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Chapter 1
Keys to the Study of Chemistry
1-1
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Chapter 1 : Keys to the Study of Chemistry
1.1 Some Fundamental Definitions
1.2 The Scientific Approach: Developing a Model
1.3 Chemical Problem Solving
1.4 Measurement in Scientific Study
1.5 Uncertainty in Measurement: Significant Figures
1-2
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Is the study of matter,
its properties,
the changes that matter undergoes,
and
the energy associated with these changes.
1-3
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Definitions
Matter anything that has mass and volume -the “stuff” of the
universe: books, planets, trees, professors, students
Composition the types and amounts of simpler substances that
make up a sample of matter
Properties
1-4
the characteristics that give each substance a unique
identity
Physical Properties
Chemical Properties
those which the substance
shows by itself without
interacting with another
substance such as color, melting
point, boiling point, density
those which the substance shows
as it interacts with, or transforms
into, other substances such as
flammability, corrosiveness
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Figure 1.1
The distinction between physical and chemical change.
A Physical change
1-5
B Chemical change
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Figure 1.2
1-6
The physical states of matter.
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Sample Problem 1.1
Distinguishing Between Physical and
Chemical Change
PROBLEM: Decide whether each of the following process is primarily a
physical or a chemical change, and explain briefly:
(a) Frost forms as the temperature drops on a humid winter night.
(b) A cornstalk grows from a seed that is watered and fertilized.
(c) Dynamite explodes to form a mixture of gases.
(d) Perspiration evaporates when you relax after jogging.
(e) A silver fork tarnishes slowly in air.
PLAN:
“Does the substance change composition or just change form?”
SOLUTION:
(a) physical change
(b) chemical change
(d) physical change
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(c) chemical change
(e) chemical change
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Energy is the capacity to do work.
Potential Energy
energy due to the position of the object or
energy from a chemical reaction
Kinetic Energy
energy due to the motion of the object
Potential and kinetic energy can be interconverted.
1-8
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Energy is the capacity to do work.
Figure 1.3A
less stable
change in potential energy
EQUALS
kinetic energy
more stable
A gravitational system. The potential energy gained when a
lifted weight is converted to kinetic energy as the weight falls.
1-9
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Energy is the capacity to do work.
Figure 1.3B
less stable
change in potential energy
EQUALS
kinetic energy
more stable
A system of two balls attached by a spring. The potential energy
gained by a stretched spring is converted to kinetic energy when the
moving balls are released.
1-10
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Energy is the capacity to do work.
Figure 1.3C
less stable
change in potential energy
EQUALS
kinetic energy
more stable
A system of oppositely charged particles. The potential energy gained
when the charges are separated is converted to kinetic energy as the
attraction pulls these charges together.
1-11
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Energy is the capacity to do work.
Figure 1.3D
less stable
change in potential energy
EQUALS
kinetic energy
more stable
A system of fuel and exhaust. A fuel is higher in chemical potential
energy than the exhaust. As the fuel burns, some of its potential energy is
converted to the kinetic energy of the moving car.
1-12
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Scientific Approach: Developing a Model
Observations :
Hypothesis:
Natural phenomena and measured events;
universally consistent ones can be stated as a
natural law.
Tentative proposal that explains observations.
revised if
experiments do
not support it
Experiment:
Model (Theory):
Procedure to test hypothesis; measures one
variable at a time.
Set of conceptual assumptions that explains
data from accumulated experiments; predicts
related phenomena.
Further Experiment: Tests predictions based on model.
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altered if
predictions do
not support it
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A Systematic Approach to Solving Chemistry Problems
•Problem statement
Clarify the known and unknown.
•Plan
Suggest steps from known to unknown.
Prepare a visual summary of steps.
•Solution
•Check
Comment and Follow-up Problem
1-14
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Sample Problem 1.2
Converting Units of Length
PROBLEM: To wire your stereo equipment, you need 325 centimeters (cm) of
speaker wire that sells for $0.15/ft. What is the price of the wire?
PLAN:
Known - length (in cm) of wire and cost per length ($/ft)
We have to convert cm to inches and inches to ft followed by
finding the cost for the length in ft.
length (cm) of wire
2.54 cm = 1 in
length (in) of wire
12 in = 1 ft
length (ft) of wire
1 ft = $0.15
Price ($) of wire
SOLUTION:
Length (in) = length (cm) x conversion factor
= 325 cm x in
= 128 in
2.54 cm
Length (ft) = length (in) x conversion factor
= 128 in x
= 10.7 ft
ft
12 in
Price ($) = length (ft) x conversion factor
= 10.7 ft x $0.15
ft
1-15
= $1.60
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Table 1. 1
Physical Quantity
(Dimension)
SI Base Units
Unit Name
Unit
Abbreviation
mass
kilogram
kg
length
meter
m
time
second
s
temperature
kelvin
K
electric current
ampere
A
amount of substance
mole
mol
luminous intensity
candela
cd
1-16
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Table 1.2
Common Decimal Prefixes Used with SI Units
Prefix
Prefix
Symbol
Word
tera
giga
mega
kilo
hecto
deka
----deci
centi
milli
micro
nano
pico
femto
T
G
M
k
h
da
---d
c
m

n
p
f
trillion
billion
million
thousand
hundred
ten
one
tenth
hundredth
thousandth
millionth
billionth
trillionth
quadrillionth
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Conventional
Notation
1,000,000,000,000
1,000,000,000
1,000,000
1,000
100
10
1
0.1
0.01
0.001
0.000001
0.000000001
0.000000000001
0.000000000000001
Exponential
Notation
1x1012
1x109
1x106
1x103
1x102
1x101
1x100
1x10-1
1x10-2
1x10-3
1x10-6
1x10-9
1x10-12
1x10-15
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Common SI-English Equivalent Quantities
Quantity
SI Unit
SI Equivalent
English Equivalent
Length
English to
1 kilometer(km)
1000(103)m
SI Equivalent
Table 1.3
0.62miles(mi)
1 mi = 1.61km
1 meter(m)
100(102)cm
1000(103)mm
1.094yards(yd)
39.37inches(in)
1 yd = 0.9144m
1 foot (ft) = 0.3048m
1 centimeter(cm)
0.01(10-2)m
0.3937in
1 kilometer(km)
1000(103)m
1-18
0.62mi
1 in = 2.54cm
(exactly!)
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Common SI-English Equivalent Quantities
Quantity
SI Unit
SI Equivalent
English Equivalent
Volume
English to
SI Equivalent
1 cubic meter(m3)
Table 1.3
1,000,000(106)
cubic centimeters
35.2cubic feet (ft3)
1 ft3 = 0.0283m3
1 cubic decimeter(dm3)
1000cm3
0.2642 gallon (gal)
1.057 quarts (qt)
1 gal = 3.785 dm3
1 qt = 0.9464 dm3
1 cubic centimeter (cm3)
0.001 dm3
0.0338 fluid ounce
1 qt = 946.4 cm3
1 fluid ounce = 29.6 cm3
1-19
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Common SI-English Equivalent Quantities
Quantity
SI Unit
SI Equivalent
English Equivalent
Mass
English to
1 kilogram (kg)
SI Equivalent
1000 grams
2,205 pounds (lb)
Table 1.3
1 (lb) = 0.4536 kg
1 gram (g)
1000 milligrams
0.03527 ounce(oz)
1 lb = 453.6 g
1 ounce = 28.35 g
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Converting Units of Volume
Sample Problem 1.3
PROBLEM: The volume of an irregularly shaped solid can be determined
from the volume of water it displaces. A graduated cylinder
contains 19.9mL of water. When a small piece of galena, an
ore of lead, is submerged in the water, the volume increases to
24.5mL. What is the volume of the piece of galena in cm3
and in L?
PLAN:
The volume of galena is equal to the change in the water
volume before and after submerging the solid.
volume (mL) before and after addition
(24.5 - 19.9)mL = volume of galena
subtract
volume (mL) of galena
1 mL = 1 cm3
volume (cm3) of
galena
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SOLUTION:
1 mL = 10-3 L
volume (L) of
galena
3
4.6 mL x 1 cm
mL
-3
4.6 mL x 10 L
mL
= 4.6 cm3
= 4.6x10-3 L
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Converting Units of Mass
Sample Problem 1.4
PROBLEM: International computer communications are often carried by optical
fibers in cables laid along the ocean floor. If one strand of optical
fiber weighs 1.19 x 10-3lbs/m, what is the total mass (in kg) of a
cable made of six strands of optical fiber, each long enough to link
New York and Paris (8.84 x 103km)?
PLAN:
The sequence of steps may vary but essentially you have to find
the length of the entire cable and convert it to mass.
SOLUTION:
length (km) of fiber
1 km = 103 m
length (m) of fiber
1 m = 1.19x10-3 lb
8.84 x
103km
8.84 x
106m
1.19 x 10 -3lbs
x
= 1.05 x 104lb
m
6 fibers = 1 cable
mass (kg) of cable
2.205 lb = 1 kg
1-22
= 8.84 x 106m
6 fibers =
1.05 x 104lb x
cable
mass (lb) of fiber
mass (lb) of cable
103m
x
km
6.30x 104lb
cable
6.30x 104lb
cable
2.86x104 kg
x
=
cable
2.205 lb
1kg
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Sample Problem 1.5
Calculating Density from Mass and Length
PROBLEM: Lithium (Li) is a soft, gray solid that has the lowest density
of any metal. If a slab of Li weighs 1.49 x 103 mg and has
sides that measure 20.9 mm by 11.1 mm by 11.9 mm, what
is the density of Li in g/cm3 ?
PLAN:
Density is expressed in g/cm3 so we need the mass in grams
and the volume in cm3.
SOLUTION:
-3
1.49x103mg x10 g
= 1.49g
1mg
10 mm = 1 cm
1cm
lengths (cm) of sides
20.9mm x
= 2.09cm
10mm
multiply lengths
Similarly the other sides will be 1.11
3
volume (cm )
cm and 1.19 cm, respectively.
lengths (mm) of sides
mass (mg) of Li
103 mg = 1 g
mass (g) of Li
2.09 x 1.11 x 1.20 = 2.76cm3
density (g/cm3) of Li
density of Li =
1-23
1.49g
2.76 cm3
= 0.540 g/cm3
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Figure 1.8
1-24
The freezing and boiling points of water.
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Temperature Scales and Interconversions
Kelvin ( K ) - The “Absolute temperature scale” begins at
absolute zero and only has positive values.
Celsius ( oC ) - The temperature scale used by science,
formally called centigrade, most commonly used scale around the
world; water freezes at 0oC, and boils at 100oC.
Fahrenheit ( oF ) - Commonly used scale in the U.S. for our
weather reports; water freezes at 32oF and boils at 212oF.
T (in K) = T (in oC) + 273.15
T (in oC) = T (in K) - 273.15
1-25
T (in oF) = 9/5 T (in oC) + 32
T (in oC) = [ T (in oF) - 32 ] 5/9
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Sample Problem 1.6
Converting Units of Temperature
PROBLEM: A child has a body temperature of 38.70C.
(a) If normal body temperature is 98.60F, does the child have a fever?
(b) What is the child’s temperature in kelvins?
PLAN:
We have to convert 0C to 0F to find out if the child has a fever
and we use the 0C to kelvin relationship to find the temperature
in kelvins.
SOLUTION:
(a) Converting from 0C to 0F
9
(38.70C) + 32 = 101.70F
5
(b) Converting from 0C to K
1-26
38.70C + 273.15 = 311.8K
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Figure 1.9A
The number of significant figures in a measurement depends
upon the measuring device.
32.330C
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32.30C
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Rules for Determining Which Digits are Significant
All digits are significant
except zeros that are used only to position the
decimal point.
•Make sure that the measured quantity has a decimal point.
•Start at the left of the number and move right until you reach the first
nonzero digit.
•Count that digit and every digit to it’s right as significant.
Zeros that end a number and lie either after or before the decimal
point are significant; thus 1.030 ml has four significant figures,
and 5300. L has four significant figures also.
Numbers such as 5300 L are assumed to only have 2 significant
figures. A terminal decimal point is often used to clarify the
situation, but scientific notation is the best!
1-28
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Sample Problem 1.7
Determining the Number of Significant Figures
PROBLEM: For each of the following quantities, underline the zeros that are
significant figures(sf), and determine the number of significant
figures in each quantity. For (d) to (f), express each in
exponential notation first.
(a) 0.0030 L
(b) 0.1044 g
(c) 53,069 mL
(d) 0.00004715 m
(e) 57,600. s
(f) 0.0000007160 cm3
PLAN:
Determine the number of sf by counting digits and paying attention
to the placement of zeros.
SOLUTION:
(a) 0.0030 L 2sf
(b) 0.1044 g 4sf
(c) 53.069 mL 5sf
(d) 0.00004715 m
(e) 57,600. s
(f) 0.0000007160 cm3
(d) 4.715x10-5 m 4sf
(e) 5.7600x104 s 5sf
(f) 7.160x10-7 cm3
1-29
4sf
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Rules for Significant Figures in Answers
1. For addition and subtraction. The answer has the
same number of decimal places as there are in the
measurement with the fewest decimal places.
Example: adding two volumes
83.5 mL
+ 23.28 mL
106.78 mL = 106.8 mL
Example: subtracting two volumes
865.9
mL
- 2.8121 mL
863.0879 mL = 863.1 mL
1-30
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Rules for Significant Figures in Answers
2. For multiplication and division. The number with the least
certainty limits the certainty of the result. Therefore, the answer
contains the same number of significant figures as there are in the
measurement with the fewest significant figures.
Multiply the following numbers:
9.2 cm x 6.8 cm x 0.3744 cm = 23.4225 cm3 = 23 cm3
1-31
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Rules for Rounding Off Numbers
1. If the digit removed is more than 5, the preceding number
increases by 1.
5.379 rounds to 5.38 if three significant figures are retained
and to 5.4 if two significant figures are retained.
2. If the digit removed is less than 5, the preceding number is
unchanged.
0.2413 rounds to 0.241 if three significant figures are retained
and to 0.24 if two significant figures are retained.
3.If the digit removed is 5, the preceding number increases by
1 if it is odd and remains unchanged if it is even.
17.75 rounds to 17.8, but 17.65 rounds to 17.6.
If the 5 is followed only by zeros, rule 3 is followed; if the 5 is
followed by nonzeros, rule 1 is followed:
17.6500 rounds to 17.6, but 17.6513 rounds to 17.7
4. Be sure to carry two or more additional significant figures
through a multistep calculation and round off only the final
answer.
1-32
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Issues Concerning Significant Figures
Electronic Calculators
be sure to correlate with the problem
FIX function on some calculators
Choice of Measuring Device
graduated cylinder < buret ≤ pipet
Exact Numbers
60 min = 1 hr
numbers with no uncertainty
1000 mg = 1 g
These have as many significant digits as the calculation requires.
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Sample Problem 1.8
Significant Figures and Rounding
PROBLEM: Perform the following calculations and round the answer to the
correct number of significant figures:
1g
4.80x104 mg 1000 mg
16.3521 cm2 - 1.448 cm2
(a)
(b)
7.085 cm
11.55 cm3
PLAN:
In (a) we subtract before we divide; for (b) we are using an exact
number.
SOLUTION:
(a)
16.3521 cm2 - 1.448 cm2
14.904 cm2
=
7.085 cm
= 2.104 cm
7.085 cm
1g
4.80x104 mg
(b)
11.55 cm3
1-34
48.0 g
1000 mg
=
= 4.16 g/ cm3
11.55 cm3
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Precision and Accuracy
Errors in Scientific Measurements
Precision Refers to reproducibility or how close the measurements are to each
other.
Accuracy Refers to how close a measurement is to the real value.
Systematic Error Values that are either all higher or all lower than the actual value.
Random Error In the absence of systematic error, some values that are higher and
some that are lower than the actual value.
1-35
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Figure 1.10 Precision and accuracy in the laboratory.
precise and accurate
precise but not accurate
1-36
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Figure 1.10
continued
Precision and accuracy in the laboratory.
random error
systematic error
1-37