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					    Measurement and Calculation

                                     Chapter 2




Zumdahl's Introductory Chemistry -               1
            Chapter 2
                             Measurement
• Quantitative Observation
• Comparison Based on an Accepted Scale
      e.g. Meter Stick
• Has 2 Parts – the Number and the Unit
      Number Tells Comparison
      Unit Tells Scale


Zumdahl's Introductory Chemistry -         2
            Chapter 2
                     Scientific Notation
• Technique Used to Express Very Large or
  Very Small Numbers
• Based on Powers of 10
• To Compare Numbers Written in Scientific
  Notation
      First Compare Exponents of 10
      Then Compare Numbers

Zumdahl's Introductory Chemistry -           3
            Chapter 2
Writing Numbers in Scientific Notation
  1      Locate the Decimal Point
  2      Move the decimal point to the right of the non-
         zero digit in the largest place
           The new number is now between 1 and 10
  3      Multiply the new number by 10n
           where n is the number of places you moved the
            decimal point
  4      Determine the sign on the exponent n
           If the decimal point was moved left, n is +
           If the decimal point was moved right, n is –
           If the decimal point was not moved, n is 0
 Zumdahl's Introductory Chemistry -                         4
             Chapter 2
Writing Numbers in Standard Form
1 Determine the sign of n of 10n
       If n is + the decimal point will move to the right
       If n is – the decimal point will move to the left
2 Determine the value of the exponent of 10
       Tells the number of places to move the decimal
        point
3 Move the decimal point and rewrite the
  number
 Zumdahl's Introductory Chemistry -                      5
             Chapter 2
Related Units in the Metric System

• All units in the metric system are related to
  the fundamental unit by a power of 10
• The power of 10 is indicated by a prefix
• The prefixes are always the same,
  regardless of the fundamental unit



Zumdahl's Introductory Chemistry -                6
            Chapter 2
                                        Length
• SI unit = meter (m)
    About 3› inches longer than a yard
         • 1 meter = one ten-millionth the distance from the North Pole to the
           Equator = distance between marks on standard metal rod in a Paris
           vault = distance covered by a certain number of wavelengths of a
           special color of light
         • Commonly use centimeters (cm)
    1 m = 100 cm
    1 cm = 0.01 m = 10 mm
    1 inch = 2.54 cm (exactly)


   Zumdahl's Introductory Chemistry -                                        7
               Chapter 2
                                       Volume
• Measure of the amount of three-dimensional space
  occupied by a substance
• SI unit = cubic meter (m3)
• Commonly measure solid volume in cubic centimeters
  (cm3)
    1 m3 = 106 cm3
    1 cm3 = 10-6 m3 = 0.000001 m3
• Commonly measure liquid or gas volume in milliliters
  (mL)
      1 L is slightly larger than 1 quart
      1 L = 1 dL3 = 1000 mL = 103 mL
      1 mL = 0.001 L = 10-3 L
      1 mL = 1 cm3
  Zumdahl's Introductory Chemistry -                     8
              Chapter 2
                                     Mass
• Measure of the amount of matter present in
  an object
• SI unit = kilogram (kg)
• Commonly measure mass in grams (g) or
  milligrams (mg)
      1 kg = 2.2046 pounds, 1 lbs. = 453.59 g
      1 kg = 1000 g = 103 g, 1 g = 1000 mg = 103 mg
      1 g = 0.001 kg = 10-3 kg, 1 mg = 0.001 g = 10-3 g

Zumdahl's Introductory Chemistry -                    9
            Chapter 2
Uncertainty in Measured Numbers
• A measurement always has some amount of
  uncertainty
• Uncertainty comes from limitations of the
  techniques used for comparison
• To understand how reliable a measurement
  is, we need to understand the limitations of
  the measurement

Zumdahl's Introductory Chemistry -           10
            Chapter 2
           Reporting Measurements
• To indicate the uncertainty of a single
  measurement scientists use a system called
  significant figures
• The last digit written in a measurement is
  the number that is considered to be
  uncertain
• Unless stated otherwise, the uncertainty in
  the last digit is ±1

Zumdahl's Introductory Chemistry -              11
            Chapter 2
Rules for Counting Significant Figures
• Nonzero integers are always significant
• Zeros
       Leading zeros never count as significant figures
       Captive zeros are always significant
       Trailing zeros are significant if the number has
        a decimal point
• Exact numbers have an unlimited number of
  significant figures

 Zumdahl's Introductory Chemistry -                    12
             Chapter 2
              Rules for Rounding Off
 • If the digit to be removed
         • is less than 5, the preceding digit stays the
           same
         • is equal to or greater than 5, the preceding
           digit is increased by 1
 • In a series of calculations, carry the extra
   digits to the final result and then round off
 • Don’t forget to add place-holding zeros
   if necessary to keep value the same!!
Zumdahl's Introductory Chemistry -                         13
            Chapter 2
                           Exact Numbers
• Exact Numbers are numbers known with certainty
• Unlimited number of significant figures
• They are either
    counting numbers
         • number of sides on a square
    or defined
         •   100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm
         •   1 kg = 1000 g, 1 lb = 16 oz
         •   1000 mL = 1 L; 1 gal = 4 qts.
         •   1 minute = 60 seconds


  Zumdahl's Introductory Chemistry -                      14
              Chapter 2
Calculations with Significant Figures

 • Calculators/computers do not know
   about significant figures!!!
 • Exact numbers do not affect the number of
   significant figures in an answer
 • Answers to calculations must be rounded to
   the proper number of significant figures
       round at the end of the calculation


 Zumdahl's Introductory Chemistry -           15
             Chapter 2
        Multiplication/Division with
            Significant Figures
•       Result has the same number of significant figures
        as the measurement with the smallest number of
        significant figures
•       Count the number of significant figures in each
        measurement
•       Round the result so it has the same number of
        significant figures as the measurement with the
        smallest number of significant figures
4.5 cm               x        0.200 cm = 0.90 cm2
    2 sig figs                       3 sig figs   2 sig figs
Zumdahl's Introductory Chemistry -                             16
            Chapter 2
         Adding/Subtracting Numbers
           with Significant Figures
•      Result is limited by the number with the
       smallest number of significant decimal places
•      Find last significant figure in each
       measurement
•      Find which one is “left-most”
•      Round answer to the same decimal place
        450 mL + 27.5 mL =                                        480 mL
precise to 10’s place              precise to 0.1’s place   precise to 10’s place

    Zumdahl's Introductory Chemistry -                                              17
                Chapter 2
Problem Solving and Dimensional Analysis
 • Many problems in chemistry involve using
   equivalence statements to convert one unit of
   measurement to another
 • Conversion factors are relationships between two units
      May be exact or measured
      Both parts of the conversion factor should have the same
       number of significant figures
 • Conversion factors generated from equivalence
   statements
      e.g. 1 inch = 2.54 cm can give 2.54cm or     1in
                                        1in       2.54cm
   Zumdahl's Introductory Chemistry -                         18
               Chapter 2
Problem Solving and Dimensional Analysis

  • Arrange conversion factors so starting unit
    cancels
         Arrange conversion factor so starting unit is on
          the bottom of the conversion factor
  • May string conversion factors



   Zumdahl's Introductory Chemistry -                    19
               Chapter 2
    Converting One Unit to Another
•      Find the relationship(s) between the
       starting and goal units. Write an
       equivalence statement for each
       relationship.
•      Write a conversion factor for each
       equivalence statement.
•      Arrange the conversion factor(s) to cancel
       starting unit and result in goal unit.

Zumdahl's Introductory Chemistry -              20
            Chapter 2
    Converting One Unit to Another
•      Check that the units cancel properly
•      Multiply and Divide the numbers to give
       the answer with the proper unit.
•      Check your significant figures
•      Check that your answer makes sense!



Zumdahl's Introductory Chemistry -               21
            Chapter 2
                      Temperature Scales
• Fahrenheit Scale, °F
     Water’s freezing point = 32°F, boiling point = 212°F
• Celsius Scale, °C
     Temperature unit larger than the Fahrenheit
     Water’s freezing point = 0°C, boiling point = 100°C
• Kelvin Scale, K
     Temperature unit same size as Celsius
     Water’s freezing point = 273 K, boiling point = 373 K


  Zumdahl's Introductory Chemistry -                          22
              Chapter 2
                                       Density
• Density is a property of matter representing the mass per unit
  volume
• For equal volumes, denser object has larger mass
• For equal masses, denser object has small volume
• Solids = g/cm3
    1 cm3 = 1 mL
                                                      Mass
• Liquids = g/mL                       Density 
• Gases = g/L
                                                     Volume
• Volume of a solid can be determined by water displacement
• Density : solids > liquids >>> gases
• In a heterogeneous mixture, denser object sinks
  Zumdahl's Introductory Chemistry -                          23
              Chapter 2
    Using Density in Calculations
                                       Mass
                            Density 
                                      Volume

                                      Mass
                            Volume 
                                     Density

                      Mass  Density Volume

Zumdahl's Introductory Chemistry -             24
            Chapter 2

				
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