Chapter 2 Measurements and Calculations

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# Chapter 2 Measurements and Calculations - PowerPoint PPT Presentation

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 2Measurements 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
• Converting between units
• Temperature scales
• Density
Quantitative Observations
• A quantitative observation generally includes a number and a unit.
• Record three quantitative observations about yourself.
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 Notation
• Express each of the following in scientific notation:

53,000

350

0.0025

0.0000050

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
• 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 Systems
• English System
• Used in U.S.
• Little logic to the units
• Examples
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

Quantity Base unit Symbol

Unit Systems - meteric
• Metric Prefixes, see page 19
Unit Systems
• Using prefixes
• Base unit = meter
• Kilometer = km = _________ m
Unit Systems
• International System (SI)
• Internationally agreed upon set of units
• Used in industry
• Some use in science
• See page 18
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 – 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 – 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 of a “block”
• Volume = length x height x width
• Volume of an irregularly shaped object
• Use water displacement
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 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 measurements

Thermometer

example

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
• 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
• 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 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
• Metric to Metric Conversions
• See board for the staircase method
• Using dimensional analysis to convert between units.
Converting Between Units, Practice!
• Miles  km
• Pounds  grams  kg
• mL  fluid ounces
• M  cm  inches
Density
• Density – the amount of matter present in a given volume of a substance
• Density = mass of an object

volume of object

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)
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?
Density
• Objects with a density greater than 1g/mL sink in water.
• Objects with a density less than 1g/mL float in water.
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”.
Density
• Calculating density from data
• In class experiment
Density
• Rearrange the density equation to solve for volume and mass:

Volume =

Mass =

Density Calculations
• Calculate the mass, in grams and in pounds, of a gold brick
• see board for the dimensions of the gold brick
Density Calculations
• Calculate the volume, in ml, of my gold cross
• Mass of cross: 4.5 g