Chapter 01
Introduction: Matter, Energy,
and Measurement
Textbook
Brown, LeMay, Bursten, Murphy, Woodward, Stoltzfus,
“Chemistry, The Central Science”, 15th Ed. (Pearson, 2018)
This electronic presentation is used
with Brown, LeMay, Bursten, Murphy, Woodward, Stoltzfus
“Chemistry, The Central Science”, 14th Ed.
All rights reserved and reproduced by permission.
Text / images may not be modified or reproduced
in any way without prior written permission of the publisher.
https://www.pearson.com/
2
Chemistry
• Chemistry is the scientific study of the properties and behavior of
matter. It is a physical science under natural sciences that covers the
elements that make up matter to the compounds made of atoms,
molecules and ions: their composition, structure, properties, behavior
and the changes they undergo during a reaction with other
substances. Chemistry also addresses the nature of chemical bonds
in chemical compounds. [ from Wikipedia ]
• Chemistry, the science that deals with the properties, composition,
and structure of substances (defined as elements and compounds),
the transformations they undergo, and the energy that is released
or absorbed during these processes. [ from Britannica ]
3
CONTENTS
1.1 The Study of Chemistry
1.2 Classifications of Matter
1.3 Properties of Matter
1.4 The Nature of Energy
1.5 Units of Measurement
1.6 Uncertainty in Measurement
1.7 Dimensional Analysis
1.1 The Study of Chemistry
• Chemistry is the study of
matter, its properties, and
the changes it undergoes.
• It is central to our fundamental
understanding of many
science‒related fields.
5
Branches of Chemistry
Chemistry is a large and
broad subject that covers
a ton of different material,
so it is separated into
different branches that focus
on one section of chemistry.
Image source: Caroline Monahan
6
The Atomic and Molecular Perspective of Chemistry
• Matter ‒ Anything that has mass and
takes up space.
• Atom ‒ The smallest stable building block
of matter.
• Molecule ‒ Groups of atoms held together
with a specific connectivity and shape.
• Composition ‒ The types of atoms that are present in a compound
and the ratio of these atoms (for example, H2O, C2H6O).
• Structure ‒ How atoms are connected (bonded) to each other, how
far apart they are, and the shape of the molecule.
7
1.2 Classifications of Matter
Methods of Classification
• State of Matter ‒ Physical state is gas, liquid, or solid.
• Composition of Matter ‒ Element, compound, or mixture
8
States of Matter
(1) Gas (vapor) ‒ has no fixed volume or
shape, uniformly expands to fill its container,
compressible, flows readily, diffusion occurs
rapidly.
(2) Liquid ‒ has a distinct volume independent
of its container, assumes the shape of the
portion of the container it occupies, not
significantly compressible, diffusion occurs
but slower than a gas.
(3) Solid ‒ has both a definite shape and
definite volume, not significantly
compressible, diffusion occurs extremely
slowly.
9
Pure Substances
• Pure Substance: Matter that has a fixed composition and distinct
properties. All substances are either elements or compounds.
– Element is a substance which can not be decomposed into simpler
substances. On the molecular level, each element is composed of
only one kind of atom.
– Compound are substances composed of two or more elements;
they contain two or more
kinds of atoms.
• Mixtures: Combinations
of two or more substances
in which each substance
retains its chemical identity.
10
Elements
• Elements are represented as symbols
with one or two letters; the first is
always capitalized.
Relative abundances of elements in
the Earth’s crust and human body.
Note the importance of oxygen!
• Some elements are based on Latin,
Greek, or other foreign language
names. → See Periodic Table (주기율표)
11
Compounds
• Elements can interact with other elements
to form compounds, and compounds can
be decomposed into elements.
• The elemental composition of a compound
is always the same, which is known as
the Law of Constant Composition
(or Law of Definite Proportions).
Compound
2 H2 + O2 → 2 H2O
Elements
12
Mixtures
• Mixtures exhibit the properties of
the substances that make them.
• Mixtures can vary in composition
throughout a sample (heterogeneous)
or can have the same composition
throughout the sample (homogeneous).
• A homogeneous mixture is also called
a solution.
13
1.3 Properties of Matter
• Physical Properties: the way observed without changing the identity
and composition of the substance.
– color, odor, density, melting point, boiling point, and hardness.
• Chemical Properties: the way a substance may change, or react, to
form other substances.
– flammability, or the ability to burn in oxygen.
• Intensive Properties: independent of the amount of the substance.
– density, boiling point, or color, etc.
• Extensive Properties: dependent upon the amount of the substance.
– mass, volume, energy, etc.
14
Physical and Chemical Changes
• Physical changes are changes in matter that do not change the
composition of a substance.
– changes of state, temperature, and volume.
• Chemical changes result in new substances.
– combustion, oxidation, and decomposition.
Cu(s) + 4HNO3(aq) → Cu(NO3)2(aq) + 2NO2(g) + 2H2O(l)
15
Completely dissolving a penny in acid
https://www.youtube.com/watch?v=FhvxaxFGO8M
16
Separation of Mixtures
• Mixtures can be separated based on physical properties of the
components of the mixture. Some methods used are
– filtration
– distillation
– chromatography
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1.4 The Nature of Energy Matter
* matter, which is anything that occupies space and
has mass. Gold and iridium are matter, as are peanuts,
people, and postage stamps. Smoke, smog, and
laughing gas are matter. Energy, light, and sound,
however, are not matter; ideas and emotions are also
not matter.
• Energy is the capacity to do work or transfer heat.
• Work is the energy transferred when a force exerted
on an object causes a displacement of that object.
• Heat is the energy used to cause the temperature of
an object to increase.
• Force is any push or pull on an object.
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Kinetic Energy and Potential Energy
• Kinetic energy is the energy of motion.
– Its magnitude depends on the object’s
1 2
mass and its velocity:
KE =
2
mv
• Potential energy of an object depends
on its relative position compared to other objects.
– Potential energy also refers to the composition of an object,
including the energy stored in chemical bonds.
❖ One of the goals in chemistry is to related the energy changes
in the macroscopic world to the kinetic or potential energy of
substances at the molecular level.
19
1.5 Units of Measurement
• Numbers play a major role in chemistry.
Many topics are quantitative (have a numerical value).
• Major role in quantifying:
– Units of measurement
– Quantities that are measured and calculated
– Uncertainty in measurement
– Significant figures
– Dimensional analysis
(e.g. 1 inch = 2.54 cm)
20
SI Units
• Système International d’Unités (“The International System of Units”)
* NIST (National Institute of Standards and Technology)
미국 국립표준기술연구소
https://physics.nist.gov/cuu/Units/index.html
Pay attention to the lowercase/uppercase (m vs M etc.)
21
Length and Mass
These are basic units we measure in science.
• Mass is a measure of the amount of material in an object. SI uses the
kilogram as the base unit. The metric system uses the gram as the
base unit.
• Length is a measure of distance. The meter is the base unit.
22
Temperature
• In general usage, temperature is considered the “hotness and
coldness” of an object that determines the direction of heat flow.
• Heat flows spontaneously from an object with a higher temperature
to an object with a lower temperature.
23
• In scientific measurements, the Celsius and Kelvin scales are most
often used.
• The Celsius scale is based on the properties of water.
– 0 °C is the freezing point of water.
K
=

C
+
273.15
– 100 °C is the boiling point of water.

F
=
9/5
(

C)
+
32
• The Kelvin is the SI unit of temperature.

C
=
5/9
(

F)
−
32
– It is based on the properties of gases.
– There are no negative Kelvin temperatures.
– The lowest possible temperature is called absolute zero (0 K).
• The Fahrenheit scale is not used in scientific measurements, but you
hear about it in weather reports!
– 32 °F is the freezing point of water.
– 212 °F is the boiling point (at standard atmospheric pressure).
24
Volume
• Note that volume is not a base unit for SI;
3
it is a derived unit from length (m × m × m = m ).
• The most commonly used metric units for volume are the liter (L) and
the milliliter (mL).
– A liter is a cube 1 decimeter (dm) long
on each side.
– A milliliter is a cube 1 centimeter (cm) long
on each side, also called 1 cubic centimeter
3
(cm × cm × cm = cm ).
−1
1 L = 1 dm = (110 m) = 10
3
3
= 1000 mL = 1000 cm
−3
m ( 1 m )
3
3
3
25
• Glassware for Measuring Volume
Uncertainty in Measurements – Different measuring devices have
different uses and different degrees of precision.
26
Density
• Density is a physical property of a substance.
• It has units that are derived from the units
for mass and volume.
•
3
The most common units are g/mL or g/cm .
mass
m
Density = d =
=
volume v
•
3
Definition of the density of water as 1.00 g/cm
27
Units of Energy
• The unit of energy: Joule (J)
• If the object is 2 kg, and it moves at 1 m/s, it will posses 1 J of
kinetic energy:
1 2 1
2
2
2
– KE = mv = (2 kg )(1 m / s ) = 1 kg  m / s  1 J
2
2
• The kJ is commonly used for chemical change.
• Historically, the calorie was used: 1 cal = 4.184 J
• This calorie is NOT the nutritional Calorie. That one is a kcal.
• 1 nutritional Calorie = 1 Cal = 1000 cal = 1 kcal.
28
1.6 Uncertainty in Measurement
• Exact numbers are counted or given by definition.
– For example, there are 12 eggs in 1 dozen.
• Inexact (or measured) numbers depend on how they were
determined. Scientific instruments have limitations (equipment errors)
and individuals can read some instrumentation differently (human
errors).
Digital Reading
Scale read by eye
The last digit measured is considered
reliable, but NOT exact.
29
Precision and Accuracy
• Precision is a measure of how closely individual measurements
agree with one another.
• Accuracy refers to how closely individual measurements agree with
the correct, or “true,” value.
• Experimentally, we often take several measurements and determine a
standard deviation. (deviation = |measurement – average|)
30
Significant Figures (유효숫자)
• All digits of a measured quantity, including the uncertain ones, are
called significant figures.
• When rounding calculated numbers, we pay attention to significant
figures so we do not overstate the accuracy of our answers.
• All nonzero digits are significant. 24.42 4 SF
1. Zeros between nonzero digits are always significant.
4.803 4 SF
2. Zeros at the beginning of a number are never significant; they
merely indicate the position of the decimal point.
0.006 61 3 SF
-3
(or 6.61 x 10 g)
3. Zeros at the end of a number are significant if the number contains
a decimal point.
55.220 5 SF
31
• Problem: whole numbers ending in zeroes.
– Zeros at the end of a number before a decimal place are
ambiguous (e.g. 23,800 g), unless a decimal point is written at
the end (i.e. 23,800. g). Assume the zeros are insignificant,
unless there is a decimal point. Avoid ambiguity by using
scientific notation (Appendix A.1).
32
Significant Figures in Calculations
• The least certain measurement limits the certainty of the calculated
quantity and thereby determines the number of significant figures in
the final answer.
• For addition and subtraction, answers are rounded to the least
significant decimal place.
• For multiplication and division, answers are rounded to the same
number of digits as the measurement with the fewest number of
significant figures.
• Know the number of appropriate digits throughout, but round off at the
end only!
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Significant Figures in Calculations
• The least certain measurement limits the certainty of the calculated
quantity and thereby determines the number of significant figures in
the final answer.
• For addition and subtraction, answers are rounded to the least
significant decimal place.
• For multiplication and division, answers are rounded to the same
number of digits as the measurement with the fewest number of
significant figures.
(5 sf) 53.451 = (3 sf) 53.5
(5 sf) 32.753 = (3 sf) 32.8
(4 sf) 53.45 = (3 sf) 53.4 (even)
(4 sf) 32.75 = (3 sf) 32.8 (odd)
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Select the number with round to nearest even!!
Class Exercise
Complete the calculations and report your answers using the correct
number of significant figures.
1) 87.25 mL + 3.0201 mL
2) 26.843 g + 12.23 g
3) 6 × 12.011
4) 2 × (1.008) g + 15.99 g
5) 137.3 + 2 × (35.45)
6) (118.7 g / 2) − 35.5 g
7) 47.23 g − (207.2 g / 5.92)
8) (77.604 / 6.467) − 4.8
9) (24.86 / 2.0) −3.26 × (0.98)
10) (15.9994 × 9) + 2.0158
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Class Exercise
Complete the calculations and report your answers using the correct
number of significant figures.
1) 87.25 mL + 3.0201 mL
2) 26.843 g + 12.23 g
3) 6 × 12.011
4) 2 × (1.008) g + 15.99 g
5) 137.3 + 2 × (35.45)
6) (118.7 g / 2) − 35.5 g
7) 47.23 g − (207.2 g / 5.92)
8) (77.604 / 6.467) − 4.8
9) (24.86 / 2.0) −3.26 × (0.98)
10) (15.9994 × 9) + 2.0158
1) 90.2701 mL = 90.27 mL
2) 39.073 g = 39.07 g
3) 72.066
4) 2.016 g + 15.99 g = 18.006 g = 18.01 g
5) 137.3 + 70.90 = 208.2
6) 59.35 g − 35.5 g = 23.85 g = 23.8 g
7) 47.23 g − 35.0 g = 12.23 g = 12.2 g
8) 12.00 − 4.8 = 7.2
9) 12.43 − 3.1948 = 9.2352 = 9.
10) 143.9946 + 2.0158 = 146.0104 = 146.010
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1.7 Dimensional Analysis
• Dimensional analysis is used to change units.
• We apply conversion factors, which are equalities.
• We can set up a ratio of comparison for the equality:
e.g., 1 in = 2.54 cm
• We use the ratio which allows us to change units (puts the units we
have in the denominator to cancel).
• We can use multiple conversions, as long as each one is an equality.
37
What’s Ahead
• 1.1 The Study of Chemistry
Learn what chemistry is, what chemists do, and why it is
useful to study chemistry.
• 1.2 Classifications of Matter
Examine fundamental ways to classify matter;
distinguish between pure substances and mixtures and
between elements and compounds.
• 1.3 Properties of Matter
Use properties to characterize, identify, and
separate substances; distinguish between
chemical and physical properties.
38
What’s Ahead
• 1.4 The Nature of Energy
Explore the nature of energy and the forms it takes,
notably kinetic energy and potential energy.
• 1.5 Units of Measurement
Learn how numbers and units of the metric system are
used in science to describe properties.
• 1.6 Uncertainty in Measurement
Use significant figures to express the inherent
uncertainty in measured quantities and in calculations.
• 1.7 Dimensional Analysis
Learn to carry numbers and units through calculations;
use units to check if a calculation is correct.
39
Learning Outcomes
[1.2] Distinguish among elements, compounds, and mixtures.
[1.2] Identify symbol of common elements.
[1.3] Distinguish between chemical and physical changes.
[1.4] Distinguish between kinetic and potential energy.
[1.4] Calculate the kinetic energy of an object.
[1.5] Identify common metric prefixes.
[1.6] Demonstrate the use of significant figures,
scientific notation, and SI units in calculations.
[1.5, 1.7] Use appropriate SI units for defined quantities,
and employ dimensional analysis in calculations.
40
Sample Exercise 1.1
Distinguishing among Elements,
Compounds, and Mixtures
“White gold” contains gold and a “white” metal, such as palladium. Two samples of white gold
differ in the relative amounts of gold and palladium they contain. Both samples are uniform in
composition throughout. Use Figure 1.9 to classify white gold.
Solution
Because the material is uniform throughout, it is homogeneous. Because its composition differs
for the two samples, it cannot be a compound. Instead, it must be a homogeneous mixture.
Practice Exercise 1
Which of the following is the correct description of the inside
of a grapefruit?
(a) It is a pure compound.
(b) It consists of a homogeneous mixture of compounds.
(c) It consists of a heterogeneous mixture of compounds.
(d) It consists of a heterogeneous mixture of elements and compounds.
(e) It consists of a single compound in different states.
Practice Exercise 2
Aspirin is composed of 60.0% carbon, 4.5% hydrogen, and
35.5% oxygen by mass, regardless of its source. Use Figure 1.9 to classify aspirin.
41
Sample Exercise 1.2
Using SI Prefixes
What is the name of the unit that equals (a) 10–9 gram; (b) 10–6 second; (c) 10–3 meter?
Solution
We can find the prefix related to each power of ten in Table 1.4:
(a) nanogram, ng; (b) microsecond, µs; (c) millimeter, mm.
Practice Exercise 1
Which of the following weights would you expect to be suitable
for weighing on an ordinary bathroom scale?
(a) 2.0 × 107 mg
(b) 2500 µg
(d) 4 × 106 cg
(e) 5.5 × 108 dg.
(c) 5 × 10–4 kg
Practice Exercise 2
(a) How many picometers are there in 1 m?
(b) Express 6.0 × 103 m using a prefix to replace the power of ten.
(c) Use exponential notation to express 4.22 mg in grams.
(d) Use decimal notation to express 4.22 mg in grams.
42
Sample Exercise 1.3
Converting Units of Temperature
A weather forecaster predicts the temperature will reach 31 °C. What is this temperature
(a) in K; (b) in °F?
Solution
(a) Equation 1.3, we have K = 31 + 273 = 304 K.
(b) Using Equation 1.4, we have
Practice Exercise 1
Using Wolfram Alpha (http://www.wolframalpha.com/) or some other reference, determine which
of these elements would be liquid at 525 K (assume samples are protected from air):
(a) bismuth, Bi; (b) platinum, Pt; (c) selenium, Se; (d) calcium, Ca; (e) copper, Cu.
Practice Exercise 2
Ethylene glycol, the major ingredient in antifreeze, freezes at –11.5 °C. What is the freezing point
in (a) K; (b) °F?
43
Sample Exercise 1.4
Determining Density and Using Density
to Determine Volume or Mass
(a) Calculate the density of mercury if 1.00 × 102 g occupies a volume of 7.36 cm3.
(b) Calculate the volume of 65.0 g of liquid methanol (wood alcohol) if its density is 0.791 g/mL.
(c) What is the mass in grams of a cube of gold (density = 19.32 g/cm3) if the length of the cube is
2.00 cm?
Solution
(a) We are given mass and volume, so Equation 1.3 yields
(b) Solving Equation 1.3 for volume and then using the given mass and density gives
(c) We can calculate the mass from the volume of the cube and its density. The volume of a cube
is given by its length cubed:
Volume = (2.00 cm)3 = (2.00)3 cm3 = 8.00 cm3
Solving Equation 1.3 for mass and substituting the volume and density of the cube, we have
44
Sample Exercise 1.4
Determining Density and Using Density to
Determine Volume or Mass
Continued
Practice Exercise 1
Platinum, Pt, is one of the rarest of the metals. Worldwide annual production is only about 130
tons. Platinum has a density of 21.4 g/cm3. If thieves were to steal platinum from a bank using a
small truck with a maximum payload capacity of 900 lb, how many 1 L bars of the metal could
they take?
(a) 19 bars
(b) 2 bars
(c) 42 bars
(d) 1 bar
(e) 47 bars.
Practice Exercise 2
(a) Calculate the density of a 374.5‒g sample of copper if it has a volume of 41.8 cm3.
(b) A student needs 15.0 g of ethanol for an experiment. If the density of ethanol is 0.789 g/mL,
how many milliliters of ethanol are needed?
(c) What is the mass, in grams, of 25.0 mL of mercury (density = 13.6 g/mL)?
45
Sample Exercise 1.5
Identifying and Calculating
Energy Changes
A standard propane (C3H8) tank used in an outdoor grill holds approximately 9.0 kg of propane.
When the grill is operating, propane reacts with oxygen to form carbon dioxide and water. For
every gram of propane that reacts with oxygen in this way, 46 kJ of energy is released as heat.
(a) How much energy is released if the entire contents of the propane tank react with oxygen?
(b) As the propane reacts, does the potential energy stored in chemical bonds increase or
decrease?
(c) If you were to store an equivalent amount of potential energy by pumping water to an
elevation of 75 m above the ground, what mass of water would be needed? (Note: The force
due to gravity acting on the water, which is the water’s weight, is F = m × g, where m Is the
mass of the object and g is the gravitational constant, g = 9.8 m/s2.)
Solution
We can calculate the amount of energy released from the propane as heat by converting the
mass of propane from kg to g and then using the fact that 46 kJ of heat are released per gram:
46
Sample Exercise 1.5
Identifying and Calculating
Energy Changes
Continued
(b) When propane reacts with oxygen, the potential energy stored in the chemical bonds is
converted to an alternate form of energy, heat. Therefore, the potential energy stored as
chemical energy must decrease.
(c) The amount of work done to pump the water to a height of 75 m can be calculated using
Equation 1.1:
w = F × d = (m × g) × d
rearranging to solve for the mass of water:
At 25 °C, this mass of water would have a volume of 560,000 L, or roughly 150,000 gallons.
Thus, we see that large amounts of potential energy can be stored as chemical energy.
47
Sample Exercise 1.5
Identifying and Calculating
Energy Changes
Continued
Practice Exercise 1
Which of the following objects has the greatest kinetic energy?
(a) a 500‒kg motorcycle moving at 100 km/h
(b) a 1,000‒kg car moving at 50 km/h
(c) a 1500‒kg car moving at 30 km/h
(d) a 5000 kg truck moving at 10 km/h
(e) a 10,000‒kg truck moving at 5 km/h.
Practice Exercise 2
A 12‒oz vanilla milkshake at a fast‒food restaurant contains 547 Calories. What quantity of
energy is this in joules?
48
Sample Exercise 1.6
Assigning Appropriate
Significant Figures
The state of Colorado is listed in a road atlas as having a population of 5,546,574 and an area of
104,091 square miles. Do the numbers of significant figures in these two quantities seem
reasonable? If not, what seems to be wrong with them?
Solution
The population of Colorado must vary from day to day as people move in or out, are born, or die.
Thus, the reported number suggests a much higher degree of accuracy than is possible.
Moreover, it would not be feasible to actually count every individual resident in the state at any
given time. Thus, the reported number suggests far greater precision than is possible. A reported
number of 5,500,000 would better reflect the actual state of knowledge.
The area of Colorado does not normally vary from time to time, so the question here is whether
the accuracy of the measurements is good to six significant figures. It would be possible to
achieve such accuracy using satellite technology, provided the legal boundaries are known with
sufficient accuracy.
49
Assigning Appropriate
Significant Figures
Sample Exercise 1.6
Continued
Practice Exercise 1
Which of the following numbers in your personal life are exact numbers?
(a) Your cell phone number
(b) your weight
(d) your driver’s license number
(c) your IQ
(e) the distance you walked yesterday.
Practice Exercise 2
The back inside cover of the book tells us that there are 5280 ft in 1 mile. Does this make the mile
an exact distance?
50
Sample Exercise 1.7
Determining the Number of Significant
Figures in a Measurement
How many significant figures are in each of the following numbers (assume that each number is a
measured quantity)?
(a) 4.003; (b) 6.023 × 1023; (c) 5000.
Solution
(a) Four; the zeros are significant figures.
(b) Four; the exponential term does not add to the number of significant figures.
(c) One; we assume that the zeros are not significant when there is no decimal point shown. If the
number has more significant figures, a decimal point should be employed or the number
written in exponential notation. Thus, 5000. has four significant figures, whereas 5.00 × 103
has three.
Practice Exercise 1
An object is determined to have a mass of 0.01080 g. How many significant figures are there in
this measurement?
(a) 2 (b) 3 (c) 4 (d) 5 (e) 6.
Practice Exercise 2
How many significant figures are in each of the following measurements?
(a) 3.549 g;
(b) 2.3 × 104 cm;
(c) 0.00134 m3.
51
Sample Exercise 1.8
Determining the Number of Significant
Figures in a Calculated Quantity
The width, length, and height of a small box are 15.5, 27.3, and 5.4 cm, respectively. Calculate
the volume of the box, using the correct number of significant figures in your answer.
Solution
In reporting the volume, we can show only as many significant figures as given in the dimension
with the fewest significant figures, which is that for the height (two significant figures):
A calculator used for this calculation shows 2285.01, which we must round off to two significant
figures. Because the resulting number is 2300, it is best reported in exponential notation,
2.3 × 103, to clearly indicate two significant figures.
52
Sample Exercise 1.8
Determining the Number of Significant
Figures in a Calculated Quantity
Continued
Practice Exercise 1
Ellen recently purchased a new hybrid car and wants to check her gas mileage. At an odometer
setting of 651.1 mi, she fills the tank. At 1314.4 mi, she requires 16.1 gal to refill the tank.
Assuming that the tank is filled to the same level both times, how is the gas mileage best
expressed?
(a) 40 mi/gal
(b) 41 mi/gal
(c) 41.2 mi/gal
(d) 41.20 mi/gal.
Practice Exercise 2
It takes 10.5 s for a sprinter to run 100.00 m. Calculate her average speed in meters per second
and express the result to the correct number of significant figures.
53
Sample Exercise 1.9
Determining the Number of Significant
Figures in a Calculated Quantity
A vessel containing a gas at 25 °C is weighed, emptied, and then reweighed as depicted in Figure
1.26. From the data provided, calculate the density of the gas at 25 °C.
Solution
To calculate the density, we must know both the mass and the volume of the gas. The mass of
the gas is just the difference in the masses of the full and empty container:
In subtracting numbers, we determine the number of significant figures
in our result by counting decimal places in each quantity.
In this case each quantity has two decimal places. Thus, the mass
of the gas, 1.38 g, has two decimal places.
Using the volume given in the question, 1.05 × 103 cm3, and the
definition of density, we have
54
Sample Exercise 1.9
Determining the Number of Significant
Figures in a Calculated Quantity
Continued
In dividing numbers, we determine the number of significant figures our result should contain by
counting the number of significant figures in each quantity. There are three significant figures in
our answer, corresponding to the number of significant figures in the two numbers that form the
ratio. Notice that in this example, following the rules for determining significant figures gives an
answer containing only three significant figures, even though the measured masses contain five
significant figures.
Practice Exercise 1
You are asked to determine the mass of a piece of copper using its reported density, 8.96 g/mL,
and a 150‒mL graduated cylinder. First, you add 105 mL of water to the graduated cylinder; then
you place the piece of copper in the cylinder and record a volume of 137 mL. What is the mass of
the copper reported with the correct number of significant figures?
(a) 287 g
(b) 3.5 × 10–3 g/mL
(c) 286.72 g/mL
(d) 3.48 × 10–3 g/mL
(e) 2.9 × 102 g/mL.
Practice Exercise 2
If the mass of the container in the sample exercise (Figure 1.26) were measured to three decimal
places before and after pumping out the gas, could the density of the gas then be calculated to
four significant figures?
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Sample Exercise 1.10 Converting Units
If a woman has a mass of 115 lb, what is her mass in grams? (Use the relationships between
units given on the back inside cover of the text.)
Solution
Because we want to change from pounds to grams, we look for a relationship between these
units of mass. The conversion factor table found on the back inside cover tells us that
1 lb = 453.6 g. To cancel pounds and leave grams, we write the conversion factor with grams in
the numerator and pounds in the denominator:
The answer can be given to only three significant figures,
the number of significant figures in 115 lb. The process
we have used is diagrammed on the top right column.
56
Sample Exercise 1.10 Converting Units
Continued
Practice Exercise 1
At a particular instant in time, the Earth is judged to be 92,955,000 miles from the Sun. What is
the distance in kilometers to four significant figures? (See the back inside cover for the
conversion factor).
(a) 5763 × 104 km
(b) 1.496 × 108 km
(d) 1.483 × 104 km
(e) 57,759,000 km.
(c) 1.49596 × 108 km
Practice Exercise 2
By using a conversion factor from the back inside cover, determine the length in kilometers of a
500.0‒mi automobile race.
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Converting Units Using Two or More
Sample Exercise 1.11
Conversion Factors
The average speed of a nitrogen molecule in air at 25 °C is 515 m/s. Convert this speed to miles
per hour.
Solution
To go from the given units, m/s, to the desired units, mi/hr, we must convert meters to miles and
seconds to hours. From our knowledge of SI prefixes we know that 1 km = 103 m. From the
relationships given on the back inside cover of the book, we find that 1 mi = 1.6093 km. Thus, we
can convert m to km and then convert km to mi. From our knowledge of time we know that
60 s = 1 min and 60 min = 1 hr. Thus, we can convert s to min and then convert min to hr. The
overall process is
Applying first the conversions for distance and then those for time, we can set up one long
equation in which unwanted units are canceled:
58
Converting Units Using Two or More
Sample Exercise 1.11
Conversion Factors
Continued
Our answer has the desired units. We can check our calculation, using the estimating procedure
described in the “Strategies in Chemistry” box. The given speed is about 500 m/s. Dividing by
1000 converts m to km, giving 0.5 km/s. Because 1 mi is about 1.6 km, this speed corresponds to
0.5/1.6 = 0.3 mi/s. Multiplying by 60 gives about 0.3 × 60 = 20 mi/min. Multiplying again by 60
gives 20 × 60 = 1200 mi/hr. The approximate solution (about 1200 mi/hr) and the detailed
solution (1150 mi/hr) are reasonably close. The answer to the detailed solution has three
significant figures, corresponding to the number of significant figures in the given speed in m/s.
Practice Exercise 1
Fabiola, who lives in Mexico City, fills her car with gas, paying 357 pesos for 40.0 L. What is her
fuel cost in dollars per gallon, if 1 peso = 0.0759 dollars?
(a) $1.18/gal
(b) $3.03/gal
(c) $1.47/gal
(d) $9.68/gal
(e) $2.56/gal.
Practice Exercise 2
A car travels 28 mi per gallon of gasoline. What is the mileage in kilometers per liter?
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Sample Exercise 1.12 Converting Volume Units
Earth’s oceans contain approximately 1.36 × 109 km3 of water. Calculate the volume in liters.
Solution
From the back inside cover, we find 1 L = 10–3 m3, but there is no relationship listed involving km3.
From our knowledge of SI prefixes, however, we know 1 km = 103 m and we can use this
relationship between lengths to write the desired conversion factor between volumes:
Thus, converting from km3 to m3 to L, we have
How many liters of water
do Earth’s oceans contain?
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Sample Exercise 1.12 Converting Volume Units
Continued
Practice Exercise 1
A barrel of oil as measured on the oil market is equal to 1.333 U.S. barrels. A U.S. barrel is equal
to 31.5 gal. If oil is on the market at $94.0 per barrel, what is the price in dollars per gallon?
(a) $2.24/gal
(b) $3.98/gal
(c) $2.98/gal
(d) $1.05/gal
(e) $8.42/gal.
Practice Exercise 2
The surface area of Earth is 510 × 106 km2, and 71% of this is ocean. Using the data from the
sample exercise, calculate the average depth of the world’s oceans in feet.
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Sample Exercise 1.13 Conversions Involving Density
What is the mass in grams of 1.00 gal of water? The density of water is 1.00 g/mL.
Solution
Before we begin solving this exercise, we note the following:
(1) We are given 1.00 gal of water (the known, or given, quantity) and asked to calculate its mass
in grams (the unknown).
(2) We have the following conversion factors either given, commonly known, or available on the
back inside cover of the text:
The first of these conversion factors must be used as written (with grams in the numerator) to
give the desired result, whereas the last conversion factor must be inverted in order to cancel
gallons:
The unit of our final answer is appropriate, and we have taken care of our significant figures. We
can further check our calculation by estimating. We can round 1.057 off to 1. Then focusing on
the numbers that do not equal 1 gives 4 × 1000 = 4000 g, in agreement with the detailed
calculation.
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Sample Exercise 1.13 Conversions Involving Density
Continued
You should also use common sense to assess the reasonableness of your answer. In this case
we know that most people can lift a gallon of milk with one hand, although
it would be tiring to carry it around all day. Milk is mostly water and will have
a density not too different from that of water. Therefore, we might estimate
that a gallon of water has mass that is more than 5 lb but less than 50 lb.
The mass we have calculated, 3.78 kg × 2.2 lb/kg = 8.3 lb, is thus reasonable.
Practice Exercise 1
Trex(composite decking) is a manufactured substitute for wood compounded
from post‒consumer plastic and wood. It is frequently used in outdoor decks.
Its density is reported as 60.0 lb/ft3. What is the density of Trex in kg/L?
(a) 138 kg/L
(b) 0.961 kg/L
Practice Exercise 2
(c) 259 kg/L
(d) 15.8 kg/L
(e) 11.5 kg/L.
A Trex deck.
The density of the organic compound benzene is 0.879 g/mL. Calculate the mass in grams of
1.00 qt of benzene.
63