Jeffrey Mack
California State University,
Sacramento
Chemistry and Its Methods
• Hypothesis: A tentative explanation or
prediction based on experimental
observations.
• Law: A concise verbal or mathematical
statement of a behavior or a relation that
seems always to be the same under the
same conditions.
• Theory: a well-tested, unifying principle that
explains a body of facts and the laws based
on them. It is capable of suggesting new
hypotheses that can be tested
experimentally.
2
Chemistry and Its Methods
3
• Experimental results should be reproducible.
• Furthermore, these results should be
reported in the scientific literature in sufficient
detail that they can be used or reproduced by
others.
• Conclusions should be reasonable and
unbiased.
• Credit should be given where it is due.
Qualitative Observations
4
• No numbers involved
• Color, appearance, statements like “large” or
“small:
• Stating that something is hot or cold without
specifying a temperature.
• Identifying something by smell
• No measurements
Qualitative Observations
• A quantity or attribute that is measureable is
specified.
• Numbers with units are expressed from
measurements.
• Dimensions are given such as mass, time,
distance, volume, density, temperature, color
specified as a wavelength etc...
5
Classifying Matter: States of Matter
6
Classifying Matter: States of Matter
7
• In solids these particles are packed closely together, usually in a
regular array. The particles vibrate back and forth about their
average positions, but seldom does a particle in a solid squeeze
past its immediate neighbors to come into contact with a new set
of particles.
• The atoms or molecules of liquids are arranged randomly rather
than in the regular patterns found in solids. Liquids and gases are
fluid because the particles are not confined to specific locations
and can move past one another.
• Under normal conditions, the particles in a gas are far apart. Gas
molecules move extremely rapidly and are not constrained by their
neighbors. The molecules of a gas fly about, colliding with one
another and with the container walls. This random motion allows
gas molecules to fill their container, so the volume of the gas
sample is the volume of the container.
States of Matter
• SOLIDS — have rigid shape, fixed volume.
External shape may reflect the atomic and
molecular arrangement.
–Reasonably well understood.
• LIQUIDS — have no fixed shape and may
not fill a container completely.
–Structure not well understood.
• GASES — expand to fill their container
completely.
–Well defined theoretical understanding.
8
Classifying Matter
9
Classifying Matter
10
Mixtures: Homogeneous and Heterogeneous
• A homogeneous mixture consists of two or
more substances in the same phase. No amount
of optical magnification will reveal a
homogeneous mixture to have different
properties in different regions.
• A heterogeneous mixture does not have
uniform composition. Its components are easily
visually distinguishable.
• When separated, the components of both types
of mixtures yields pure substances.
Classifying Matter
11
Classifying Matter
Pure Substances
• A pure substance has well defined physical
and chemical properties.
• Pure substances can be classified as
elements or compounds.
• Compounds can be further reduced into two
or more elements.
• Elements consist of only one type of atom.
They cannot be decomposed or further
simplified by ordinary means.
12
Matter and its Representation
What we observe…
To what
we can’t
see!
Chemical symbols allow us to connect…
13
The Representation of Matter
In chemistry we use chemical formulas and
symbols to represent matter.
Why?
We are “macroscopic”:
large in size on the order of 100’s of cm.
Atoms and molecules are “microscopic”:
on the order of 10-12 cm
14
Elements
• The elements are recorded on the PERIODIC TABLE
• There are 117 recorded elements at this time.
• The Periodic table will be discussed further in chapter 2.
15
Chemical Compounds
Chemical compounds are composed of two or more
atoms.
16
Chemical Compounds
Molecule:
Ammonia (NH3)
Ionic Compound
Iron pyrite (FeS2)
17
Chemical Compounds
18
• All Compounds are made up of molecules or
ions.
• A molecule is the is the smallest unit of a
compound that retains its chemical
characteristics.
• Ionic compounds are described by a “formula
unit”.
• Molecules are described by a “molecular
formula”.
Molecular Formula
• A molecule is the smallest unit of a compound
that retains the chemical characteristics of the
compound.
• Composition of molecules is given by a
molecular formula.
H2O
C8H10N4O2 - caffeine
19
Physical Properties
Some physical properties:
− Color
− State (s, g or liq)
− Melting and Boiling point
− Density (mass/unit volume)
Extensive properties (mass)
depend upon the amount of
substance.
Intensive properties (density)
do not.
20
21
Physical Properties
Physical properties are a function of intermolecular
forces.
H
Water (18 g/mol)
liquid at 25oC
Methane (16 g/mol)
gas at 25oC
H
C
H
H
O
H
H
• Water molecules are attracted to one another by
“hydrogen bonds”.
• Methane molecules only exhibit week “London
Forces”.
Physical Properties
Physical properties are
affected by
temperature
(molecular motion).
The density of water is
seen to change with
temperature.
22
Physical Properties
Mixtures may be separated by physical properties:
Physical Property
Means of Separation
Density
Decantation,
centrifugation
Boiling point
Distillation
State of Matter
Filtration
Intermolecular Forces
Chromatography
Vapor pressure
Evaporation
Magnetism
Magnets
Solubility
Filtration
23
Chemical Properties
• Chemical properties are really chemical changes.
• The chemical properties of elements and
compounds are related to periodic trends and
molecular structure.
24
Chemical Properties
A chemical property indicates whether and
sometimes how readily a material undergoes
a chemical change with another material.
For example, a chemical property of hydrogen
gas is that it reacts vigorously with oxygen
gas.
25
26
The Nature of Matter
Gold
Mercury
Chemists are interested in the nature of matter
and how this is related to its atoms and
molecules.
A Chemist’s View
of Water
Macroscopic
H 2O
(gas, liquid, solid)
Particulate
Symbolic
2 H2(g) + O2 (g)  2 H2O(g)
Energy: Some Basic Principles
Energy can be classified as Kinetic or Potential.
• Kinetic energy is energy associated with motion such
as:
• The motion at the particulate level (thermal energy).
• The motion of macroscopic objects like a thrown
baseball, falling water.
• The movement of electrons in a conductor (electrical
energy).
• Wave motion, transverse (water) and compression
(acoustic).
Matter consists of atoms and molecules in motion.
28
Energy: Some Basic Principles
Potential energy results from an object’s
position:
• Gravitational: An object held at a height,
waterfalls.
• Energy stored in an extended spring.
• Energy stored in molecules (chemical energy,
food)
• The energy associated with charged or partially
charged particles (electrostatic energy)
• Nuclear energy (fission, fusion).
29
Jeffrey Mack
California State University,
Sacramento
The Tools of Quantitative Chemistry
31
"In physical science the first essential step in the direction
of learning any subject is to find principles of numerical
reckoning and practicable methods for measuring some
quality connected with it.
I often say that when you can measure what you are
speaking about, and express it in numbers, you know
something about it; but when you cannot measure it, when
you cannot express it in numbers, your knowledge is of a
meager and unsatisfactory kind; it may be the beginning
of knowledge, but you have scarcely in your thoughts
advanced to the state of Science, whatever the matter may
be."
Lord Kelvin, "Electrical Units of Measurement", 1883-05-03
Note About Math & Chemistry
32
Numbers and mathematics are an inherent and
unavoidable part of general chemistry.
Students must possess secondary algebra
skills and the ability to recognize orders of
magnitude quickly with respect to numerical
information to assure success in this course.
The material presented in this chapter is
considered to be prerequisite to this course.
Units of Measure
33
Science predominantly uses the “SI” (System
International) system of units, more commonly known
as the “Metric System”.
Units of Measure
The base units are modified by a series of prefixes
which you will need to memorize.
34
Temperature Units
Temperature is measured in the Celsius an the
Kelvin temperature scale.
35
Temperature Conversion
1K
T(K) 
  TC  273.15C 
1C
1K
 298.2K
 25.0C  273.15C  
1C
36
Length, Volume, and Mass
The base unit of length in the metric system is
the meter.
Depending on the object measured, the meter
is scaled accordingly.
37
Length, Volume, and Mass
Unit conversions: How many picometers are there in
25.4 nm? How many yards?
nm  m  pm
1m
1 1012 pm
4
25.4nm 

 2.54  10 pm
9
1 10 nm
1m
m  cm  in  ft  yd
102 cm
1in
1ft 1yd
25.4m 



 27.8 yards
1m
2.54cm 12in 3ft
38
Length, Volume, and Mass
39
The base unit of volume in the metric system is
the liter.
1 L = 103 mL 1 mL=1 cm3 1 cm3 = 1 mL
L  mL  cm
3
3
3
10 mL 1cm
4
3
25.4 L 

 2.54  10 cm
1L
1 mL
Length, Volume, and Mass
40
The base unit of volume in the metric system is
the gram.
1kg = 103g
ng  g  kg
1g
1kg
11
25.4ng 

 2.54  10 g
9
3
1 10 ng 1 10 g
Energy Units
41
Energy is confined as the capacity to do work.
The SI unite for energy is the joule (J).
kg × m
1J =
s2
Energy is also measured in calories (cal)
1 cal = 4.184J
2
A kcal (kilocalorie) is often written as Cal.
1 Cal =103 cal
Making Measurements: Precision
The precision of a measurement indicates how well
several determinations of the same quantity agree.
42
Making Measurements: Accuracy
43
Accuracy is the agreement of a measurement
with the accepted value of the quantity.
Accuracy is often reflected by Experimental
error.
Experimental value - Accepted value
Percent Error =
´ 100
Accepted value
Making Measurements:
Standard Deviation
44
The Standard Deviation of a series of
measurements is equal to the square root of
the sum of the squares of the deviations for
each measurement from the average divided
by one less than the number of measurements
(n).
_ 2
Standard Deviaton =
æ
ö
å çè xn - x ÷ø
n -1
Measurements are often reported to  the
standard deviation to report the precision of a
measurement.
Mathematics of Chemistry
45
Exponential or Scientific Notation:
Most often in science, numbers are expressed
in a format the conveys the order of magnitude.
3285 ft = 3.285  103 ft
0.00215kg = 2.15  103 kg
Exponential or Scientific Notation
1.23  10
4
Coefficient or Mantissa
Base
Exponent
(this number is 1 and
<10 in scientific notation
Exponential
part
46
Mathematics of Chemistry
47
Significant figures: The number of digits
represented in a number conveys the precision
of the number or measurement.
A mass measured to  0.1g is far less precise
than a mass measured to  0.0001g.
1.1g
vs. 1.0001g
(2 sig. figs.
vs.
5 sig. figs)
In order to be successful in this course, you will
need to master the identification and use of
significant figures in measurements and
calculations!
Counting Significant Figures
48
1. All non zero numbers are significant
2. All zeros between non zero numbers are
significant
3. Leading zeros are NEVER significant.
(Leading zeros are the zeros to the left of
your first non zero number)
4. Trailing zeros are significant ONLY if a
decimal point is part of the number. (Trailing
zeros are the zeros to the right of your last
non zero number).
Determining Significant Figures
Determine the
number of Sig.
Figs. in the
following
numbers
zeros written
explicitly behind
the decimal are
significant…
1256
4 sf
1056007
7 sf
0.000345
3 sf
0.00046909
5 sf
1780
3 sf
770.0
4 sf
0.08040
4 sf
not trapped by a
decimal place.
49
Rounding Numbers
1. Find the last digit that is to be kept.
2. Check the number immediately to the right:
If that number is less than 5 leave the last
digit alone.
If that number is 5 or greater increase the
previous digit by one.
50
Rounding Numbers
Round the following to 2 significant figures:
1056007
1100000
0.000345
0.00035
1780
1800
51
Sig. Figures in Calculations
52
Multiplication/Division
The number of significant figures in the answer is
limited by the factor with the smallest number of
significant figures.
Addition/Subtraction
The number of significant figures in the answer is
limited by the least precise number (the number
with its last digit at the highest place value).
NOTE: counted numbers like 10 dimes never limit
calculations.
Sig. Figures in Calculations
Determine the correct number of sig. figs. in the
following calculation, express the answer in scientific
notation.
from the calculator:
4 sf
2 sf
4 sf
23.50  0.2001  17 = 1996.501749 10 sf
Your calculator knows nothing of sig. figs. !!!
53
Sig. Figures in Calculations
Determine the correct number of sig. figs. in the
following calculation, express the answer in scientific
notation.
in sci. notation:
1.996501749  103
Rounding to 2 sf:
2.0  103
54
Sig. Figures in Calculations
Determine the correct number of sig. figs. in the
following calculation:
391  12.6 + 156.1456
55
Sig. Figures in Calculations
56
To determine the correct decimal to round to, align
the numbers at the decimal place:
391  12.6 +156.1456
391
12.6
+156.1456
no digits here
One must round the calculation to the least significant
decimal.
Sig. Figures in Calculations
391
-12.6
+156.1456
534.5456
one must round to here
(answer from calculator)
round to here (units place)
Answer: 535
57
Sig. Figures in Calculations
58
Combined Operations: When there are both
addition & subtraction and or multiplication & division
operations, the correct number of sf must be
determined by examination of each step.
Example: Complete the following math mathematical
operation and report the value with the correct # of
sig. figs.
(26.05 + 32.1)  (0.0032 + 7.7) = ???
Sig. Figures in Calculations
59
Example: Complete the following math mathematical
operation and report the value with the correct # of
sig. figs.
(26.05 + 32.1)  (0.0032 + 7.7) = ???
(26.05 + 32.1)
=
(0.0032 + 7.7)
1st
determine the correct #
of sf in the numerator (top)
2nd determine the correct #
of sf in the denominator
(bottom)
The result will be limited by the least # of sf (division rule)
Sig. Figures in Calculations
60
3 sf
26.05
(26.05 + 32.1)
=
(0.0032 + 7.7)
+ 32.1
58.150
=
0.0032
7.7032
+ 7.7
2 sf
The result
may only have
2 sf
Sig. Figures in Calculations
61
Carry all of the digits through the calculation and round at the
end.
58.150
3 sig figs
(26.05 + 32.1)
(0.0032 + 7.7)
=
= 7.5488
7.7032
= 7.5
2 sf
Round to here
2 sig figs!
Problem Solving and
Chemical Arithmetic
62
Dimensional Analysis:
Dimensional analysis converts one unit to another by
using conversion factors (CF’s).
unit (1)  conversion factor
= unit (2)
The resulting quantity is equivalent to the original
quantity, it differs only by the units.
Problem Solving and
Chemical Arithmetic
Dimensional Analysis:
Dimensional analysis converts one unit to another by
using conversion factors (CF’s).
Conversion factors come from equalities:
1 m = 100 cm
1m
100 cm
or
100 cm
1m
63
Examples of Conversion Factors
Exact Conversion Factors: Those in the same
system of units
1 m = 100 cm
1m
102 cm
or
102 cm
1m
Use of exact CF’s will not affect the significant
figures in a calculation.
64
Examples of Conversion Factors
Inexact Conversion Factors: CF’s that relate
quantities in different systems of units
1.000 kg = 2.205 lb
SI units
1 .000 kg
(4 sig. figs.)
2.205 lb
British Std.
or
2.205 lb
1.000 kg
Use of inexact CF’s will affect significant figures.
65
Problem Solving and
Chemical Arithmetic
• Problem solving in chemistry requires “critical
thinking skills”.
• Most questions go beyond basic knowledge and
comprehension. (Who is buried in Grant’s tomb?)
• You must first have a plan to solve a problem
before you plug in numbers.
• You must evaluate the result to see if it makes
sense. (units, order of magnitude)
• You must also practice to become proficient
because...
Chem – is – try
66
Problem Solving and
Chemical Arithmetic
• Before starting a
problem, devise a
“Strategy Map”.
• Use this to collect the
information given to
work your way through
the problem.
• Solve the problem using
Dimensional Analysis.
• Check to see that you
have the correct units
along the way.
67
Problem Solving and
Chemical Arithmetic
68
Most importantly, before you start...
PUT YOUR CALCULATOR DOWN!
Your calculator wont help you until you are ready to
solve the problem based on your strategy map.
Problem Solving and
Chemical Arithmetic
Example: How many meters are there in 125 miles?
First: Outline of the conversion:
69
Problem Solving and
Chemical Arithmetic
Example: How many meters are there in 125 miles?
First: Outline of the conversion:
miles  ft  in  cm  m
Each arrow indicates the use of a conversion factor.
70
Problem Solving and
Chemical Arithmetic
Example: How many meters are there in 125 miles?
Second: Setup the problem using Dimensional
Analysis:
miles  ft  in  cm  m
5280 ft 12 in 2.54 cm 1 m
´ 2
125 miles ´

´
=
10 cm
1 in
1 mile 1 ft
71
Problem Solving and
Chemical Arithmetic
72
Example: How many meters are there in 125 miles?
Third: Check your sig. figs. & cancel out units.
miles  ft  in  cm  m
1m
2.54 cm
5280 ft/ 12 in
/
/
125 miles
=
/ ´ 1 mile ´ 1 ft/  1 in/ ´ 102 cm
/
/
3 sf
exact
exact
3 sf
exact
Problem Solving and
Chemical Arithmetic
73
Example: How many meters are there in 125 miles?
Fourth: Now use your calculator. :
miles  ft  in  cm  m
1m
2.54 cm
5280 ft
12 in
/
/
/
125 miles
=
/ ´ 1 mile ´ 1 ft  1 in ´ 102 cm
/
/
/
/
3 sf
exact
exact
3 sf
exact
Carry though all digits, round at end
Problem Solving and
Chemical Arithmetic
74
Example: How many meters are there in 125 miles?
Lastly: Check your answer for sig. figs & magnitude.
miles  ft  in  cm  m
2.54 cm

1m
5280 ft/ 12 in
/
/
1 in ´ 2
125 miles
=
/ ´ 1 mile ´ 1 ft
10 cm
/
/
/
/
3 sf
exact
2.01168  105
exact
or
3 sf
exact
2.01  105 m
(3 sf)
Problem Solving and
Chemical Arithmetic
Example: How many square feet are there in 25.4
cm2?
Map out your conversion:
cm2  in2  ft2
2
2
æ 1.00 in
ö æ 1 ft ö
/
25.4 cm
÷ = 2.73403  10-2 ft2
÷ ´ç
/ ´ çè 2.54cm
/ ø è 12 in/ ø
2
3 sf
or
exact
2.73  10-2 ft2
exact
(3 sf)
75
Problem Solving and
Chemical Arithmetic
Example: How many cubic feet are there in 25.4
cm3?
Map out your conversion:
cm3  in3  ft3
3
3
æ 1.00 in
ö æ 1 ft ö
/
25.4 cm
÷ = 8.96993  10-4 ft3
÷ ´ç
/ ´ çè 2.54cm
/ ø è 12 in
/ø
3
3 sf
or
exact
8.97  10-4 ft3
exact
(3 sf)
76
Problem Solving and
Chemical Arithmetic
77
Example: What volume in cubic feet would 0.851
grams of air occupy if the density is 1.29 g/L?
Map out your conversion:
g
L
cm3 
in3 
ft3
3
3
1 L/ 10 cm
æ 1 in
ö æ 1 ft ö
/
/
0.851 g/ ´
´
´ç
÷ ´ç
÷ =
1.29g/
1 L/
è 2.54 cm
/ ø è 12 in
/ ø
3
3 sf
3 sf
3 sf
3
3 sf
2.33 ´ 10-2 ft 3 3 sf
exact