Chapter 2: Analyzing Data CHEMISTRY Matter and Change.

Chapter 2: Analyzing DataChapter 2: Analyzing Data

CHEMISTRY Matter and Change

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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CHAPTER

2 Table Of Contents

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

mass: a measurement that reflects the amount of matter an object contains

• Explain how adding a prefix changes a unit.

• Compare the derived units for volume and density.

SECTION2.1

Units and Measurements

base unit

second

meter

kilogram

Chemists use an internationally recognized system of units to communicate their findings.

kelvin

derived unit

liter

density

SECTION2.1


• 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.

SECTION2.1


Units

SECTION2.1

Units and MeasurementsSECTION2.1


Units (cont.)

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

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.

SECTION2.1


Units (cont.)

• 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.

SECTION2.1


Derived Units

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

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.

SECTION2.1


Derived Units (cont.)

Which of the following is a derived unit?

A. yard

B. second

C. liter

D. kilogram

Section CheckSECTION2.1

What is the relationship between mass and volume called?

A. density

B. space

C. matter

D. weight


• Express numbers in scientific notation.

quantitative data: numerical information describing how much, how little, how big, how tall, how fast, and so on

• Convert between units using dimensional analysis.

SECTION2.2

Scientific Notation and Dimensional Analysis

scientific notation

dimensional analysis

conversion factor

Scientists often express numbers in scientific notation and solve problems using dimensional analysis.

SECTION2.2


• 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.

SECTION2.2


Scientific Notation

800 = 8.0 102

0.0000343 = 3.43 10–5

• 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.

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

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

SECTION2.2



• 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.

SECTION2.2



• 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.

SECTION2.2


Dimensional Analysis

• 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.

SECTION2.2


Dimensional Analysis (cont.)

• Using conversion factors

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

SECTION2.2


Dimensional Analysis (cont.)

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

SECTION2.2

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

SECTION2.2

Section Check

• Define and compare accuracy and precision.

experiment: a set of controlled observations that test a hypothesis

• Describe the accuracy of experimental data using error and percent error.

• Apply rules for significant figures to express uncertainty in measured and calculated values.

SECTION2.3

Uncertainty in Data

accuracy

precision

error

Measurements contain uncertainties that affect how a result is presented.

percent error

significant figures

SECTION2.3

Uncertainty in Data

• 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.

SECTION2.3

Uncertainty in Data

Accuracy and Precision

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

SECTION2.3

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.

SECTION2.3

Uncertainty in Data

Accuracy and Precision (cont.)

• Often, precision is limited by the tools available.

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

SECTION2.3

Uncertainty in Data

Significant Figures

• 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.

SECTION2.3

Uncertainty in Data

Significant Figures (cont.)

• 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.

SECTION2.3

Uncertainty in Data

Rounding Numbers

• 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.

SECTION2.3

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.

SECTION2.3

Uncertainty in Data


• 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.

SECTION2.3

Uncertainty in Data


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

SECTION2.3

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%

SECTION2.3

Section Check

• Create graphics to reveal patterns in data.

independent variable: the variable that is changed during an experiment

graph

• Interpret graphs.

Graphs visually depict data, making it easier to see patterns and trends.

SECTION2.4

Representing Data

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

SECTION2.4

Representing Data

Graphing

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

SECTION2.4

Representing Data

Graphing (cont.)

SECTION2.4

Representing Data

Graphing (cont.)

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

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

SECTION2.4

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.

SECTION2.4

Representing Data

Graphing (cont.)

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

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

SECTION2.4

Representing Data

Interpreting Graphs

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

SECTION2.4

Representing Data

Interpreting Graphs (cont.)

____ variables are plotted on the____-axis in a line graph.

A. independent, x

B. independent, y

C. dependent, x

D. dependent, z


What kind of graph shows how quantities vary across categories?

A. pie charts

B. line graphs

C. Venn diagrams

D. bar graphs


Chemistry Online

Study Guide

Chapter Assessment

Standardized Test Practice

CHAPTER

2 Analyzing Data

Resources

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.

SECTION2.1


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.

SECTION2.2


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

SECTION2.3

Uncertainty in Data

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.

SECTION2.3

Uncertainty in Data

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.

Study Guide

SECTION2.4

Representing Data

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. deci-

B. hemi-

C. kilo-

D. 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

2 Analyzing Data

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

Chapter Assessment

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


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


How many significant figures are there in 0.0000245010 meters?

A. 4

B. 5

C. 6

D. 11

CHAPTER

2 Analyzing Data


Which is NOT a quantitative measurement of a liquid?

A. color

B. volume

C. mass

D. density

CHAPTER

2 Analyzing Data


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Chapter 2: Analyzing Data CHEMISTRY Matter and Change.

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