Lecture Presentation
Chapter 1
Chemistry in
Our Lives
Karen C. Timberlake
What is Chemistry?
Chemistry
• is the study of composition,
structure, properties, and
reactions of matter.
• happens all around you
every day.
Antacid tablets undergo a
chemical reaction when dropped
in water.
Chemistry and Matter
Matter is another word for all substances that make up our world.
Matter is defined as anything that has mass and occupies space
(volume)
•
Antacid tablets are matter.
•
Water is matter.
•
Glass is matter.
•
Air is matter.
Math Skills Needed For Chemistry
Identifying Place Values
For any number, we can identify the place value
for each of the digits in that number.
The place values for two numbers are listed
below:
A premature baby has a
mass of 2518 grams.
A silver coin has a
mass of 6.407 grams.
Key Math Skill Identifying Place Values
Solving Equations
Equations can be rearranged to solve for an unknown
variable.
1.
Place all like items on one side.
2.
Isolate the variable you need to solve for.
3.
Check your answer.
Key Math Skill Solving Equations
Study Check
Solve the following equation for P1.
Solution
Solve the following equation for P1.
To solve for P1, divide both sides by V1.
Scientific Notation
People have an average of 1 × 105 hairs on the
scalp. Each hair is about 8 × 10−6 m wide.
Key Math Skill Writing Numbers in Scientific Notation
1. Scientific Notation
Scientists use scientific notation for two reasons:
1. To make it easier to report extremely large or
extremely small measurements
2. To report the correct number of significant digits
in a measuremed or calculated value
We will first focus on reason 1.
1. Scientific Notation
Rules for writing a number in scientific notation:
Numbers written in scientific notation have two parts:
1. A Coefficient
2. A Power of 10
To write 2400 in the correct scientific notation,
• Move the decimal place to the left until there is only 1 non zero
digit to the left of the decimal place - the coefficient is 2.4.
• Count the number of places the decimal place was moved – that
become the coefficient on the the power of 10, which is 3.
• write the product of the coefficient multiplied by a power of 10.
2.4 × 103
Guide to Converting a Number in Standard Notation Into
Scientific Notation – Numbers 10 or Greater
Step 1:
Move the decimal point on the original
number to the left until there is only 1
nonzero digit to the left of the decimal
place. This becomes the “coefficient”
in scientific notation. Count the
number of “number places” the
decimal place was moved to the left.
This becomes the positive exponent
on the power of 10.
Step 2: Write the coefficient multiplied
by the power of ten, the exponent on
the power of 10 is the number of
“places” you moved the decimal.
Scientific Notation Examples:
Numbers 10 or greater
2 400
 3 places
= 2.4 × 1 000
=
2.4 × 103
Coefficient × Power of 10
Guide to Converting a Number in Standard Notation Into
Scientific Notation – Numbers less than 1
Step 1:
Move the decimal point on the original
number to the right until there is only
1 nonzero digit to the left of the
decimal place. This becomes the
“coefficient” in scientific notation.
Count the number of “number places”
the decimal place was moved to the
right. This becomes the negative
exponent on the power of 10.
Step 2: Write the coefficient multiplied
by the power of ten, the exponent on
the power of 10 is the number of
“places” you moved the decimal.
Scientific Notation Examples – numbers
less than 1
0.00086 =
4 places 
=
8.6 × 10−4
Coefficient × Power of 10
Measurements Using Scientific Notation
Example: the diameter of chickenpox virus is 0.000 000 3 m
= 3 × 10−7 m
Study Check
Write each of the following in correct scientific
notation:
A. 64 000
B. 0.021
Lecture Presentation
Chapter 2
Chemistry and
Measurements
Karen C. Timberlake
2.1 Units of Measurement
The metric system is the
standard system of
measurement used in
chemistry.
Learning Goal Write the names and abbreviations for the metric
or SI units used in measurements of length, volume, mass,
temperature, and time.
Units of Measurement
Scientists use the metric system of measurement and have adopted
a modification of the metric system called the International System
of Units as a worldwide standard.
The International System of Units (SI) is an official system of
measurement used throughout the world for units of length, volume,
mass, temperature, and time.
Units of Measurement: Metric and SI
Length: Meter (m), Centimeter (cm)
Length in the metric and SI systems is based on the meter, which is
slightly longer than a yard.
1 m = 100 cm
1 m = 39.4 in.
1m = 1.09 yd
2.54 cm = 1 in.
Volume: Liter (L), Milliliter (mL)
Volume is the space occupied
by a substance. The SI unit of
volume is m3; however, in the
metric system, volume is based
on the liter, which is slightly
larger than a quart.
1L
= 1000 mL
1L
= 1.06 qt
946 mL = 1 qt
Graduated cylinders are used
to measure small volumes.
Mass: Gram (g), Kilogram (kg)
The mass of an object is a measure
of the quantity of material it
contains.
1 kg
= 1000 g
1 kg
= 2.20 lb
454 g
= 1 lb
The SI unit of mass, the kilogram
(kg), is used for larger masses. The
metric unit for mass is the gram
(g), which is used for smaller
masses.
On an electronic balance, the
digital readout gives the mass
of a nickel, which is 5.01 g.
Temperature: Celsius (°C), Kelvin (K)
Temperature tells us how hot or cold
something is.
Temperature is measured using
• Celsius (°C) in the metric system.
• Kelvin (K) in the SI system.
Water freezes at 32 °F, or 0 °C.
The Kelvin scale for temperature begins
at the lowest possible temperature, 0 K.
A thermometer is used to
measure temperature.
2.2 Measured Numbers and
Significant Figures
Length is measured by observing the marked lines at the end of
a ruler. The last digit in your measurement is an estimate,
obtained by visually dividing the space between the marked
lines.
Learning Goal Identify a number as measured or exact;
determine the number of significant figures in a measured
number.
Measured Numbers
Measured numbers are the numbers obtained when you
measure a quantity such as your height, weight, or
temperature.
To write a measured number,
• observe the numerical values of the marked lines.
• estimate the value of the number between the marks.
The estimated number is the final number in your measured
number.
Measured Numbers for Length
The lengths of the objects are
measured as
A. 4.5 cm.
B. 4.55 cm.
C. 3.0 cm
Significant Figures
In a measured number, the significant figures (SFs) are all the digits,
including the estimated digit.
Significant figures
• are used to represent the amount of error associated with a
measurement.
• are all nonzero digits and zeros between digits.
• are not zeros that act as placeholders before digits.
• are zeros at the end of a decimal number.
Core Chemistry Skill Counting Significant Figures
Measured Numbers: Significant Figures
A number is a significant figure (SF) if it is/has
The Atlantic-Pacific Rule For Significant Digits
 Imagine your number in the middle of the
country
Pacific
Atlantic
 If a decimal point is present, start counting
digits from the Pacific (left) side of the
number,
 The first sig fig is the first nonzero digit, then
any digit after that.
e.g. 0.003100 would have 4 sig figs
© 2013 Pearson Education, Inc.
Chapter 1, Section 1
31
The Atlantic-Pacific Rule For Significant Digits
 Imagine your number in the middle of the
country
Pacific
Atlantic
 If the decimal point is absent, start counting
digits from the Atlantic (right) side, starting
with the first non-zero digit. The first sig fig is
the first nonzero digit, then any digit after that
e.g. 31,400
( 3 sig. figs.)
© 2013 Pearson Education, Inc.
Chapter 1, Section 1
32
Scientific Notation and Significant Zeros
When one or more zeros in a large number are significant,
• they are shown clearly by writing the number in scientific
notation.
In this book, we place a decimal point after a significant zero
at the end of a number.
For example, if only the first zero in the measurement 300 m is
significant, the measurement is written as 3.0 × 102 m.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Scientific Notation and Significant Zeros
Zeros at the end of large standard numbers without a
decimal point are not significant.
•
400 000 g is written with one SF as 4 × 105 g.
•
850 000 m is written with two SFs as 8.5 × 105 m.
Zeros at the beginning of a decimal number are used as
placeholders and are not significant.
•
0.000 4 s is written with one SF as 4 × 10−4 s.
•
0.000 0046 g is written with two SFs as 4.6 × 10−6 g.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Identify the significant and nonsignificant zeros in each of
the following numbers, and write them in the correct
scientific notation.
A. 0.002 650 m
B. 43.026 g
C. 1 044 000 L
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Identify the significant and nonsignificant zeros in each of the
following numbers, and write them in the correct scientific
notation.
A. 0.002 650 m is written as 2.650 × 10−3 m. four SFs
• The zeros preceding the 2 are not significant.
• The digits 2, 6, 5 are significant.
• The zero in the last decimal place is significant.
B. 43.026 g is written as 4.3026 × 101 g.
five SFs
• The zeros between nonzero digits or at the end of
decimal numbers are significant.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Identify the significant zeros and nonsignificant zeros in each
of the following numbers, and write them in the correct
scientific notation.
C. 1 044 000 L is written as 1.044 × 106 L. four SFs
• The zeros between nonzero digits are significant.
• The zeros at end of a number with no decimal point
are not significant.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Exact Numbers
Exact numbers are
• not measured and do not have a limited number of
significant figures.
• not used to find the number of significant figures in a
calculated answer.
• numbers obtained by counting.
8 cookies
• definitions that compare two units.
6 eggs
• definitions in the same measuring system.
1 qt = 4 cups
1 kg = 1 000 g
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Exact Numbers
Examples of exact numbers include the following:
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Identify the numbers below as measured or exact, and give
the number of significant figures in each measured number.
A. 3 coins
B. The diameter of a circle is 7.902 cm.
C. 60 min = 1 h
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
2.3 Significant Figures in Calculations
A calculator is helpful in
working problems and
doing calculations faster.
Learning Goal Adjust calculated answers to give the
correct number of significant figures.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Rules for Rounding Off
1. If the first digit to be dropped is 4 or less, then it and all
the following digits are dropped from the number.
2. If the first digit to be dropped is 5 or greater, then the last
retained digit of the number is increased by 1.
Key Math Skill Rounding Off
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Write the correct value when 3.1457 g is rounded to each of
the following:
A. three significant figures
B. two significant figures
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Write the correct value when 3.1457 g is rounded to each of
the following:
A. To round 3.1457 to three significant figures,
• drop the final digits, 57.
• increase the last remaining digit by 1.
The answer is 3.15 g.
B. To round 3.1457 g to two significant figures,
• drop the final digits, 457.
• do not increase the last number by 1, since the first digit
dropped is 4.
The answer is 3.1 g.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Multiplication and Division:
Measured Numbers
In multiplication or division, the final answer is written so that it
has the same number of significant figures (SFs) as the
measurement with the fewest significant figures.
Example 1 Multiply the following measured numbers:
24.66 cm × 0.35 cm
= 8.631 (calculator display)
= 8.6 cm2 (two significant figures)
Multiplying four SFs by two SFs gives us an answer with
two SFs.
Core Chemistry Skill Using Significant Figures in Calculations
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Multiplication and Division:
Measured Numbers
Example 2 Multiply and divide the following measured
numbers:
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Adding Significant Zeros
Adding Zeros: When the calculator display contains fewer SFs
than needed, add one or more significant zeros to obtain the
correct number of significant figures.
Example: Multiply and divide the following measured numbers:
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Perform the following calculation of measured numbers. Give
the answer in the correct number of significant figures.
×
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Perform the following calculation of measured numbers. Give
the answer in the correct number of significant figures.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Measured Numbers: Addition and
Subtraction
In addition or subtraction, the final answer is written so
that it has the same number of decimal places as the
measurement with the fewest decimal places.
Example 1 Add the following measured numbers:
2.012
61.09
+ 3.0
Thousandths place
Hundredths place
Tenths place
66.102
Calculator display
66.1
Answer rounded to the tenths place
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Measured Numbers: Addition and
Subtraction
Example 2 Subtract the following measured numbers:
65.09
Hundredths place
− 3.0
Tenths place
62.09
Calculator display
62.1
Answer rounded to the tenths place
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Add the following measured numbers:
82.409 mg
+ 22.0
mg
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Add the following measured numbers:
82.409 mg
Thousandths place
+ 22.0
mg
Tenths place
104.409 mg
Calculator display
104.4
mg
Answer rounded to the tenths place
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
2.4 Prefixes and Equalities
Using a retinal camera,
an ophthalmologist
photographs the retina of
the eye.
Learning Goal Use the numerical values of prefixes to write
a metric equality.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Prefixes
A special feature of the SI as well as the metric system is
that a prefix can be placed in front of any unit to increase
or decrease its size by some factor of ten.
For example, the prefixes milli and micro are used to make
the smaller units.
milligram
(mg)
microgram (μg or mcg)
Core Chemistry Skill Using Prefixes
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Metric and SI Prefixes
Prefixes That Increase the Size of the Unit
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Metric and SI Prefixes
Prefixes That Increase Decrease the Size of the Unit
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Prefixes and Equalities
•
The relationship of a prefix to a unit can be
expressed by replacing the prefix with its numerical
value.
•
For example, when the prefix kilo in kilometer is
replaced with its value of 1000, we find that a
kilometer is equal to 1000 meters.
kilometer =
1000 meters (103 m)
kiloliter
=
1000 liters (103 L)
kilogram
=
1000 grams (103 g)
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Fill in the blanks with the correct prefix:
A. 1000 m = 1 ___ m
B. 1 × 10−3 g = 1 ___ g
C. 0.01 m = 1 ___ m
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Measuring Length
Ophthalmologists measure the diameter of the eye’s retina in
centimeters (cm), while a surgeon measures the length of a
nerve in millimeters (mm).
Each of the following equalities describes the same length in a
different unit.
1 m = 100 cm
= 1 × 102 cm
1 m = 1000 mm = 1 × 103 mm
1 cm = 10 mm
= 1 × 101 mm
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Measuring Volume
Volumes of 1 L or smaller are common in the health sciences.
When a liter is divided into 10 equal portions, each portion is
called a deciliter (dL).
Examples of some volume equalities include the following:
1L
= 10 dL
= 1 × 101 dL
1L
= 1000 mL = 1 × 103 mL
1 dL = 100 mL
= 1 × 102 mL
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Measuring Volume
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
The Cubic Centimeter
The cubic centimeter (abbreviated as cm3 or cc) is the
volume of a cube whose dimensions are 1 cm on each side.
A cubic centimeter has the same volume as a milliliter, and
the units are often used interchangeably.
1 cm3 = 1 cc = 1 mL and
1000 cm3 = 1000 mL = 1 L
A plastic intravenous fluid
container contains 1000 mL.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
The Cubic Centimeter
A cube measuring 10 cm on each side has a volume of
1000 cm3.
10 cm × 10 cm × 10 cm = 1000 cm3 = 1000 mL = 1 L
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Measuring Mass
When you visit the doctor for a physical examination, he or she
records your mass in kilograms (kg) and laboratory results in
micrograms (μg or mcg).
Examples of equalities between different metric units of mass
are as follows:
1 kg = 1000 g
= 1 × 103 g
1g
= 1000 mg = 1 × 103 mg
1g
= 100 cg
= 1 × 102 cg
1 mg = 1000 μg, 1000 mcg = 1 × 103 μg
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Identify the larger unit in each of the following:
A. mm or cm
B. kilogram or centigram
C. mL or μL
D. kL or mcL
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
2.5 Writing Conversion Factors
In the United States, the contents of many packaged foods are
listed in both U.S. and metric units.
Learning Goal Write a conversion factor for two units that
describe the same quantity.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Equalities
Equalities
• use two different units to describe the same measured
amount.
• are written for relationships between units of the metric
system, U.S. units, or between metric and U.S. units.
For example,
1m
= 1000 mm (103 mm)
1 lb
= 16 oz
2.20 lb = 1 kg
Core Chemistry Skill Writing Conversion Factors from
Equalities
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Equalities: Conversion Factors
Any equality can be written as conversion factors.
Conversion Factors for the Equality 60 min = 1 h
Conversion Factors for the Metric Equality 1 m = 100 cm
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Equalities: Conversion Factors and SF
The numbers in
• any equality between two metric units or between two
U.S. system units are obtained by definition and are,
therefore, exact numbers.
• As definitions are exact, they are not used to determine
significant figures.
• an equality between metric and U.S. units contains one
number obtained by measurement and therefore counts
toward the significant figures.
Exception: The equality 1 in. = 2.54 cm has been defined as
an exact relationship. Therefore, 2.54 is an exact number.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Some Common Equalities
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Metric Conversion Factors
We can write metric conversion factors.
Both are proper conversion factors for the relationship; on
is just the inverse of the other.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Metric–U.S. System Conversion Factors
We can write metric–U.S.
system conversion factors.
In the United States, the contents
of many packaged foods are listed
in both U.S. and metric units.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Write conversion factors from the equality for each of the
following:
A. liters and milliliters
B. meters and inches
C. meters and kilometers
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Write conversion factors from the equality for each of the
following:
A.
B.
C.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Equalities and Conversion Factors Within a
Problem
An equality may also be stated within a problem that applies
only to that problem.
The car was traveling at a speed of 85 km/h.
One tablet contains 500 mg of vitamin C.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Conversion Factors: Dosage Problems
Equalities stated within dosage
problems for medication can also be
written as conversion factors.
Keflex (Cephalexin), an antibiotic used
for respiratory and ear infections, is
available in 250-mg capsules.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Conversion Factors: Percentage, ppm, ppb
A percentage (%) is written as a conversion factor by choosing
a unit and expressing the numerical relationship of the parts of
this unit to 100 parts of the whole.
A person might have 18% body fat by mass.
To indicate very small ratios, we use parts per million (ppm)
and parts per billion (ppb).
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
Write the equality and its corresponding conversion factors.
Identify each number as exact, or give its significant figures in
the following statement:
Salmon contains 1.9% omega-3 fatty acids.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Write the equality and its corresponding conversion factors.
Identify each number as exact, or give its significant figures in
the following statement:
Salmon contains 1.9% omega-3 fatty acids.
Exact
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
Two SFs
© 2016 Pearson Education, Inc.
Study Check
Write the equality and conversion factor for each of the
following:
A. Meters and centimeters (length)
B. Jewelry that contains 18% gold (percentage)
C. One gallon of gas is $3.40.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
Write the equality and conversion factor for each of the
following:
A. Meters and centimeters
B. Jewelry that contains 18% gold
C. One gallon of gas is $3.40.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
2.6 Problem Solving Using Unit Conversion (Also called
Dimensional Analysis)
Exercising regularly
helps reduce body fat.
Learning Goal Use conversion factors to change from one
unit to another.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Guide to Problem Solving Using Unit
Conversion (Dimensional Analysis)
The process of problem solving in chemistry often requires
one or more conversion factors to change a given unit to
the needed unit.
Problem solving in chemistry requires
• identification of the given quantity units.
• determination of the units needed.
• identification of conversion factors that connect the given
and needed units.
Core Chemistry Skill Using Conversion Factors
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Guide to Problem Solving Using Unit
Conversion
Steps for solving
problems that contain
unit conversions
include the following:
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solving Problems Using Unit Conversion
Example: If a person weighs 164 lb, what is the body mass
in kilograms?
STEP 1 State the given and needed quantities.
STEP 2 Write a unit plan to convert the given unit
to the needed unit.
pounds
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
kilograms
© 2016 Pearson Education, Inc.
Solving Problems Using Unit Conversion
Example: If a person weighs 164 lb, what is the body mass in
kilograms?
STEP 3 State the equalities and conversion factors.
STEP 4 Set up the problem to cancel units and
calculate the answer.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
A rattlesnake is 2.44-m long. How many centimeters long is
the snake?
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A rattlesnake is 2.44-m long. How many centimeters long is
the snake?
STEP 1 State the given and needed quantities.
ANALYZE
THE PROBLEM
GIVEN
2.44 m
NEED
centimeters
STEP 2 Write a unit plan to convert the given unit
to the needed unit.
meters
centimeters
Metric
Factor
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A rattlesnake is 2.44-m long. How many centimeters long is
the snake?
STEP 3 State the equalities and conversion factors.
STEP 4 Set up the problem to cancel units and
calculate the answer.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Using Two or More Conversion Factors
In problem solving,
• two or more conversion factors are often needed to
complete the change of units.
• in setting up these problems, one factor follows the other.
• each factor is arranged to cancel the preceding unit until
the needed unit is obtained.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Using Two or More Conversion Factors
Example: A doctor’s order prescribed a dosage of 0.150 mg of
Synthroid. If tablets contain 75 mcg of Synthroid, how many
tablets are required to provide the prescribed medication?
STEP 1 State the given and needed quantities.
ANALYZE
THE PROBLEM
GIVEN
NEED
0.150 mg Synthroid number of tablets
STEP 2 Write a plan to convert the given unit to
the needed unit.
number
Metric
Clinical
of
milligrams Factor
micrograms Factor
tablets
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Using Two or More Conversion Factors
Example: A doctor’s order prescribed a dosage of 0.150 mg of
Synthroid. If tablets contain 75 mcg (75 µg) of Synthroid, how many
tablets are required to provide the prescribed medication?
STEP 3 State the equalities and conversion factors.
STEP 4 Set up the problem to cancel units and
calculate the answer.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
How many minutes are in 1.4 days?
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
How many minutes are in 1.4 days?
STEP 1 State the given and needed quantities.
ANALYZE
THE PROBLEM
GIVEN
1.4 days
NEED
minutes
STEP 2 Write a plan to convert the given unit to
the needed unit.
days
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
Time
Factor
hours
Time
Factor
minutes
© 2016 Pearson Education, Inc.
Solution
How many minutes are in 1.4 days?
STEP 3 State the equalities and conversion factors.
STEP 4 Set up the problem to cancel units and
calculate the answer.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
A red blood cell has a diameter of approximately 10 µm.
What is the diameter of the red blood cell in cm?
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
A red blood cell has a diameter of approximately 10 µm. What
is the diameter of the red blood cell in cm?
STEP 1 State the given and needed quantities.
ANALYZE
THE PROBLEM
GIVEN
10 µm
NEED
cm
STEP 2 Write a unit plan to convert the given unit
to the needed unit.
micrometers
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
Metric
Factor
meters
Metric
factor
centimeters
© 2016 Pearson Education, Inc.
Solution
A red blood cell has a diameter of approximately 10 µm. What
is the diameter of the red blood cell in cm?
STEP 3 State the equalities and conversion factors.
1 µm = 10-6 m
1 µm or 10-6 m
10-6 m
1 µm
1 cm = 10-2 m
1 cm or 10-2 m
10-2 m
1 cm
STEP 4 Set up the problem to cancel units and
calculate the answer.
10 µm x 10-6 m x 1 cm = 1 x 10-3 cm
1µm
10-2 m
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
If your pace on a treadmill is 65 meters per minute, how
many minutes will it take for you to walk a distance of
7.5 kilometers?
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
If your pace on a treadmill is 65 meters per minute, how
many minutes will it take for you to walk a distance of
7.5 kilometers?
STEP 1 State the given and needed quantities.
ANALYZE
THE PROBLEM
GIVEN
NEED
65 meters/min minutes
7.5 kilometers
STEP 2 Write a plan to convert the given unit to
the needed unit.
Metric
kilometers Factor
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
meters
Speed
Factor
minutes
© 2016 Pearson Education, Inc.
Solution
If your pace on a treadmill is 65 meters per minute, how
many minutes will it take for you to walk a distance of
7.5 kilometers?
STEP 3 State the equalities and conversion factors.
STEP 4 Set up the problem to cancel units and
calculate the answer.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
2.7 Density
Learning Goal
Calculate the
density of a
substance; use the
density to calculate
the mass or volume
of a substance.
Objects that sink
in water are more
dense than water;
objects that float are
less dense.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Densities of Common Substances
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Calculating Density
Density compares the mass of an object to its volume.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Density of Solids
The density of a solid can be determined by dividing the mass
of an object by its volume.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Density Using Volume Displacement
The density of the solid zinc object is calculated by dividing
its mass by its displaced volume.
To determine its displaced volume, submerge the solid in
water so that it displaces water that is equal to its own
volume.
45.0 mL − 35.5 mL = 9.5 mL = 9.5 cm3
Density calculation:
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
What is the density (g/cm3) of a 48.0–g sample of a metal if
the level of water in a graduated cylinder rises from 25.0 mL
to 33.0 mL after the metal is added?
25.0 mL
33.0 mL
object
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Solution
What is the density (g/cm3) of a 48.0–g sample of a metal if
the level of water in a graduated cylinder rises from 25.0 mL
to 33.0 mL after the metal is added?
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Problem Solving Using Density
If the volume and the density of a sample are known, the
mass in grams of the sample can be calculated by using
density as a conversion factor.
Core Chemistry Skill Using Density as a Conversion Factor
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Problem Solving Using Density
Example: John took 2.0 teaspoons (tsp) of cough syrup. If the
syrup had a density of 1.20 g/mL and there is 5.0 mL in 1 tsp,
what was the mass, in grams, of the cough syrup?
STEP 1 State the given and needed quantities.
ANALYZE
THE PROBLEM
GIVEN
2.0 tsp syrup
density of syrup (1.20 g/mL)
NEED
grams of syrup
STEP 2 Write a plan to calculate the needed quantity.
teaspoons U.S.−Metric
Factor
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
milliliters
Density
Factor
grams
© 2016 Pearson Education, Inc.
Problem Solving Using Density
John took 2.0 teaspoons (tsp) of cough syrup. If the syrup had
a density of 1.20 g/mL and there is 5.0 mL in 1 tsp, what was
the mass, in grams, of the cough syrup?
STEP 3 Write the equalities and their conversion
factors, including density.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Problem Solving Using Density
John took 2.0 teaspoons (tsp) of cough syrup. If the syrup had
a density of 1.20 g/mL and there is 5.0 mL in 1 tsp, what was
the mass, in grams, of the cough syrup?
STEP 4 Set up the problem to calculate the needed
quantity.
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Specific Gravity
Specific gravity (sp gr)
• is a relationship between the density of a substance and
the density of water.
• is calculated by dividing the density of a sample by the
density of water, which is 1.00 g/mL at 4 °C.
• is a unitless quantity.
A substance with a specific gravity of 1.00 has the same
numerical value as the density of water (1.00 g/mL).
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Study Check
An unknown liquid has a density of 1.32 g/mL. What is the
volume (mL) of a 14.7-g sample of the liquid?
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.
Specific Gravity
Specific gravity (sp gr)
• is a relationship between the density of a substance and
the density of water.
• is calculated by dividing the density of a sample by the
density of water, which is 1.00 g/mL at 4 °C.
• is a unitless quantity.
A substance with a specific gravity of 1.00 has the same
numerical value as the density of water (1.00 g/mL).
General, Organic, and Biological Chemistry: Structures of Life, 5/e
Karen C. Timberlake
© 2016 Pearson Education, Inc.