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Chapter 2 Measurements and Calculations. Chapter Outline. Expressing numbers in scientific notation Unit systems (3) What chemists commonly measure How to take measurements Uncertainty in measurements Significant Figures – brief introduction Rules for rounding off

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chapter outline
Chapter Outline
  • Expressing numbers in scientific notation
  • Unit systems (3)
  • What chemists commonly measure
  • How to take measurements
    • Uncertainty in measurements
    • Significant Figures – brief introduction
    • Rules for rounding off
  • Converting between units
  • Temperature scales
  • Density
quantitative observations
Quantitative Observations
  • A quantitative observation generally includes a number and a unit.
    • Record three quantitative observations about yourself.
scientific notation
Scientific Notation
  • Goal: to express numbers in scientific notation and as ordinary decimal numbers
    • Scientific notation
      • A number between 1 and less than 10 multiplied by 10 raised to an exponent.
      • Examples
    • Why is scientific notation useful?
  • Review powers of 10
scientific notation5
Scientific Notation
  • Express each of the following in scientific notation:

53,000

350

0.0025

0.0000050

scientific notation6
Scientific Notation
  • Express each of the following as an ordinary decimal number

3.2 x 103

1.8 x 10-2

5.03 x 105

2.3 x 108

unit systems
Unit Systems
  • English system
    • Used in United States
  • Metric system
    • Used in science
  • International system (SI)
    • Based on the metric system

UNITS MATTER! See page 19

unit systems8
Unit Systems
  • English System
    • Used in U.S.
    • Little logic to the units
      • Examples
unit systems9
Unit Systems
  • Metric System
    • Developed in the late 1700’s and adopted after the French Revolution
    • A base (or fundamental) unit is defined for each quantity measured
      • The size of the base unit can be modified by adding a prefix
metric system
Metric System

Quantity Base unit Symbol

unit systems meteric
Unit Systems - meteric
  • Metric Prefixes, see page 19
unit systems12
Unit Systems
  • Using prefixes
    • Base unit = meter
    • Kilometer = km = _________ m
unit systems13
Unit Systems
  • International System (SI)
    • Adopted in 1960
    • Internationally agreed upon set of units
    • Used in industry
      • Some use in science
    • See page 18
what chemists measure
What chemists measure
  • Length – distance between 2 points
    • Metric base = ____________
    • 1 inch = 2.54 cm exactly
    • Other commonly used multiples:
      • km
      • cm
      • mm
      • mcm
      • nm
mass and weight
Mass and Weight
  • Mass – quantity of matter present
    • Base unit: __________
    • Measure on a balance
  • Weight – measure of gravitational pull on an object
    • Base unit:
    • Measure on a scale
volume
Volume
  • Volume – amount of three dimensional space occupied by an object
    • SI base = meter3
    • Metric base = Liter
    • Liter = 10 cm x 10 cm x 10 cm
    • mL = ________ = ___________
measuring volume
Measuring Volume
  • Measuring Volume of a “block”
      • Volume = length x height x width
  • Volume of an irregularly shaped object
      • Use water displacement
taking measurements
Taking measurements
  • Use a measuring device to take measurements
    • All measurements recorded include some degree of uncertainty
    • A properly taken measurement includes one estimated digit
taking measurements20
Taking measurements
  • Measuring devices have units marked on them
  • When taking a measurement you record:
      • All known digits
        • those marked on the measuring device
      • One estimated digit
        • Estimated digit is 1/10 the smallest marked unit on the measuring device
taking measurements21
Taking measurements
  • Graduated cylinder example

Thermometer

example

significant figures
Significant Figures
  • The last digit recorded in a measurement is estimated/uncertain.
  • The numbers recorded in a measurement are called the significant figures.
  • When measurements are used in calculations the answer to the calculation is rounded off so that the last digit is also an estimate.
significant figures goals
Significant Figures - Goals
  • Your goal is to:
    • Record all measurements correctly
    • Recognize the estimated digit
    • Define the term significant figures
    • State the number of significant figures in a measurement you take.
    • Round answers to calculations as instructed
rounding off
Rounding Off
  • If the first digit to be removed is:
    • 5 or greater then the preceding digit is increased by 1 (round up)
    • Less than 5 then the preceding digit remains the same (round down)
rounding off25
Rounding Off
  • Round 1345.493 to:
    • 2 decimal places
    • 1 decimal place
    • The 1’s (ones)
    • The 10’s (tens)
    • The 100’s (hundreds)
converting between units
Converting Between Units
  • Metric to Metric Conversions
    • See board for the staircase method
  • Using dimensional analysis to convert between units.
converting between units practice
Converting Between Units, Practice!
  • Miles  km
  • Pounds  grams  kg
  • mL  fluid ounces
  • M  cm  inches
density
Density
  • Density – the amount of matter present in a given volume of a substance
  • Density = mass of an object

volume of object

density units
Density Units
  • The mass of the object is expressed in grams and the volume is expressed in:
      • mL or cm3 for solids and liquids
      • L for gases
  • Density units:
    • g/mL or g/cm3 – solids and liquids
    • g/L - gases
    • Other: Pounds/foot3(English system)
density30
Density
  • Density of water is ~ 1g/mL at room temperature.
    • What is the approximate mass of water in a 0.5 L water bottle?
    • What is the volume of 150 grams of water?
density31
Density
  • Objects with a density greater than 1g/mL sink in water.
  • Objects with a density less than 1g/mL float in water.
density32
Density
  • The density of the elements can be found on the periodic table.
    • Examples:
  • The density of compounds must be looked up in reference “books”.
density33
Density
  • Calculating density from data
    • In class experiment
density34
Density
  • Rearrange the density equation to solve for volume and mass:

Volume =

Mass =

density calculations
Density Calculations
  • Calculate the mass, in grams and in pounds, of a gold brick
    • see board for the dimensions of the gold brick
density calculations36
Density Calculations
  • Calculate the volume, in ml, of my gold cross
    • Mass of cross: 4.5 g
      • Round your answer to 2 decimal places
temperature
Temperature

Temperature Scales (3)

  • Fahrenheit
  • Celsius
  • Kelvin
temperature conversions40
Temperature Conversions
  • Shark fishing example
  • Convert room temperature to:
    • 0 C and K
  • Sauna example