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Chapter 2
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A logical approach to solving problems
by observing and collecting data,
formulating hypotheses, testing
hypotheses, and formulating theories
that are supported by data
There are 4 steps.
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OHEC! (A way to remember this.)
Observation (use your senses)
Hypothesis (the educated guess)
Experiments (test the hypothesis)
Conclusion (a broad explanation)
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A conclusion leads to:
Model: an explanation of how phenomena occur or how sata or events are related
Can be visual, verbal or mathematical
Theory – a broad generalization that explains a body of facts of phenomena
A scientific law is a concise statement to summarize results
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Hypothesis - testable statement
Based on the observations that were made
TESTING HYPOTHESIS
Requires experimentation!
Controls – experimental conditions that remain constant
Variables – conditions that change
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To learn more about matter, chemists study systems
System – a specific portion of matter in a given region of space that has been selected for study during an experiment or observation ◦ Ex: reaction in a test tube
◦ Ex: reaction in a beaker
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Comparing one object to a standard
There are two types of measurements:
◦ Qualitative & Quantitative
In science we use the SI units
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A measurement that is descriptive
and non-numerical in form
A measurement with definite form,
numbers and units
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SI Measurement
AKA –
the Metric System!
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Americans only use feet, inches, yards…
◦ Based on the king!
New king… new units!
◦ Yard: length of his arm
◦ Foot: size of his foot
◦ Pound: how many marbles he could pick up
with one fist
Metric System – based on powers of 10
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Le Systeme International d’Unites The SI Units are a revised version of the metric system
There are 7 base units
All the rest are derived units
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Length: meter (m)
Mass: kilogram (kg)
Temperature: kelvin (K)
Time: second (s)
Quantity: mole (mol)
Luminosity: candela (cd)
Current: ampere (A)
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Prefix Symbol Scientific
Notation
Meaning
Mega- M 106 Million times
kilo- k 103 thousand times
hecto- h 102 Hundred times
deca- da 101 Ten times
BASE ~ ~ Base Unit
deci- d 10-1 1 / tenth
centi- c 10-2 1 / hundredth
milli- m 10-3 1 / thousandth
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Prefix Symbol Scientific
Notation
Pnemonic Device
Mega- M 106 Most
kilo- k 103 Kittens
hecto- h 102 Hate
deca- da 101 Dogs
BASE ~ ~ Because
deci- d 10-1 Dogs
centi- c 10-2 Can’t
milli- m 10-3 Meow !
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Tera (T) = 1x1012
Giga (G) = 1x109
Hecto (h) = 1x102
Micro (µ) = 1 x 10-6 Nano (n) = 1 x 10-9
Pico (p) = 1 x 10-12
Femto (f) = 1x10-15
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Derived Units – combinations of
SI base units
◦area, volume, density, molar mass,
molar volume, & energy
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Volume – amount of space occupied by an object V = L x W x H
V measured in m3, cm3, mL, L
1 cm3 = 1 mL
1000 mL = 1 L
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Density – ratio of an objects
mass to its volume
)3
volume(cm
(g) mass D
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Substance Density (g/cm3) Substance Density (g/cm3)
Cork 0.24 Gasoline 0.67
Ice 0.92 Ethanol 0.79
Bone 1.85 Water 1.00
Lead 11.35 Mercury 13.6
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A sample of aluminum metal has a
mass of 8.4 g. The volume of the
sample is 3.1 cm3. Calculate the
density of aluminum.
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Given: mass (m) = 8.4 g
volume (v) = 3.1 cm3
Unknown: density (D) = ?
Equation:
Solve: D = 8.4 g = 2.7 g/cm3
3.1 cm3
v
m D
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Dimensional analysis is a way
to analyze and solve problems
using the units, or dimensions
of the measurements.
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Conversion factors: ratios of
equivalent measurements used
in dimensional analysis
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What does $1 = ?
4 quarters = 10 dimes = 20 nickels = 100 pennies…
Conversion Factor – a ratio of equivalent
measurements (can be written as a dimension)
1 ft = 12 in or 12 in = 1 ft
1 ft 12 in
12 in 1 ft
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Three steps to problem
solving:
1. Analyze
2. Calculate
3. Evaluate
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Read problem carefully
Read the problem several times if
necessary
Find out what the problem is asking
Write down important information
such as units!
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Make all your calculations:
May involve conversions,
substitutions etc…
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Check your answer- ◦Does your answer make sense? Is it reasonable?
◦Is it in the correct units? ◦Is it in the correct number of significant figures
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How many days are there in 6 weeks?
You are looking
for this!
This is your “given”.
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Figure out what relationships you
will have to know in order to
convert from 1 unit to another.
1 week = 7 days
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Start with given and work toward what you are looking for.
6weeks = ? days
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Conversion Factor : top and bottom must be
equal in value
days week 1
days 7x weeks 6
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6 weeks x = 42 days 1 week
7 days
Cancel units : cancel
units to leave correct
units for the answer
Calculate : multiply
across top and bottom
and divide to get final
answer
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Uncertainty in Measurement
A digit that must be estimated is called
uncertain.
A measurement always has some
degree of uncertainty.
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Why Is there Uncertainty?
• Measurements are performed with instruments
• No instrument can read to an infinite number
of decimal places
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Precision and Accuracy
Accuracy refers to the agreement of a particular value with the true value.
Precision refers to the degree of agreement among several measurements made in the same manner.
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Neither
accurate nor
precise
Precise but
not accurate
Precise
AND
accurate
Precision and Accuracy
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Accepted/actual value – the correct value based on reliable references
Experimental value – the value measured in the lab
Error – difference between actual and experimental values
100
value Accepted
valueal Experiment-value Accepted Error %
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numbers that include all the
digits that can be known
accurately plus a last digit
that must be estimated
◦digits that have meaning
Definition:
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Rules for Sig Figs
Nonzero integers always count as
significant figures.
3456 has 4 sig figs.
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Rules for Sig Figs
Zeros
Leading zeros do not count as
significant figures.
0.0486 has
3 sig figs.
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Rules for Sig Figs
Zeros
Captive zeros always count as
significant figures.
16.07 has
4 sig figs.
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Rules for Sig Figs
Zeros
Trailing zeros are significant only
if the number contains a decimal
point.
9.300 has 4 sig figs.
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Rules for Sig Figs
Exact numbers have an
infinite number of significant
figures.
1 inch = 2.54 cm, exactly
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Sig Fig Practice #1
How many significant figures in each of the following?
1.0070 m 5 sig figs
17.10 kg 4 sig figs
3.29 x 103 s 3 sig figs
0.0054 cm 2 sig figs
3,200,000 2 sig figs
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Mathematical Operations
Multiplication and Division: # sig figs in the result equals the number
in the least precise measurement used in
the calculation.
6.38 x 2.0 =
12.76 13 (2 sig figs)
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Sig Fig Practice #2
3.24 m x 7.0 m
Calculation Calculator says: Answer
22.68 m2 23 m2
100.0 g 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2
710 m 3.0 s 236.6666667 m/s 240 m/s
1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft
1.030 g 2.87 mL 2.9561 g/mL 2.96 g/mL
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Mathematical Operations
Addition and Subtraction: The number of
decimal places in the result equals the
number of decimal places in the least
precise measurement.
6.8 + 11.934 =
18.734 18.7 (3 sig figs)
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Sig Fig Practice #3
3.24 m + 7.0 m
Calculation Calculator says: Answer
10.24 m 10.2 m
100.0 g - 23.73 g 76.27 g 76.3 g
0.02 cm + 2.371 cm 2.391 cm 2.39 cm
713.1 L - 3.872 L 709.228 L 709.2 L
1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb
2.030 mL - 1.870 mL 0.16 mL 0.160 mL
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What is the difference between a directly proportional
relationship and an inversely proportional
relationship?
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Directly proportional = when two quantities are divided by one another and gives a constant value
y x or “y is proportional to x”
k
x
y
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When x increases,
y increases and vice
versa!
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D.D. = direct (relationship?), then
divide!
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Inversely proportional – when two quantities products give a constant
“y is proportional to 1 divided by x”
or
x
1 y kxy
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When x increases,
y decreases and
vise versa!