicated operations and identify the number of significant figures.

1. a. How many milligrams are there in 624 grams?
2. b. A mixture of water and clay has a mass of 34 g and a volume of 125 mL. What is the density?
3. c. What is the amount in Liters of a volume of 3000.2 dL?
4. d. How much mass, in mg, does a 7.84x10⁹ ng sample have?
5. e. How far away is a 0.0000024 km destination in mm?

(15) An adult multivitamin supplement contains 0.4 ng of folic acid, 75 mcg of boron and 2 mg of silicon. How many grams of each vitamin does the vitamin contain?

(16) Using a multi-step conversion, calculate how many seconds there are in 2 decades. Express the answer in scientific notation and use 3 significant figures.

(17) Use English-to-Metric and Metric-to-English conversion factors to calculate the following:

1. 14.8 lbs to kg
2. 400 m to miles
3. 65 miles per hour to meters per second

(18) If there are four quarts in a gallon, and 4 cups in a quart, how many cups are there in 6.50 gallons?

(19) A doctor prescribes a medication dosage of 55 mg/kg of body weight to be taken twice a day in equal amounts. If a patient weighs 90. lbs, how many milligrams per dose should they take?

(20) A dosage is listed as 50. mg/kg of body weight for a prescription for a baby weighing 10. lbs. A report comes out that says a child should not receive more than 200 mg a day. Does the dosage that was prescribed exceed the safety limit from the report?

(21) Given the density of iron is 7.9 g/mL, if a sample of iron shavings is added to a graduated cylinder filled with water and the volume increases by 1.8 mL, what was the total mass of the iron?

(22) What is the mass of a 27 mL sample of alcohol? The density is 0.79 g/mL.

(23) A base unit of mass is grams. How many powers of 10 differ between a kilogram and a gram? How many are there between a milligram and a gram? Using this information, convert 253 g to kg, and then to mg.

(24) Volume can be measured in units other than Liters and its metric constituents. Arrange the following volumes in order from smallest to largest.

1. 15 cm³
2. 62 dL
3. 2.0x105 mcL
4. 1 L

Additional Exercises

25. A sample of urine has a density of 1.105 g/cm³. What is the mass of 0.255 L of this urine?

26. The hardest bone in the body is tooth enamel, which has a density of 2.91 g/cm³. What is the volume, in liters, of 75.9 g of tooth enamel?

27. Some brands of aspirin have 81 mg of aspirin in each tablet. If a person takes 8 tablets per day, how many grams of aspirin is that person consuming every day?

28. The US government has a recommended daily intake (RDI) of 5 µg of vitamin D per day. (The name recommended daily allowance was changed to RDI in 1997.) If milk contains 1.2 µg per 8 fl oz glass, how many fluid ounces of milk are needed to supply the RDI of vitamin D?

29. The population of the United States, according to the 2000 census, was 281.4 million people.

    1. How many significant figures does this number have?
    2. What is the unit in this quantity?
    3. Express this quantity in proper scientific notation.

30. The United States produces 34,800,000,000 lb of sugar each year, and much of it is exported to other countries.

    1. How many significant figures does this number have?
    2. What is the unit in this quantity?
    3. Express this quantity in proper scientific notation.

31. Construct a conversion factor that can convert from one unit to the other in each pair of units.

    1. from millimeters to kilometers
    2. from kilograms to micrograms
    3. from centimeters to micrometers

32. Construct a conversion factor that can convert from one unit to the other in each pair of units.

    1. from kilometers to micrometers
    2. from decaliters to milliliters
    3. from megagrams to milligrams

33. What is the density of a dextrose solution if 355 mL of the solution has a mass of 406.9 g?

34. What is the density of a dental amalgam (an alloy used to fill cavities) if 1.005 kg of the material has a volume of 433 mL? Express your final answer in grams per milliliter.

For Exercises 35–38, see the accompanying table for the relationships between English and SI units.

1 m ≈ 39.36 in. ≈ 3.28 ft ≈ 1.09 yd

1 cm ≈ 2.54 in.

1 km ≈ 0.62 mi

1 kg ≈ 2.20 lb

1 lb ≈ 454 g

1 L ≈ 1.06 qt

1 qt ≈ 0.946 L

35. Approximately how many inches are in 4.76 m?

36. Approximately how many liters are in 1 gal, which is exactly 4 qt?

37. Approximately how many kilograms are in a person who weighs 170 lb?

38. The average distance between Earth and the sun is 9.3 × 10⁷ mi. How many kilometers is that?