Chemistry: Matter and Change

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CHEMISTRY Matter and Change
Chapter 2 Analyzing Data
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Table Of Contents
CHAPTER2
Section 2.1 Units and Measurements Section
2.2 Scientific Notation and Dimensional
Analysis Section 2.3 Uncertainty in Data Section
2.4 Representing Data
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Units and Measurements
SECTION2.1

• Define SI base units for time, length, mass, and
  temperature.

• Explain how adding a prefix changes a unit.
• Compare the derived units for volume and density.

mass a measurement that reflects the amount of
matter an object contains
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Units and Measurements
SECTION2.1
base unit second meter kilogram
kelvin derived unit liter density
Chemists use an internationally recognized system
of units to communicate their findings.
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Units and Measurements
SECTION2.1
Units

• Système Internationale d'Unités (SI) is an
  internationally agreed upon system of
  measurements.

• A base unit is a defined unit in a system of
  measurement that is based on an object or event
  in the physical world, and is independent of
  other units.

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Units and Measurements
Units and Measurements
SECTION2.1
SECTION2.1
Units (cont.)
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Units and Measurements
SECTION2.1
Units (cont.)
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Units and Measurements
SECTION2.1
Units (cont.)

• The SI base unit of time is the second (s),
  based on the frequency of radiation given off by
  a cesium-133 atom.

• The SI base unit for length is the meter (m), the
  distance light travels in a vacuum in
  1/299,792,458th of a second.
• The SI base unit of mass is the kilogram (kg),
  about 2.2 pounds

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Units and Measurements
SECTION2.1
Units (cont.)

• The SI base unit of temperature is the kelvin (K).

• Zero kelvin is the point where there is virtually
  no particle motion or kinetic energy, also known
  as absolute zero.
• Two other temperature scales are Celsius and
  Fahrenheit.

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Units and Measurements
SECTION2.1
Derived Units

• Not all quantities can be measured with SI base
  units.

• A unit that is defined by a combination of base
  units is called a derived unit.

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Units and Measurements
SECTION2.1
Derived Units (cont.)

• Volume is measured in cubic meters (m3), but this
  is very large. A more convenient measure is the
  liter, or one cubic decimeter (dm3).

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Units and Measurements
SECTION2.1
Derived Units (cont.)

• Density is a derived unit, g/cm3, the amount of
  mass per unit volume.

• The density equation is density mass/volume.

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Section Check
SECTION2.1
Which of the following is a derived unit?
A. yard B. second C. liter D. kilogram
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Section Check
SECTION2.1
What is the relationship between mass and volume
called? A. density B. space C. matter D. weight

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Scientific Notation and Dimensional Analysis
SECTION2.2

• Express numbers in scientific notation.

• Convert between units using dimensional analysis.

quantitative data numerical information
describing how much, how little, how big, how
tall, how fast, and so on
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Scientific Notation and Dimensional Analysis
SECTION2.2
scientific notation dimensional
analysis conversion factor
Scientists often express numbers in scientific
notation and solve problems using dimensional
analysis.
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Scientific Notation and Dimensional Analysis
SECTION2.2
Scientific Notation

• Scientific notation can be used to express any
  number as a number between 1 and 10 (known as the
  coefficient) multiplied by 10 raised to a power
  (known as the exponent).
• Carbon atoms in the Hope Diamond 4.6 x 1023
• 4.6 is the coefficient and 23 is the exponent.

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Scientific Notation and Dimensional Analysis
SECTION2.2
Scientific Notation (cont.)

• Count the number of places the decimal point must
  be moved to give a coefficient between 1 and 10.

• The number of places moved equals the value of
  the exponent.

• The exponent is positive when the decimal moves
  to the left and negative when the decimal moves
  to the right.

800 8.0 ? 102 0.0000343 3.43 ? 105
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Scientific Notation and Dimensional Analysis
SECTION2.2
Scientific Notation (cont.)

• Addition and subtraction

• Exponents must be the same.
• Rewrite values to make exponents the same.
• Ex. 2.840 x 1018 3.60 x 1017, you must rewrite
  one of these numbers so their exponents are the
  same. Remember that moving the decimal to the
  right or left changes the exponent.
• 2.840 x 1018 0.360 x 1018
• Add or subtract coefficients.
• Ex. 2.840 x 1018 0.360 x 1017 3.2 x 1018

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Scientific Notation and Dimensional Analysis
SECTION2.2
Scientific Notation (cont.)

• Multiplication and division

• To multiply, multiply the coefficients, then add
  the exponents.
• Ex. (4.6 x 1023)(2 x 10-23) 9.2 x 100
• To divide, divide the coefficients, then subtract
  the exponent of the divisor from the exponent of
  the dividend.
• Ex. (9 x 107) (3 x 10-3) 3 x 1010
• Note Any number raised to a power of 0 is equal
  to 1 thus, 9.2 x 100 is equal to 9.2.

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Scientific Notation and Dimensional Analysis
SECTION2.2
Dimensional Analysis

• Dimensional analysis is a systematic approach to
  problem solving that uses conversion factors to
  move, or convert, from one unit to another.

• A conversion factor is a ratio of equivalent
  values having different units.

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Scientific Notation and Dimensional Analysis
SECTION2.2
Dimensional Analysis (cont.)

• Writing conversion factors

• Conversion factors are derived from equality
  relationships, such as 1 dozen eggs 12 eggs.
• Percentages can also be used as conversion
  factors. They relate the number of parts of one
  component to 100 total parts.

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Scientific Notation and Dimensional Analysis
SECTION2.2
Dimensional Analysis (cont.)

• Using conversion factors

• A conversion factor must cancel one unit and
  introduce a new one.

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Section Check
SECTION2.2
What is a systematic approach to problem solving
that converts from one unit to another?
A. conversion ratio B. conversion
factor C. scientific notation D. dimensional
analysis
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Section Check
SECTION2.2
Which of the following expresses 9,640,000 in the
correct scientific notation? A. 9.64 ? 104
B. 9.64 ? 105 C. 9.64 106 D. 9.64 ? 610
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Uncertainty in Data
SECTION2.3

• Define and compare accuracy and precision.

• Describe the accuracy of experimental data using
  error and percent error.
• Apply rules for significant figures to express
  uncertainty in measured and calculated values.

experiment a set of controlled observations that
test a hypothesis
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Uncertainty in Data
SECTION2.3
accuracy precision error
percent error significant figures
Measurements contain uncertainties that affect
how a result is presented.
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Uncertainty in Data
SECTION2.3
Accuracy and Precision

• Accuracy refers to how close a measured value is
  to an accepted value.

• Precision refers to how close a series of
  measurements are to one another.

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Uncertainty in Data
SECTION2.3
Accuracy and Precision (cont.)

• Error is defined as the difference between an
  experimental value and an accepted value.

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Uncertainty in Data
SECTION2.3
Accuracy and Precision (cont.)

• The error equation is error experimental value
  accepted value.

• Percent error expresses error as a percentage of
  the accepted value.

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Uncertainty in Data
SECTION2.3
Significant Figures

• Often, precision is limited by the tools
  available.

• Significant figures include all known digits plus
  one estimated digit.

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Uncertainty in Data
SECTION2.3
Significant Figures (cont.)

• Rules for significant figures

• Rule 1 Nonzero numbers are always significant.
• Rule 2 Zeros between nonzero numbers are always
  significant.
• Rule 3 All final zeros to the right of the
  decimal are significant.
• Rule 4 Placeholder zeros are not significant.
  To remove placeholder zeros, rewrite the number
  in scientific notation.
• Rule 5 Counting numbers and defined constants
  have an infinite number of significant figures.

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Uncertainty in Data
SECTION2.3
Rounding Numbers

• Calculators are not aware of significant figures.

• Answers should not have more significant figures
  than the original data with the fewest figures,
  and should be rounded.

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Uncertainty in Data
SECTION2.3
Rounding Numbers (cont.)

• Rules for rounding

• Rule 1 If the digit to the right of the last
  significant figure is less than 5, do not change
  the last significant figure.
• Rule 2 If the digit to the right of the last
  significant figure is greater than 5, round up
  the last significant figure.
• Rule 3 If the digits to the right of the last
  significant figure are a 5 followed by a nonzero
  digit, round up the last significant figure.

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Uncertainty in Data
SECTION2.3
Rounding Numbers (cont.)

• Rules for rounding (cont.)

• Rule 4 If the digits to the right of the last
  significant figure are a 5 followed by a 0 or no
  other number at all, look at the last significant
  figure. If it is odd, round it up if it is even,
  do not round up.

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Uncertainty in Data
SECTION2.3
Rounding Numbers (cont.)

• Addition and subtraction

• Round the answer to the same number of decimal
  places as the original measurement with the
  fewest decimal places.

• Multiplication and division

• Round the answer to the same number of
  significant figures as the original measurement
  with the fewest significant figures.

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Section Check
SECTION2.3
Determine the number of significant figures in
the following 8,200, 723.0, and 0.01. A. 4, 4,
and 3 B. 4, 3, and 3 C. 2, 3, and 1 D. 2, 4, and
1
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Section Check
SECTION2.3
A substance has an accepted density of 2.00 g/L.
You measured the density as 1.80 g/L. What is the
percent error? A. 20 B. 20 C. 10 D. 90
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Representing Data
SECTION2.4

• Create graphics to reveal patterns in data.

independent variable the variable that is
changed during an experiment

• Interpret graphs.

graph
Graphs visually depict data, making it easier to
see patterns and trends.
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Representing Data
SECTION2.4
Graphing

• A graph is a visual display of data that makes
  trends easier to see than in a table.

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Representing Data
SECTION2.4
Graphing (cont.)

• A circle graph, or pie chart, has wedges that
  visually represent percentages of a fixed whole.

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Representing Data
SECTION2.4
Graphing (cont.)

• Bar graphs are often used to show how a quantity
  varies across categories.

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Representing Data
SECTION2.4
Graphing (cont.)

• On line graphs, independent variables are plotted
  on the x-axis and dependent variables are plotted
  on the y-axis.

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Representing Data
SECTION2.4
Graphing (cont.)

• If a line through the points is straight, the
  relationship is linear and can be analyzed
  further by examining the slope.

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Representing Data
SECTION2.4
Interpreting Graphs

• Interpolation is reading and estimating values
  falling between points on the graph.

• Extrapolation is estimating values outside the
  points by extending the line.

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Representing Data
SECTION2.4
Interpreting Graphs (cont.)

• This graph shows important ozone measurements and
  helps the viewer visualize a trend from two
  different time periods.

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Section Check
SECTION2.4
____ variables are plotted on the____-axis in a
line graph. A. independent, x B. independent,
y C. dependent, x D. dependent, z
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Section Check
SECTION2.4
What kind of graph shows how quantities vary
across categories? A. pie charts B. line
graphs C. Venn diagrams D. bar graphs
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Analyzing Data
CHAPTER2
Resources
Chemistry Online Study Guide Chapter
Assessment Standardized Test Practice
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Units and Measurements
SECTION2.1
Study Guide
Key Concepts

• SI measurement units allow scientists to report
  data to other scientists.

• Adding prefixes to SI units extends the range of
  possible measurements.
• To convert to Kelvin temperature, add 273 to the
  Celsius temperature. K C 273
• Volume and density have derived units. Density,
  which is a ratio of mass to volume, can be used
  to identify an unknown sample of matter.

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Scientific Notation and Dimensional Analysis
SECTION2.2
Study Guide
Key Concepts

• A number expressed in scientific notation is
  written as a coefficient between 1 and 10
  multiplied by 10 raised to a power.

• To add or subtract numbers in scientific
  notation, the numbers must have the same
  exponent.
• To multiply or divide numbers in scientific
  notation, multiply or divide the coefficients and
  then add or subtract the exponents, respectively.
  
• Dimensional analysis uses conversion factors to
  solve problems.

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Uncertainty in Data
SECTION2.3
Study Guide
Key Concepts

• An accurate measurement is close to the accepted
  value. A set of precise measurements shows little
  variation.

• The measurement device determines the degree of
  precision possible.
• Error is the difference between the measured
  value and the accepted value. Percent error gives
  the percent deviation from the accepted
  value. error experimental value accepted
  value

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Uncertainty in Data
SECTION2.3
Study Guide
Key Concepts

• The number of significant figures reflects the
  precision of reported data.

• Calculations should be rounded to the correct
  number of significant figures.

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Representing Data
SECTION2.4
Study Guide
Key Concepts

• Circle graphs show parts of a whole. Bar graphs
  show how a factor varies with time, location, or
  temperature.

• Independent (x-axis) variables and dependent
  (y-axis) variables can be related in a linear or
  a nonlinear manner. The slope of a straight line
  is defined as rise/run, or ?y/?x.

• Because line graph data are considered
  continuous, you can interpolate between data
  points or extrapolate beyond them.

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Analyzing Data
CHAPTER2
Chapter Assessment
Which of the following is the SI derived unit of
volume? A. gallon B. quart C. m3 D. kilogram
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Analyzing Data
CHAPTER2
Chapter Assessment
Which prefix means 1/10th? A. deci-
B. hemi- C. kilo- D. centi-
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Analyzing Data
CHAPTER2
Chapter Assessment
Divide 6.0 ? 109 by 1.5 ? 103. A. 4.0 ? 106
B. 4.5 ? 103 C. 4.0 ? 103 D. 4.5 ? 106
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Analyzing Data
CHAPTER2
Chapter Assessment
Round 2.3450 to 3 significant figures. A. 2.35
B. 2.345 C. 2.34 D. 2.40
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Analyzing Data
CHAPTER2
Chapter Assessment
The rise divided by the run on a line graph is
the ____. A. x-axis B. slope C. y-axis D. y-int
ercept
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Analyzing Data
CHAPTER2
Chapter Assessment
Which is NOT an SI base unit? A. meter
B. second C. liter D. kelvin
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Analyzing Data
CHAPTER2
Standardized Test Practice
Which value is NOT equivalent to the others?
A. 800 m B. 0.8 km C. 80 dm D. 8.0 x 104 cm
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Analyzing Data
CHAPTER2
Standardized Test Practice
Find the solution with the correct number of
significant figures25 ? 0.25 A. 6.25
B. 6.2 C. 6.3 D. 6.250
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Analyzing Data
CHAPTER2
Standardized Test Practice
How many significant figures are there in
0.0000245010 meters? A. 4 B. 5 C. 6 D. 11
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Analyzing Data
CHAPTER2
Standardized Test Practice
Which is NOT a quantitative measurement of a
liquid? A. color B. volume C. mass D. density
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