Chapter 2

Measurements in Chemistry

Chapter 2 suggested problems: 36, 38, 40, 48, 50, 52, 64, 70

Class Notes

  1. Chemistry is empirical, based on observation and measurement

  2. Scientific notation and powers of 10

    1. Base 10 number system

      1. numbers greater than 1: 4321 = (4 x 10 x 10 x 10) + (3 x 10 x 10) + (2 x 10) +
        (1 x 1)

      2. numbers less than 1: 0.5678 = (5 x .1) + (6 x .01) + (7 x .001) + (8 x .0001)

    2. Scientific notation is a shorthand representation of a number

      1. 4321 = 4.321 x 103

      2. 0.5678 = 5.678 x 10-1

    3. Examples

      1. 54405 = 5.4405 x 104

      2. 0.000006036 = 6.036 x 10-6

      3. 2.01 x 105 = 201,000

      4. 2.3473 x 10-2 = 0.023473

  3. Measurements and significant figures

    1. Accuracy and precision

      1. Precision: the closeness of a series of measurements to each other

      2. Accuracy - the closeness of one or of a series of measurements to the actual or correct value

    2. Significant figures - all of the certain figures plus the first uncertain figure

      1. Leading zeros

      2. Captive zeros

      3. Trailing zeros

    3. Examples

      1. 1234 - 4 sf

      2. 10101 - captive zeros are significant - 5 sf

      3. 0.000604999 - leading zeros - are not significant - 6 sf

      4. 555,000 vs. 555,000. - trailing zeros are only significant if there is a decimal to indicate accuracy - 3 sf vs. 6 sf

    4. Rounding-off rules: 0-0.49, .51-.99; rounding reserved until all calculations are completed

  4. SI units

    1. Base units

      1. Mass - kilogram (kg)

      2. Length - meter (m)

      3. Time - second (s)

      4. Temperature - Kelvin (K; note: not degrees Kelvin)

      5. Quantity - mole

    2. Prefixes


      1. tera
        T
        1012
        giga
        G
        109
        mega
        M
        106
        kilo
        k
        103
        deci
        d
        10-1
        centi
        c
        10-2
        milli
        m
        10-3
        micro
        u
        10-6
        nano
        n
        10-9
        pico
        p
        10-12
        femto
        f
        10-15
        atto
        a
        10-18

      2. Note: much femto/atto scale work is at the cutting edge of chemistry

  5. Measurements and measured quantities

    1. Length: measured in m, cm, mm

    2. Mass

      1. Mass is measured in kilograms.

      2. There is a difference between mass and weight.

      3. Mass is the amount of matter present in a substance and does not change with respect to local gravitational fields.

    3. Temperature

      1. Fahrenheit - based on the boiling point (BP) and the melting point (MP) of water at 212 °F and 32 °F respectively.

      2. Celsius (Centigrade) - based on based on the boiling point (BP) and the melting point (MP) of water at 100 °C and 0°C respectively.
        Note that 1 °C = 1.8 °F (i.e., the Celsius degree is bigger)

      3. Kelvin - based on 0 K at Absolute Zero - the point at which all molecular motion stops, MP water at 273 K, BP water at 373 K
        Note that 1K = 1°C (i.e., they are the same size)

      4. Relationships and conversions

        1. F to C: (F -32) / 1.8

        2. C to F: (C x 1.8) + 32

        3. C to K: C + 273

        4. K to C: K - 273

        5. K to F: convert K to C and then convert to F

        6. F to K: convert F to C and then convert to K

  6. Derived quantities

    1. Volume:

      1. Volume is the product of length, width, and height.

      2. Volume is measured in cubic meters (m3) but this is too large to be practical in many cases, so cubic centimeters (cm3) is more common.

      3. 0.001 m3 = 1 dm3 = 1 liter (L)

      4. 1000 mL = 1 L; 1 cm3 = 1 mL

    2. Density - the ratio of mass and volume

      1. Density is an important physical property of substances

      2. Density is determined by the careful measurement of a substance's mass and volume

      3. Density gives information about a substance at both a macroscopic and a microscopic level

        1. Given samples of two substances, the more dense material either has more particles per unit volume, heavier particles, or both

        2. Densities: Au - 19.32 g/cm3; Ag - 10.5 g/cm3 - what does this tell you about gold and silver at a microscopic level? (compare atomic masses)

      4. Examples

        1. 10.0 g of liquid occupies 13.5 mL of space; density = m/V = 0.741 g/mL

        2. Pure gold (24 K) has a density of 19.32 g/cm3 . A wedding band weights 3.50 grams. How much water must it displace (i.e., what must its volume be?) if the band is in fact 24 K gold?
          (answer: 0.181 cm3)

        3. Benzene has a density of 0.880 g/mL. If you need exactly 78.12 grams of benzene, what volume would you measure out?
          (answer: 88.77 mL)

  7. Energy and heat

    1. Energy - the capacity to do useful work

    2. Potential and kinetic energy

    3. Exothermic and endothermic reactions

    4. Energy is often used to increase the temperature of a substance

    5. Calorie - the amount of heat required to raise the temperature of 1 g of water 1°C

      1. SI unit of energy - Joule (J) - 4.184 J = 1 cal

    6. Specific heat - the amount of heat required to raise the temperature of 1 g of substance by 1°C

      1. specific heat units: J/g°C

  8. Dimensional analysis and problem solving

    1. Conversion factors

      1. Multiplicitive identity: any number multiplied by 1 will result in that number i.e., 1 x y = y

      2. A conversion factor permits the conversion from one set of units to another without changing the true value of the number associated with the units

      3. Creation of conversion factors

        1. 1 mile = 5280 feet => (1 mile / 5280 feet) = (5280 feet / 5280 feet) => (1 mile / 5280 feet) = 1

        2. 1 foot = 12 inches => (1 foot / 12 inches) = (12 inches / 12 inches) => (1 foot / 12 inches) = 1

        3. 1 hour = 3600 seconds => (1 hour / 3600 seconds) = (3600 seconds / 3600 seconds) => (1 hour / 3600 seconds) = 1

    2. Dimensional analysis - the process of problem solving using conversion factors (also called factor label method, factorial analysis, etc.)

      1. The process using an example: convert 150 lbs to kg

      2. What is given? how should the problem wind up?

        1. Given: 150 lbs; the problem should wind up with units in kg

      3. What conversion factors are needed?

        1. 1 kg = 2.2 lbs => (1 kg / 2.2 lbs) = 1

      4. After using the conversion factor do the units cancel? is another conversion factor needed?

        1. 150 lbs x (1 kg / 2.2 lbs) = kg; the units are correct, no additional conversion factors are needed

      5. Do the arithmetic

        1. 150 lbs x (1 kg / 2.2 lbs) = 68.2 kg

    3. Additional examples

      1. Convert 62.5 cm to inches

        1. 1 inch = 2.54 cm

        2. 62.5 cm x (1 inch / 2.54 cm) = 24.6 inches

      2. Convert 3.62 ounces to mg

        1. 1 lb = 16 oz; 1 lb = 453.6 g; 1 g = 1000 mg

        2. (3.62 oz) x (1 lb / 16 oz) x (453.6 g / 1 lb) x (1000 mg / 1 g) = 102,627 mg = 1.02 x 105 mg

      3. Convert 1100 m/s to mph

        1. 60 sec = 1 minute; 60 min = 1 hr; 1 m = 100 cm; 1 in = 2.54 cm; 1 ft = 12 in; 1 mile = 5280 ft

        2. (1100 m/s) x (60 s / 1 min) x (60 min / 1 hr) x (100 cm / m) x (1 in / 2.54 cm) x (1 ft / 12 in) x
          (1 mile / 5280 ft) = 2460.6 mile/hr = 2500 mph

      4. Convert the area of an 8.5" by 11" piece of paper to cm2

        1. 1 in = 2.54 cm

        2. 8.5 in x 11 in = 93.5 in2

        3. (93.5 in2) x (2.54 cm / 1 in)2 = 603.2 cm2 = 6.0 x 102 cm2

      5. Convert 6 yds3 of cement to cm3

        1. 1 yd = 3 ft; 1 ft = 12 in; 1 in = 2.54 cm

        2. (6 yds3) x (3 ft / 1 yd)3 x (12 in / 1 ft)3 x (2.54 cm / 1 in)3 = 4,587,329.1 cm3 = 5 x 106 cm3

      6. Hexane is an organic liquid used in the manufacture of gasoline. If a railroad car contains 2.5 x 104 gallons of hexane, how much does the liquid weigh in pounds? (note: the density of hexane is 0.6594 g/mL)

        1. 1 gal = 4 qt; 1 L = 1.057 qt; 1000 mL = 1 L; 1 lb = 453.6 g

        2. (2.5 x 104 gallons) x (4 qt / 1 gal) x (1 L / 1.057 qt) x (1000 mL / 1 L) = 94,607,379.376 mL

        3. (94,607,379.376 mL) x (0.6594 g / mL) x (1 lb / 453.6 g) = 137,531.1 lbs = 1.4 x 105 lbs

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