Transcript Significant figures

CH110
Foundations of
GENERAL, ORGANIC,
& BIOCHEMISTRY
CHEMEKETA COMMUNITY COLLEGE
INSTRUCTOR: Larry Emme
1
1st Day Stuff
Who are you? Are you in the right place?
GOB
CTV Introduction
Privacy waver
Course Syllabus & requirements
Who am I?
2
Prologue
P.2
Scientific Method:
Thinking like a Scientist
3
Scientific Method
The scientific method
is the process used
by scientists to explain
observations in nature.
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Scientific Method
The scientific method involves
Making Observations
Writing a Hypothesis
Doing Experiments
Proposing a Theory
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Features of the Scientific Method
Observations
Facts obtained by observing and measuring events in nature.
Hypothesis
A statement that explains the observations.
Experiments
Procedures that test the hypothesis.
Theory
A model that describes how the observations occur using
experimental results.
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Summary of the Scientific Method
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Major divisions of Chemistry
 General
 Inorganic
Elements besides Carbon
 Analytical
Methods of analysis
 Physical
Theory and concepts
Organic
Carbon based compounds
 Biochemistry
Chemistry of living things
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Chapter 1:
Measurement
Units of Measurement
Significant Figures
Conversion Calculations
Density
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Measurements in chemistry
See Handout Sheet of
Units of Measurements
10
Units of Measurement
Metric
SI
Common
Conversions
Length
meter (m)
1 m = 1.09 yd
Volume
Mass
liter (L)
1 L = 1.06 qt
gram (g)
1 kg = 2.2 lb
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Matter
=The stuff things are made of.
(Air, water, rocks, etc..)
Matter has Mass and takes up space.
=The amount of stuff (in g’s)
(Bowling Ball > Balloon)
Weight on earth.
=Pull of Gravity on matter.
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Mass Vs. Weight
How much would you weigh
on another planet?
http://www.exploratorium.edu/ronh/weight/
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Scientific notation
If a number is larger than 1
• Move decimal point X places left to get a
number between 1 and 10.
1 2 3 , 0 0 0 , 0 0 0.
=
1.23 x 108
•The resulting number is multiplied by 10X.
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Scientific notation
If a number is smaller than 1
• Move decimal point X places right to get
a number between 1 and 10.
0. 0 0 0 0 0 0 1 2 3
=
1.23 x 10-7
•The resulting number is multiplied by 10-X.
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Examples
Write in Scientific Notation:
25 =
8931.5 =
0.000593 =
0.0000004 =
3,210. =
2.5  10 1
8.9315  10 3
5.93  10 - 4
4  10 - 7
3.210  103
Do not press this on your calculator!
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Scientific notation
1.44939 × 10-2 =
0.0144939
1.44939E -2
On Calculator
1.44939 EE (-) 2
Means
×10
×10
Change
Sign
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Measured & Exact Numbers
Exact Numbers =
from counting or by definition
12 coins per package
12 coins
1 package
=
1 package
12 coins
12 coins
1 dozen coins
=
1 dozen coins
12 coins
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Measured & Exact Numbers
Measured Numbers =
estimated using a tool
All measurements contain some uncertainty.
• We make errors
• Tools have limits
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Accuracy
How close are we
to the true value?
Truth
Precision
How well do our
values agree?
Consistency
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Significant figures
Length of object is between 6.7 and 6.8
The next digit would be a guess.
If use 6.76 then have error of + 0.01cm
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Significant figures
Expresses accuracy & precision.
You can’t report numbers better than the
method used to measure them.
6.76 units = 3 sig figures
Certain
Digits
Uncertain
Digit
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Significant figures
Sig Figs don’t depend on the decimal point.
255 millimeters
25.5 centimeters
2.55 decimeters
0.255 meters
0.0255 decameters
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Significant figures: Rules for zeros
Leading zeros are not significant.
Leading zero
0.00421
3 sig figs
Captive zeros are significant.
4012
4 sig figs
Captive zero
Trailing zeros behind decimal are significant.
114.20
5 sig figs
Trailing zero
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Significant figures: Rules for zeros
32,000
Are the 0’s significant?
2 sig figs =
32,000 or 3.2
_
3 sig figs =
x 104
32000 or 3.20 x 104
_
4 sig figs =
5 sig figs =
32000 or 3.200 x 104
_
32000 or 3.2000 x 104
32000.
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Significant figures: Rules for zeros
1025 km
Four (Captive zeros are significant)
2.00 mg
Three (trailing zeros behind decimal
are significant)
0.00570
Three (only trailing zero behind decimal
is significant, leading zeros are not)
520
Two (No decimal, zero assumed insignif)
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Rounding
Write with 4 Significant Figures:
2.5795035
becomes 2.580
> 5 round up
1st insignificant digit
34.204221
< 5 round down.
becomes 34.20
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Significant figures
and calculations
An answer can’t have greater significance
than the quantities used to produce it.
Example
How fast did you run if you 0.3333333333
went 1.0 km in 3.00 minutes?
cos tan
speed = 1.0 km
3.00 min
=?
CE
ln
7
8
9
/
log
4
5
6
x
1/x
1
2
3
-
x2
EE
0
.
+
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Simplified rules for significant figures
Multiplication & Division Problems:
• Do calculations.
speed = 1.0 km = 0.333333333 km
min
3.00 min
•Look at sig figs for each value in calculation.
(Constants don’t count.)
3 sig figs
2 sig figs
•Report answer with same sig figs as least
significant value.
•Round off as needed. = 0.33 km
min
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Simplified rules for significant figures
Addition & Subtraction Problems:
• Do calculations.
Significant to .1
1.9
+ 18.65
Significant to .01
20.55
•Look at least significant place for each value
in calculation.
•Report answer to least significant place.
•Round off as needed.
= 20.6 Significant to .1
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Metric prefixes
Changing the prefix alters the size of a unit.
Prefix Symbol
Factor (multiple)
mega
M
106
1,000,000
kilo
k
103
1,000
100
1
deci
d
10-1
0.1
centi
c
10-2
0.01
milli
m
10-3
0.001
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Problem Solving Using
Conversion Factors
Many problems require a change of
one unit to another unit by using
conversion factors (fractions).
unit1 × conversion factor = unit2
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How many feet are there in 22.5 inches?
The conversion factor must
unit
factor = unit2
accomplish
two things:
1 × conversion
inches × conversion factor = feet
It must cancel
inches.
It must
introduce feet
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The conversion factor takes a fractional
form.
ft
in 
= ft
in
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Putting in the measured value and the
ratio of feet to inches produces:
1 ft
22.5 in 
= 1.875 ft
12 in
= 1.88 ft
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Convert 3.7×1015 inches to miles.
Inches can be converted to miles by writing
down conversion factors in succession.
in  ft  miles
3.7  10 in
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1 mile
1 ft
10
x
x
= 5.8 10 miles
5280 ft
12 in
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Convert 4.51030 cm to kilometers.
Centimeters can be converted to kilometers by
writing down conversion factors in succession.
cm  m  km
1 km
1m
25
x
4.5  10 cm x
= 4.5  10 km
100 cm 1000 m
30
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Conversion of units
Examples:
10.7 T = ? fl oz
62.04 mi = ? in
5 kg = ? mg
9.3 ft = ? cm
5.7 g/ml = ? lbs/qt
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Density =
Density
Mass
Volume
1cc = 1 cm3 = 1 ml = 1 g water
g
cm3 or
Water 1.0
Air
0.0013
Gold 19.3
g
ml
Urine
Bone
Oil
o
At 4 C
1.01 - 1.03
1.7 - 2.0
0.8 - 0.9
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Density calculation
What is the density of 5.00 ml of
serum if it has a mass of 5.230 g?
d =m
V
V =m
d
d = 5.230 g
5.00 ml
m=Vd
= 1.05 g
ml
40
Specific gravity
density of substance g
Specific Gravity =
ml
density of reference g
ml
Reference
commonly
water at
4oC
•Specific Gravity is unitless.
•At 4oC, density = specific gravity.
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Specific gravity
Hydrometer
•Commonly used to test
sugar in urine.
•Float height will be
based on Specific
Gravity.
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Density as a Conversion
A liquid sample with a density of 1.09 g/mL is
found to weigh 7.453 grams. What is the
volume of the liquid in mLs?
• Identify any conversion factors.
• What is unique to the problem?
7.453 g 1.0 ml = 6.837614 ml = 6.84 ml
1.09 g
•How should the answer look?
1.09 g
1 ml
1 ml
1.09 g
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