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1.8 End-of-Chapter Material

Chapter Summary

To ensure that you understand the material in this chapter, you should review the meanings of the bold terms in the following summary and ask yourself how they relate to the topics in the chapter.

Chemistry is the study of matter, which is anything that has mass and takes up space. Chemistry is one branch of science, which is the study of the natural universe. Like all branches of science, chemistry relies on the scientific method, which is a process of learning about the world around us. In the scientific method, a guess or hypothesis is tested through experiment and measurement.

Matter can be described in a number of ways. Physical properties describe characteristics of a sample that do not change the chemical identity of the material (size, shape, color, and so on), while chemical properties describe how a sample of matter changes its chemical composition. A substance is any material that has the same physical and chemical properties throughout. An element is a substance that cannot be broken down into chemically simpler components. The smallest chemically identifiable piece of an element is an atom. A substance that can be broken down into simpler chemical components is a compound. The smallest chemically identifiable piece of a compound is a molecule. Two or more substances combine physically to make a mixture. If the mixture is composed of discrete regions that maintain their own identity, the mixture is a heterogeneous mixture. If the mixture is so thoroughly mixed that the different components are evenly distributed throughout, it is a homogeneous mixture. Another name for a homogeneous mixture is a solution. Substances can also be described by their phase: solid, liquid, or gas.

Scientists learn about the universe by making measurements of quantities, which consist of numbers (how many) and units (of what). The numerical portion of a quantity can be expressed using scientific notation, which is based on powers, or exponents, of 10. Large numbers have positive powers of 10, while numbers less than 1 have negative powers of 10. The proper reporting of a measurement requires proper use of significant figures, which are all the known digits of a measurement plus the first estimated digit. The number of figures to report in the result of a calculation based on measured quantities depends on the numbers of significant figures in those quantities. For addition and subtraction, the number of significant figures is determined by position; for multiplication and division, it is decided by the number of significant figures in the original measured values. Nonsignificant digits are dropped from a final answer in accordance with the rules of rounding.

Chemistry uses SI, a system of units based on seven basic units. The most important ones for chemistry are the units for length, mass, amount, time, and temperature. Basic units can be combined with numerical prefixes to change the size of the units. They can also be combined with other units to make derived units, which are used to express other quantities such as volume, density, or energy. A formal conversion from one unit to another uses a conversion factor, which is constructed from the relationship between the two units. Numbers in conversion factors may affect the number of significant figures in a calculated quantity, depending on whether the conversion factor is exact. Conversion factors can be applied in separate computations, or several can be used at once in a single, longer computation.

Additional Exercises

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

  2. 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?

  3. 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?

  4. 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 oz glass, how many ounces of milk are needed to supply the RDI of vitamin D?

  5. 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.
  6. 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.
  7. 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
  8. 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
  9. What is the density of a dextrose solution if 355 mL of the solution has a mass of 406.9 g?

  10. 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 11–16, 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
  1. Approximately how many inches are in 4.76 m?

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

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

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

  5. Show mathematically that 1 L equals 1 dm3.

  6. Show mathematically that 1 L equals 1,000 cm3.

Answers

  1. 282 g

  2. 650 mg

    1. four significant figures
    2. people
    3. 2.841 × 108 people
    1. 1 km106 mm
    2. 109 μg1 kg
    3. 104 μm1 cm
  3. 1.15 g/mL

  1. 187 in.

  2. 77 kg

  3. 1 L = 0.001 m3×( 1 dm 0.1 m )3=1 dm3