chapter 3 – scientific measurement 2h notes.pdf · prefix symbol scientific notation meaning...
TRANSCRIPT
Chapter 2
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.
OHEC! (A way to remember this.)
Observation (use your senses)
Hypothesis (the educated guess)
Experiments (test the hypothesis)
Conclusion (a broad explanation)
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
Hypothesis - testable statement
Based on the observations that were made
TESTING HYPOTHESIS
Requires experimentation!
Controls – experimental conditions that remain constant
Variables – conditions that change
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
Comparing one object to a standard
There are two types of measurements:
◦ Qualitative & Quantitative
In science we use the SI units
A measurement that is descriptive
and non-numerical in form
A measurement with definite form,
numbers and units
SI Measurement
AKA –
the Metric System!
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
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
Length: meter (m)
Mass: kilogram (kg)
Temperature: kelvin (K)
Time: second (s)
Quantity: mole (mol)
Luminosity: candela (cd)
Current: ampere (A)
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
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 !
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
Derived Units – combinations of
SI base units
◦area, volume, density, molar mass,
molar volume, & energy
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
Density – ratio of an objects
mass to its volume
)3
volume(cm
(g) mass D
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
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.
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
Dimensional analysis is a way
to analyze and solve problems
using the units, or dimensions
of the measurements.
Conversion factors: ratios of
equivalent measurements used
in dimensional analysis
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
Three steps to problem
solving:
1. Analyze
2. Calculate
3. Evaluate
Read problem carefully
Read the problem several times if
necessary
Find out what the problem is asking
Write down important information
such as units!
Make all your calculations:
May involve conversions,
substitutions etc…
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
How many days are there in 6 weeks?
You are looking
for this!
This is your “given”.
Figure out what relationships you
will have to know in order to
convert from 1 unit to another.
1 week = 7 days
Start with given and work toward what you are looking for.
6weeks = ? days
Conversion Factor : top and bottom must be
equal in value
days week 1
days 7x weeks 6
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
Uncertainty in Measurement
A digit that must be estimated is called
uncertain.
A measurement always has some
degree of uncertainty.
Why Is there Uncertainty?
• Measurements are performed with instruments
• No instrument can read to an infinite number
of decimal places
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.
Neither
accurate nor
precise
Precise but
not accurate
Precise
AND
accurate
Precision and Accuracy
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 %
numbers that include all the
digits that can be known
accurately plus a last digit
that must be estimated
◦digits that have meaning
Definition:
Rules for Sig Figs
Nonzero integers always count as
significant figures.
3456 has 4 sig figs.
Rules for Sig Figs
Zeros
Leading zeros do not count as
significant figures.
0.0486 has
3 sig figs.
Rules for Sig Figs
Zeros
Captive zeros always count as
significant figures.
16.07 has
4 sig figs.
Rules for Sig Figs
Zeros
Trailing zeros are significant only
if the number contains a decimal
point.
9.300 has 4 sig figs.
Rules for Sig Figs
Exact numbers have an
infinite number of significant
figures.
1 inch = 2.54 cm, exactly
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
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)
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
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)
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
What is the difference between a directly proportional
relationship and an inversely proportional
relationship?
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
When x increases,
y increases and vice
versa!
D.D. = direct (relationship?), then
divide!
Inversely proportional – when two quantities products give a constant
“y is proportional to 1 divided by x”
or
x
1 y kxy
When x increases,
y decreases and
vise versa!