Transcript Metric and Measurement

Chapter 2-1
Method, Measurement
and Problem Solving
I. What is Chemistry?
A. Chemistry is the study of all matter and the changes it
can undergo.
B. Chemistry has been called the central science because it
overlaps so many sciences.
C. Chemical – any substance with a definite composition.
Ex) dihydrogen monoxide = H2O
A common misperception of science is
that science defines "truth." Science
does not define truth, but rather it
defines a way of thought. It is a process
by which experiments are used to answer
questions. This process is called the
scientific method and involves several
steps:
II. The Scientific Method: (2.2)
A. A systematic approach to gathering knowledge.
B. Steps to the Scientific Method:
1.
2.
3.
4.
5.
observation
question
hypothesis
experiment
conclusion
*Note: All hypotheses must be able to be
tested in order to be a true hypothesis.
C. Many Experiments 
Natural Law

Theory
(how nature behaves) (why nature behaves)
III. Scientific Notation: Shorthand
way of expressing very large or very
small numbers. (2.3)
Power of 10
Equivalent #
Reason
100
1
Any # to the zero power is 1
101
10
10 x 1
102
100
10 x 10
103
1,000
10 x 10 x 10
105
100,000
10 x 10 x 10 x 10 x 10
10-1
0.1
1/10
10-3
0.001
1/(10x10x10) = 1/1000
10-5
0.00001
1/(10x10x10x10x10) = 1/100,000
• B. Express Numbers in
Scientific Notation – move the
decimal point so that there is
only 1 non-zero digit to the left
of the decimal point. Moving
the decimal point left the
power will be -, right the power
will be +.
Try these examples: top of page 2 in the notes!
1) 2700
2.7 x 103
3) 2,640,000,000
2) 0.0035
3.5 x 10-3
4) 0.010
1.0 x 10-2
2.64 x 109
C. Express Numbers in regular form – reverse the process.
5) 8.65 x 106
8,650,000
6) 9.73 x 10-8
0.000 000 0973
Complete the front of the Scientific Notation Worksheet
Small Numbers – negative exponents
are all between 0 and 1
Negative
Numbers
Large
Numbers
1x10-10
1x10-1
0
1x102
4x101
1x100 = 1
1st Commandment of Chemistry: KNOW THY CALCULATOR!
Find the “EE” key – it may
be a 2nd function!
If you have a
graphing
calculator look
for the following
keys:
Find the (-) key.
Find the “Exp” or “x10x”
1st Law of Chemistry:
Know Thy Calculator!
Look at the
calculator that is
similar to
yours…
Find the “(-)” or the
“+/-” key.
Try these examples:
Ex. #7) 8.08 x 10-5 - 2.07 x 10-6 =
Ex. #8) 3.7 x 102 x 5.1 x 103 =
Ex. #9)
2.3 x 10-3

-7
4.6 x 10
5000 or 5 x 103
7.87 x 10-5
1,887,000 or
1.887 x 106
Origin of the Metric System


During the18th century
scientists measured the
distance from the earth’s
equator to the North
Pole and divided it into
ten million parts.
This number is equal to
exactly 1 meter.
The Meter



The standard for the meter is kept in a safe in
France.
The meter stick is a replica of that standard.
A meter is made up of 100 centimeters and
1000 millimeters.
Demo Volunteers!
The Liter
=




The liter is 1000 mL
10cm x 10cm x 10cm
1 liter = 1000 cm3 = 1 dm3
1 milliliter = 1 cm3 = 1 cc = 20 drops
The Gram



Mass is the amount of
matter in an object.
1 cm3 of water = 1 gram.
The standard kilogram is
kept under lock and key
at the Bureau of
International Weights and
Measures in Sevres,
France.
The Time standard

During the 15th
century a
scientist named
Galileo set the
standard of
time known as
the second.

Why do we need standards????
Mars Climate Orbiter
Mistake


In December 1998 two
different groups of scientists
were working on calculations
to land a probe on Mars.
The American team did their
calculations in the English
system and the other team
did their calculations in the
metric system – the $125
million probe crashed onto
Mars in September 1999.
Medication Dose Errors


In 2004, doctors prescribed 0.75
mL of Zantac Syrup twice a day
to a baby, but the pharmacist
labeled the bottle, “Give 3/4
teaspoonful twice a day.”
A teaspoon is about 4.9 mL…
The mistake was 5 times the
correct dose!
Length Relationships
IV. Metric System: (1.2)
A. International System of
Measurements (SI): standard
system used by all scientists. It
is based upon multiples of 10.
Measurement
Unit
Instrument
Equation
Derived Unit
Mass
gram
triple beam balance
------------
---------------
length
Meter
meterstick
------------
---------------
time
second
watch
------------
---------------
Temperature
Kelvin/
celcius
thermometer
------------
---------------
Quantity
mole
-----------------------
------------
---------------
Area
m2/cm2
meterstick
LxW
cm2
Volume
m3/cm3
Graduated cylinder
LxWxH
L
Density
g/cm3
----------------------
D = M/V
g/cm3
Pressure
Atm/kPa
barometer
Force/area
N/m2
Energy
Cal or J
Calorimeter
----------------
Cal/Joules
Prefix
Abbreviation
Meaning
Scientific Notation
Giga
G
1,000,000,000
1 x 109
Mega-
M
1,000,000
1 x 106
kilo-
k
1,000
1 x 103
hecto-
h
100
1 x 102
deka-
da or dk
10
1 x 10
BASE UNIT
meter/liter/gram
1
1
deci-
d
0.1
1 x 10-1
centi-
c
0.01
1 x 10-2
milli-
m
0.001
1 x 10-3
micro-
µ
0.000 001
1 x 10-6
nano-
n
0.000 000 001
1 x 10-9
pico-
p
0.000 000 000 001
1 x 10-12
D. Metric Conversions using the
Factor-Label Method (Dimensional Analysis)
Ex. #1) Convert $72 to quarters:
 4 quarters 
72 dollars 

 1 dollar 
Write the given with the units. Then look at the
unit and use a conversion factor that relates to
the unit you need.
See page 3 in the notes
V. Uncertainty in Measurement: (2.3)
A. Measurements are uncertain because:
1. Instruments are not free from
error.
2. Measuring always involves some
estimation.
B. Estimating with a scale
1. Estimate 1 digit more than the
instrument measures.
2. “” is used to show uncertainty.
READ the length of the lines:
2.00cm .01cm
2.83cm .01cm
Smallest graduations on the
ruler are 0.1cm therefore you
should measure to 0.01cm!
C. Precision: When the instrument gives you about the
same results under similar conditions.
D. Accuracy: When the experimental value is close to the
true or actual value. The smaller the increments of
measurement an instrument has, the more accurate it
can be.
E. An instrument is precise (numbers repeatable to a
certain number of places) the operator makes it
accurate (close to the right answer by using it
correctly).
Ex. Precise, Accurate, Both or Neither
(Accepted Value = 15g)
1. 200g, 1g, 40g neither
2. 78g, 80.g, 79g precise
3. 16g, 14g, 17g both precise and accurate
What is the goal for a game of darts?
Hitting the Bulls Eye!
Reading a Metric Ruler
Meter
sticks and paperclips!
Rulers
3
4
3.6 cm
5
3.6 cm
3
4
5
3.62 cm
3
4
5
How to use a
graduated cylinder
Read the
meniscus
How to use a graduated cylinder
36.4 mL
19.0 mL
6.25 mL
More Graduated Cylinders
15.2 mL
8.69 mL
17 mL
Because the smallest
increments on the graduated
cylinder are 0.1 mL, you
estimate the .01 place…
The cylinder reads 8.76 mL
130.510 g
Triple Beam Balance
0
100
200
0
10
20
30
40
50
60
70
80
90
100
0
1
2
3
4
5
6
7
8
9
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Reading a Triple Beam Balance
146.440 g
How to read a Triple Beam Balance
28.570 g
Ohaus Triple Beam Balance Tutorial
Reading A Triple Beam Balance Tutorial
How to read a Triple Beam Balance
109.076 g
Ohaus Triple Beam Balance Tutorial
Reading A Triple Beam Balance Tutorial
D. Factors in an Experiment
1.
2.
3.
Independent: most regular variable – goes on the X-axis
Dependent: what you are testing – goes on the Y-axis
Experimental Control: part of the experiment that stays
the same.
Dependent variable
“Y” axis
Independent variable
“X” axis
Drawing a Graph in Chemistry:
•
Label each axis with a name and a unit.
•
Number by regular increments! This
means by 1’s, 2’s, 5’s, 10’s etc.
NOT by 3’s,7’s or 9’s!
•
Unless otherwise noted include zero.
•
Include a title that states what is being
tested…this would include the dependent
variable and any change that occurs for
different trials.
•
Include a key for different trials. This
could be different colors or one in pen
and one in pencil.
•
Write a statement or conclusion on the
graph that states; “This graph shows…”
to explain the results of the experiment.
•
If necessary, extend the graph
(extrapolate) to predict additional data
points with a dashed (-----) line.
Title: How pressure changes
with increased volume.
Statement: This graph
shows that pressure
decreases with increased
volume.
Key:
Trial 1
Trial 2
Graphing: How do you determine the best-fit line
through data points? The line may pass through some,
all or none of the data points.
y-variable
x-variable
Are the data directly or indirectly related, is
the general trend 1st degree (straight line) or
2nd degree (curved)?
Rules for Significant Digits!






Can you think of a map
of the United States?
All nonzero digits are significant.
All zeros between two nonzero digits are significant.
All zeros to the left of an understood decimal point,
but to the right of a nonzero digit are not significant.
All zeros to the left of an expressed decimal point, and
to the right of a nonzero digit are significant.
All zeros to the right of a decimal point, but to the left
of a nonzero digit are not significant.
All zeros to the right of a decimal point and to the
right of a nonzero digit are significant.
Then you can do
significant digits!
VI. Significant Digits
A. Significant Digits include measured digits and
estimated digits.
 Use Atlantic-Pacific Rule – imagine a US map

decimal
decimal
point
point
Pacific
Atlantic
1100
1100.
2 significant digits
4 significant digits
11.010000
8 significant digits
2 significant digits
0.025
0.00035000
1,000,100
Decimal
Present
Start
counting
with the 1st
nonzero
digit and
count all
the rest.
5 significant digits
5 significant digits
Decimal
Absent
Start
counting
with the 1st
nonzero
digit and
count all
the rest.
B. Significant Digits in Addition and Subtraction
1. Add or Subtract numbers.
2. Answer must be based on the number with the
largest uncertainty (look at least places.)
Ex.
951.0 g
1407
g
23.911g
158.18 g +
2540.091g ?
2540.g
tenths place
ones place
thousandths place
hundredths place
Which is the least precise place??? Round your answer to
that place:
B. Multiplication and Division
1.
2.
Multiply or Divide numbers.
Round answer to the same number of significant
digits as number with fewest significant digits.
4
Ex #1)
7.079 cm
0.535 cm
= 13.2 no units!
3
Ex #2) V = L x W x H
V= 3.05 m x 2.10 m x 0.75 m = 4.8 m3
3
3
2
Ex. #3) A = L x W
A= 3200 cm x 2500 cm = ?
 Always write down the answer your calculator
gives you, then round to the correct # of S.D.
 = 8,000,000 cm2
 This only has 1 S.D.
 How many S.D. should the answer have? 2
 If you can’t round, write the number in scientific
notation:
 = 8.0 x 106 cm2

VII. Important Formulas:
A.
Percent Error: Comparing a measurement obtained
experimentally with an accepted value. It is
always expressed as a positive %.
% error =
measured value - accepted value
x 100% =
accepted value
Ex.) If a student calculates the density of
aluminum to be 2.5 g/cm3, and the accepted
value is 2.7g/cm3, what was her % error?
Ex.) If a student calculates the density of aluminum
to be 2.5 g/cm3, and the accepted value is 2.7g/cm3,
what was her % error?
% error =
measured value - accepted value
x 100%
accepted value
2.5 g/cm3 - 2.7 g/cm3

x 100%
3
2.7 g/cm
.2 g/cm3

x 100% = 7.4 = 7%
3
2.7 g/cm
Density is defined as mass per unit volume. It is a measure of
how tightly packed and how heavy the molecules are in an
object. Density is the amount of matter within a certain volume.
Which is less dense???
Units for density
Formula: M = mass
M=DxV
3
g/cm or
g/ml
V= volume D = density
V=M/D
D=M/V
To find density:
1) Find the mass of the object with the triple
beam balance…you may have to subtract
the mass of the container!
2) Find the volume of the object – use a
graduated cylinder for liquids and a
centimeter ruler for regular solids.
3) Divide : Density =
Mass
Volume
What if it’s an irregular shaped solid and not a liquid???
Density of an Irregular solid:
1- Find the mass of the object
2- Find the volume of the
object by water
displacement!
B. (1.2) Density M=VD
V=
M
D
• Ex.) If a metal block has a mass of 75.355 g and a
volume of 22.0 cm3, what is the density?
D=
Mass
Volume
75.355 g
3
D=
=
3.43
g/cm
22.0 cm3
What is the density of
1.0 g/mL
water?
Would the above metal block float or sink in water???
VIII. Dimensional Analysis
(The Factor-Label Method): (1.2)
A. Uses unit equalities to convert between units.
A unit equality is an equation that relates 2 units.

Ex.) 12in = 1ft
60sec = 1min
1kg = 1000g
B. Unit equalities are used to write conversion factors
which are always equal to “1.”

Ex)
1000 m
=1
1 km
or
1 km
=1
1000 m

C. The conversion factor is a definition, and therefore
infinitely precise, so the number of significant
digits in the answer is equal to the number in the given.
These conversion
factors will NOT
be given on the
test. In addition
you need to know
the 6 basic
metric prefixes.
Useful Chemistry
Conversion Factors
1 in. = 2.54 cm
1 ft. = 12 in.
1 mile = 5280 ft.
1 min. = 60 s
1 hr. = 60 min.
1 atm = 760 mm Hg
1 atm = 101,325 Pa
1 cal. = 4.184 J
1 gal. = 3.785 L

Ex. #1) How many seconds are in 22.0 hours?
 60 min  60s 
22.0 hr 

  79,200s
 1 hr  1min 

Ex. #2) How many years are in 3 x 108 seconds?
 1 min  1 hr  1 day   1 year 
3 x 10 sec 
  10 years



 60 sec  60 min  24 hours   365 days 
8

Ex. #3) If there are 9 dibs in 1 sob, 3 sobs in 1 tog, 1 tog in 6 pons, and
12 pons in 1 gob. How many gobs are in 27 dibs?
 1 sob   1 tog   6 pons   1 gob 
27 dibs 
 0.50 gobs





 9 dibs   3 sobs   1 tog   12 pons 
Ex #4) Calculate the number of feet in a
5.00 km race. (1 inch = 2.54 cm)
 1000 m   100 cm   1 inch   1 ft 
5.00 km 



  16,400 ft
 1 km   1 m   2.54 cm   12 in 