CHAPTER 2
DATA ANALYSIS
I. UNITS OF MEASUREMENT
A. Metric Prefixes
Prefix
Symbol
Meaning
Scientific
Notation
1 x 109
giga
G
mega
M
1 000 000 000 times larger than
base unit
1 000 000 times larger
kilo
K
1000 times larger
1 x 103
base unit
deci
(g, m, s, L) 1 base unit
d
10 times smaller (1/10 of base)
1 x 10-1
centi
C
100 times smaller (1/100 )
1 x 10-2
milli
m
1000 times smaller (1/1000)
1 x 10-3
micro
µ
1 million times smaller
(1/1,000,000)
1 billion times smaller
(1/1,000,000,000)
1 trillion times smaller
(1/1,000,000,000,000)
1 x 10-6
Nano
Pico
1 x 106
1 x 10-9
1 x 10-12
Example
gigameter
Gm
megagram
Mg
kilometer
km
deciliter
dL
centimeter
cm
milligram
mg
microgram
μg
nanometer
nm
picometer
pm
B. THE INTERNATIONAL SYSTEM OF UNITS (SI)
Base Unit - a defined unit in a system of measurement that is based on an object or event in
the physical world
There are 7 Metric base units
MEMORIZE the first five!!
Quantity Measured
SI Unit/ Lab Unit
SI Symbol
Length
Mass
Time
Temperature
Amount of substance
Electric current
Luminous Intensity
Meter/ Centimeter
Kilogram/ gram
Second
Kelvin/ Celsius
mole
ampere
candela
m/ cm
kg/ g
S
K /°C
mol
A
Cd
1. Mass
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a) the amount of matter in a substance [recall that weight is
a measure of the force of gravity between two objects]
b) kilogram (kg) is official base unit
[too large for chemistry so we use gram (g)]
c) measured on a balance
2. Length
a) distance covered by a straight line connecting two points
b) meter (m) is base unit cm is the unit we use in lab
c) measured with a ruler or similar device
3. Time
a) the interval between two occurrences
b) measured in seconds (s)
c) measured with clock or watch
4. Temperature
a) the measure of the average kinetic energy of the particles of
sample
b) metric temperature scale (Celsius, °C):
0° C = freezing point of water at 1 atmosphere of pressure
100°C = boiling point of water at 1 atmosphere of pressure
room temperature = about 25°C
body temperature = about 37°C
c) absolute temperature scale (Kelvin, K)
0 K = absence of all molecular motion (absolute zero)
273 K = freezing point of water
373 K = boiling point of water
298 K = room temperature
d) Related to Celsius by:
°C + 273 = K
II.
a
DENSITY
DERIVED UNIT - a unit that is defined as a combination of base units
Density = mass per unit volume = D = m/V
A. Mass = m
• measured in grams
• measured on a balance
• may be calculated "by difference"
mass the empty container first
add desired material
mass the full container
subtract to find mass of material
B.
Volume = V
• measure of the amount of space matter occupies
• measured in cm3 or mL
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•
•
•
C.
D.
1 cm3 = 1 mL (MEMORIZE THIS)
if liquid, measure in a graduated cylinder:
read bottom of meniscus
if regular solid, measure with ruler:
length x width x height = V
if irregular solid, measure by water displacement:
fill graduated cylinder to specific volume (record)
add irregular shaped object
record the new volume
subtract: final vol. - initial vol. = object vol.
Units of density
D = m = g or
V
mL
g
cm3
Density problems
ex. #1 - density of a liquid
mass = 4.98 g
volume = 2.36 mL
density = ?
ex. #2 - density of a regular solid cube
mass = 3.2 g
length = 2 cm
width = 2 cm
height = 2 cm
volume = ?
density = ?
ex. #3 - density of an irregular solid
mass = 7.8 g
initial water level = 10.0 mL
final water level = 17.4 mL
volume = ?
density = ?
E.
Using the density formula
• rearrange the basic formula to find mass or volume
• plug data into the new formula; solve
ex #1 - finding mass
D=m/V so D•V = m
density = 1.02 g/mL
volume = 3.45 mL
mass = ? g
ex. #2 - finding volume
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D=m/V, so V = m/D
density = 2.1 g/mL
mass = 3.5 g
volume = ? mL
III. CRITICAL MATH SKILLS
INTRODUCTION:
It is possible to study chemistry and gain some appreciation and understanding of it without
mathematics. However, the depth of your comprehension of chemistry (and almost every other
subject) is directly related to your math skills that you should master before studying chemistry.
It is critical that you seek tutoring at any time you do not understand a topic in this unit.
A. Math Review --- Getting to know your calculator
1. Parentheses
try this: 4(3 + 5)
or:
4.184 x 10.0 (100.0 - 92.1)
2. Scientific Notation
a) use for very large (>1000) or very small
numbers (<.001) (more than 3 digits)
b) LARGE NUMBERS have POSITIVE exponents
small numbers have negative exponents
c) Standard scientific notation:
only one number in front of the decimal point
d) Self-Test
Put these numbers in scientific notation.
a) 40,230,000
b) 0.0099
Write these numbers in ordinary form:
a) 7.3 x 10-3
b) 3.18 x 104
Now let's add a and b on your calculator.
On your calculator, punch 7.3 2nd comma button( this is the EE button) then
punch (-) button (to the left of Enter) and then 3 plus 3.18 2nd comma button
4.
Some of you may be used to using the  button. This does not work all the
time. Get use to using the 2nd comma button.
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IV.
V.
Accuracy and Precision
Accuracy
• how close a measurement is to the true value
Precision
• how close a series of measurements are to each other
Percent Error
• use when determining an experimental value for quantity that is
already known.
• used to compare your value to the "book" or known value
Percent Error = |experimental value - "book" value| x 100%
"book" value
• always positive number
ex. I find the density of water to be 0.92 g/cm3. The actual value is 1.00 g/cm3.
What is the percent error of my value?
VI.
Significant Figures
• only represents numbers actually measured and one estimate position
• depends on the instrument's precision
RULES
1.
All non-zero digits are significant
EX: 456
932.76
2.
Leading zeros are NEVER significant
EX: 0.0000234
0.002
3.
Middle zeros are ALWAYS significant
EX: 1002
9.0043
4.
Trailing zeros are significant ONLY IF THERE IS A DECIMAL
POINT IN THE NUMBER
EX: 223.0
200
9.87000
5.
Counting numbers and defined constants have an infinite number
of significant figures.
EX: 6 molecules
60 s =1 min
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Rounding Off
1.
Calculations with measurements must maintain proper degree of
certainty.
2.
Rules:
a.
In multiplication and division, the answer may not
contain any more SIGNIFICANT DIGITS than the number in the
calculation with the fewest significant digits.
ex: 1.5 grams = 0.375 g/mL
4 mL
ROUND THIS TO: 0.4 g/mL
b.
In addition and subtraction, the answer may not contain
any more DECIMAL PLACES than the number in the calculation with the
fewest decimal places.
ex.
VII.
98
+ 213.67
311.67
ROUND THIS TO: 312
REPRESENTING DATA
GRAPHING
A graph is a visual display of data.
Types of Graphs
Circle Graph, also called a pie chart.
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Bar Graph
Line Graph
Points on a line graph represent the intersection of data for two variables
Independent variable, variable which the scientist deliberately changes during and
experiment, is plotted on the x-axis.
Dependent variable is plotted on the y-axis
Best fit line is a line that must be drawn so that about as many points fall above the line as
fall below it. If the best fit line is straight the independent and dependent variables are
directly related. This can be described by the slope of the line. If the line rises to the
right, the slope is positive. Positive slope indicates that the dependent variable increases
as the independent variable increases. If the line sinks to the right, the slope is negative
and indicates that the dependent variable decreases as the independent variable increases.
Slope can be calculated using the following equation:
Slope = y2 – y1
x2 – x1
Interpreting graphs
Interpolation – reading data from a graph that falls between measured points
Extrapolation – extending the line beyond the plotted points and estimate values for the
variables
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