Transcript Chemistry: Matter and Change

CHEMISTRY
Matter and Change
Chapter 2: Analyzing Data
CHAPTER
2
Table Of Contents
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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SECTION
2.1
Units and Measurements
• 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
SECTION
2.1
Units and Measurements
base unit
kelvin
second
derived unit
meter
liter
kilogram
density
Chemists use an internationally recognized
system of units to communicate their
findings.
SECTION
Units and Measurements
2.1
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.
SECTION
2.1
Units (cont.)
Units and Measurements
SECTION
2.1
Units (cont.)
Units and Measurements
SECTION
Units and Measurements
2.1
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
SECTION
Units and Measurements
2.1
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.
SECTION
2.1
Units and Measurements
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.
SECTION
2.1
Units and Measurements
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).
SECTION
2.1
Units and Measurements
Derived Units (cont.)
• Density is a derived unit, g/cm3, the amount of
mass per unit volume.
• The density equation is density = mass/volume.
SECTION
2.1
Section Check
Which of the following is a derived unit?
A. yard
B. second
C. liter
D. kilogram
SECTION
2.1
Section Check
What is the relationship between mass
and volume called?
A. density
B. space
C. matter
D. weight
SECTION
2.2
Scientific Notation and Dimensional Analysis
• 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
SECTION
2.2
Scientific Notation and Dimensional Analysis
scientific notation
dimensional analysis
conversion factor
Scientists often express numbers in
scientific notation and solve problems
using dimensional analysis.
SECTION
2.2
Scientific Notation and Dimensional Analysis
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.
SECTION
2.2
Scientific Notation and Dimensional Analysis
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  10–5
SECTION
2.2
Scientific Notation and Dimensional Analysis
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
SECTION
2.2
Scientific Notation and Dimensional Analysis
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.
SECTION
2.2
Scientific Notation and Dimensional Analysis
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.
SECTION
2.2
Scientific Notation and Dimensional Analysis
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.
SECTION
2.2
Scientific Notation and Dimensional Analysis
Dimensional Analysis (cont.)
• Using conversion factors
– A conversion factor must cancel one unit
and introduce a new one.
SECTION
2.2
Section Check
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
SECTION
2.2
Section Check
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
SECTION
2.3
Uncertainty in Data
• 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
SECTION
2.3
Uncertainty in Data
accuracy
percent error
precision
significant figures
error
Measurements contain uncertainties
that affect how a result is presented.
SECTION
2.3
Uncertainty in Data
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.
SECTION
2.3
Uncertainty in Data
Accuracy and Precision (cont.)
• Error is defined as the difference between
an experimental value and an accepted
value.
SECTION
2.3
Uncertainty in Data
Accuracy and Precision (cont.)
• The error equation is
error = experimental value – accepted value.
• Percent error expresses error as a
percentage of the accepted value.
SECTION
2.3
Uncertainty in Data
Significant Figures
• Often, precision is limited by the tools available.
• Significant figures include all known digits plus
one estimated digit.
SECTION
2.3
Uncertainty in Data
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.
SECTION
2.3
Uncertainty in Data
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.
SECTION
2.3
Uncertainty in Data
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.
SECTION
2.3
Uncertainty in Data
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.
SECTION
2.3
Uncertainty in Data
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.
SECTION
2.3
Section Check
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
SECTION
2.3
Section Check
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%
SECTION
2.4
Representing Data
• Create graphics to
reveal patterns in data.
• Interpret graphs.
independent variable:
the variable that is
changed during an
experiment
graph
Graphs visually depict data, making it
easier to see patterns and trends.
SECTION
Representing Data
2.4
Graphing
• A graph is a visual display of data that makes
trends easier to see than in a table.
SECTION
2.4
Representing Data
Graphing (cont.)
• A circle graph, or pie chart, has wedges that
visually represent percentages of a fixed whole.
SECTION
2.4
Representing Data
Graphing (cont.)
• Bar graphs are often used to show how a
quantity varies across categories.
SECTION
2.4
Representing Data
Graphing (cont.)
• On line graphs, independent variables are
plotted on the x-axis and dependent variables
are plotted on the y-axis.
SECTION
2.4
Representing Data
Graphing (cont.)
• If a line through the points is straight, the
relationship is linear and can be analyzed
further by examining the slope.
SECTION
2.4
Representing Data
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.
SECTION
2.4
Representing Data
Interpreting Graphs (cont.)
• This graph shows important ozone
measurements and helps the viewer visualize a
trend from two different time periods.
SECTION
2.4
Section Check
____ variables are plotted on the
____-axis in a line graph.
A. independent, x
B. independent, y
C. dependent, x
D. dependent, z
SECTION
2.4
Section Check
What kind of graph shows how quantities
vary across categories?
A. pie charts
B. line graphs
C. Venn diagrams
D. bar graphs
CHAPTER
Analyzing Data
2
Resources
Chemistry Online
Study Guide
Chapter Assessment
Standardized Test Practice
SECTION
Units and Measurements
2.1
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.
SECTION
2.2
Scientific Notation and Dimensional Analysis
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.
SECTION
Uncertainty in Data
2.3
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
SECTION
Uncertainty in Data
2.3
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.
SECTION
Representing Data
2.4
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.
CHAPTER
2
Analyzing Data
Chapter Assessment
Which of the following is the SI derived
unit of volume?
A. gallon
B. quart
C. m3
D. kilogram
CHAPTER
2
Analyzing Data
Chapter Assessment
Which prefix means 1/10th?
A. deciB. hemi-
C. kiloD. centi-
CHAPTER
2
Analyzing Data
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
CHAPTER
Analyzing Data
2
Chapter Assessment
Round 2.3450 to 3 significant figures.
A. 2.35
B. 2.345
C. 2.34
D. 2.40
CHAPTER
2
Analyzing Data
Chapter Assessment
The rise divided by the run on a line graph
is the ____.
A. x-axis
B. slope
C. y-axis
D. y-intercept
CHAPTER
2
Analyzing Data
Chapter Assessment
Which is NOT an SI base unit?
A. meter
B. second
C. liter
D. kelvin
CHAPTER
2
Analyzing Data
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
CHAPTER
2
Analyzing Data
Standardized Test Practice
Find the solution with the correct number
of significant figures:
25  0.25
A. 6.25
B. 6.2
C. 6.3
D. 6.250
CHAPTER
2
Analyzing Data
Standardized Test Practice
How many significant figures are there in
0.0000245010 meters?
A. 4
B. 5
C. 6
D. 11
CHAPTER
2
Analyzing Data
Standardized Test Practice
Which is NOT a quantitative measurement
of a liquid?
A. color
B. volume
C. mass
D. density
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