Transcript measured numbers

Physical Chemistry
Environmental Chemistry
CHEMISTRY
Nanotechnology
Organic Chemistry
Biochemistry
Chemical
Engineering
Inorganic Chemistry
Measurement
• Metric system (National Assembly of France, 1790)
• International System of Units (SI, 1960)
Derived units: combinations of fundamental units
Ex. Speed (m/s)
3
Equipment for Measurement
Length
Volume
Mass
Temp
Time
4
Scientific Notation
Width of a human hair = 0.000008 m
Coefficient
Coefficient? 8
Power of Ten: 10x
Power?
10-6
8 x 10-6 m
5
Scientific Notation
• How many atoms of water are in a Lake
Washington?
97,000,000,000,000,000,000,000,
000,000,000,000,000 atoms
-or-
9.7 x 1037 atoms
6
Scientific Notation on Calculators
Your calculator should work with scientific notation!
Look for:
EE
EXP
Note:
9.64 x 105 = 9.65 E5
Coefficient
Power of Ten
2. x 10-8 = 2.E-8
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Scientific Notation
Conversion to a standard number
3.252 x 106
3252000
4.56 x 10-3
0.00456
If power of ten is positive,
move decimal point to the RIGHT
(add zeros if necessary)
If power of ten is negative,
move decimal point to the LEFT
(add zeros if necessary)
8
Measured Numbers
– Numbers obtained when you measure a quantity
– Estimate the final digit
1
2
3
4
5
6
4.8 in
Read greater than 4 and less than 5; estimate last digit
1
2
3
4
5
6
4.84 in
Read greater than 4.8 and less than 4.9; estimate last digit
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Significant Figures
• All measured digits, including the estimated digit
4.84 cm
2045 g
2.333 x 10-5 L
50. s
• Zeros not significant in 2 situations:
– At the beginning of a decimal number
– At the end of a number without decimal point
4500 cm
0.0063 kg
0.05202 L
10
Exact Numbers
• A counted number (not measured!)
– Ex. # of students in this classroom
• A definition comparing two units in same
measurement system
– Ex. 1 ft = 12 in
– Ex. 1 kg = 1000 g
NOT considered as significant figures!
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Significant Figures in Calculations
• In lab, at work, we measure things. Then what?
• The number of sig figs in measured numbers limits
the number of sig figs in a calculated answer.
You can’t have more detail in your answer than
you have in your measurements
Number of sig figs in answer depends on what type of
calculations you performed
12
Sig Figs in Calculations
• Multiplication and Division:
– Final answer has the same number of sig figs as the
measurement with the fewest significant figures
• Addition and Subtraction:
– Final answer has the same number of decimal places
as the measurement with the fewest decimal places
24.64 x 3.2 = 78.848
3.525 - 5.2 = -1.675
3.525 + 6.475 = 10
79.
-1.7
10.000
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Rounding Rules
How do we limit the number of sig figs? Rounding!
Look at first non-significant number (to be dropped)
Is this number 4 or less?
Is this number 5 or more?
2390.321
to 4 sig figs
0.0056194 to 2 sig fig
688511 to 3 sig figs
Round “down”
Round “up”
2390.
0.0056
689000
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Prefixes
Is it easier to write:
• 590000 g or 590 kg?
• 0.0004 g or 0.4 mg?
Prefixes can be attached to units to increase
or decrease size by a factor of 10
(multiply by 10 or divide by 10)
Multiply by 10x
Multiply by 10-x
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Common Prefixes with SI Units
Equalities used in Measurements
Equality:
A relationship between two units that measure
the same quantity
• Length:
1 m = 100 cm = 1000 mm
Cubic centimeter: cc
• Volume:
1 L = 10 dL = 1000 mL
1 dL = 100 mL
1 cm x 1 cm x 1 cm = 1 cm3
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Volume Conversions
If 1 cubic centimeter equals 1 mL,
how many milliliters does 1 cubic meter equal?
1 m = 100 cm
100 cm x 100 cm x 100 cm = 1000000 cm3
1000000 cm3 = 1000000 mL
1 x 106 mL
1 x 103 L
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Conversion Factors:
Changing Between Units
1 hr = 60 min
Conversion Factor:
1 hr
60 min
1 hr
1
1 hr
Metric Conversion Factor:
1m
100 cm
60 min
1 hr
60 min
1
60 min
100 cm
1m
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More Conversion Factors
Metric Conversion Factors:
1 mL
1 cm 3
1 cm3
1 mL
1L
1000 mL
1000 mL
1L
Metric- U.S. System Conversion Factors:
1 kg = 2.20 lb
1 km = 0.621 mi
1 kg
2.20 lb
2.20 lb
1 kg
1 km
0.621 mi
0.621 mi
1 km
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More Conversion Factors
• Standard equalities can be looked up in a table
(Table 1.9 in your book, for example)
• Other equalities may be stated in a problem
Examples:
• The average speed of cars driving on I-5 during rush
hour is 11 mph.
Equality: 11 miles = 1 hour
11 mi
1h
• One five pound bag of sugar costs $4.00.
Equality: 1 bag = 5 lb = $4.00
1h
11 mi
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Percents as Conversion Factors
• Percent means 1 per 100
Example:
• If a person is 20% body fat by mass, then:
20 kg fat = 100 kg body total
20 kg fat
100 kg body
100 kg body
20 kg fat
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End of class Practice Questions
• How many sig figs are in each the following?
 0.00500 L
 53,069 s
 0.00004715 m
 0.509 kg
• Write the numbers above in scientific notation.
– How many sig figs does each have now?
• Write a conversion factor relating micrograms to grams
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Practice Questions
What is the temperature on
each (˚C) thermometer
shown? (sig figs!)
4.9 ˚C
61.5 ˚C
Is each of the following an exact or measured number?
•
•
•
•
The
The
The
The
number of chair legs in this room Exact
length of your benchtop in inches Measured
length of your benchtop in cm Measured
area of the projector screen
Measured
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Using Conversion Factors
Your patient tells you that she recently lost 15 kg.
How many pounds has she lost?
1.
What’s given?
What do we want to know?
weight lost (kg)= 15 kg
weight lost (lb)= ? lb
2. What conversion factors do I need? kg  lb
2.20 lb = 1 kg
3. Set up problem
1 kg
2.20 lb
2.20 lb
1 kg
Given  conversion factor(s)
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Using Conversion Factors
kg  lb
3. Set up problem
Given  conversion factor(s)
15 kg
x
1 kg
2.20 lb
2.20 lb
1 kg
?
1 kg
15 kg 
2.20 lb
kg  kg
 6.81818
lb
2.20 lb
15 kg 
1 kg
lb  kg
 33
kg
 33 lb
Check
sig figs!
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Using Conversion Factors
The recommended daily value of vitamin C is 60 mg.
If an average orange contains 45 mg of vitamin C,
how many oranges should you eat in a week?
1.
What’s given?
What do we want to know?
1 week
# of oranges
2. What conversion factors do I need?
week 
1 week
7 days
days

60 mg
1 day
mg vitamin C
 # oranges
45 mg vitamin C
1 orange
1 week  7 days  60 mg  1 orange  9.33333 oranges
1 week
45 mg
1 day
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 9 oranges
Physical Properties of Materials
• Physical Property:
– can be measured or perceived without changing
the material’s identity
– Intensive
• Independent of amount of substance
• Ex. Boiling point
– Extensive
• Depends on amount of substance
• Ex. Mass, volume
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Density
• Relationship between mass and volume
mass
m
density 

volume
V
• Density is a physical property
• Density is an intensive property
4 times more mass
4 times more volume
4 m
m

4 V
V
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Density
• Units:
– SI: kg/m3
– often use:
g/L
g/mL
g/cm3
g/cc
• Density of water (at 20˚C and typical room pressure)
1 g/cc
1 g/mL
30
Density of Solids
• How can we determine the density of a solid?
– Need to know mass
– Need to know volume
mass
density 
volume
Measure displacement
of water
Does this method work
for all solid materials?
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Density Table
Density can be used as a conversion factor!
(relates mass to volume)
32
Specific Gravity (sp gr)
Ratio between density of substance & density of water
density of sample
specific gravity 
density of water
Measure sp gr with a hydrometer
Units for sp gr?
density of sample 1.2 g ml

sp gr 
1.1 g ml
density of water
Unitless!
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Temperature
• Measure of how hot or cold a substance is relative
to another substance
• Scales and Units
Scale
Celsius
˚C
Fahrenheit
˚F
Kelvin
K
Boiling Point H2O Freezing Point H2O
100˚C
0˚C
212˚F
32˚F
373.15 K
Note: the unit is not ˚K
273.15 K
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Temperature Conversions
How many units are between boiling point and
freezing point of water?
Scale
Celsius
˚C
Fahrenheit
˚F
Kelvin
K
100˚C – 0˚C
= 100 units
212˚F – 32˚F = 180 units
373 K –273 K
= 100 units
the unit 1 Kelvin equals the unit 1 degree Celsius
TK  TC  273
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Converting Units Fahrenheit to Units Celsius
180 Fahrenheit degrees = 100 Celsius degrees
180 Fahrenheit degrees
100 Celsius degrees
1 .8 o F
 o
1 C
1.8 o F  TC 
o
TF 

32
1 oC
TF  1.8(TC )  32 o
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Things to Remember about the
Temperature Scales
1. 0 K is absolute zero
2. You can never (ever ever ever) have a temperature
of negative K
3. The unit for the Celsius scale is the degree C (˚C)
4. The unit for the Fahrenheit scale is the degree F (˚F)
5. The units for the Kelvin scale is the Kelvin (K)
6. A change of x Kelvin = a change of x ˚C
350 K - 300 K
350 o C - 300 o C
Start value and end values are different;
Both changed the same amount (50 K units = 50 ˚C units)
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Precision and Accuracy
• Precision: reproducibility
• Accuracy: how close to actual value
Temp
(˚C)
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