Download 3 sig figs

The numerical side of chemistry
Chapter 2
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Outline
•
•
•
•
•
•
Precision and Accuracy
Uncertainty and Significant figures
Zeros and Significant figures
Scientific notation
Units of measure
Conversion factors and Algebraic
manipulations
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Accuracy and Precision
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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.
Neither
accurate nor
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Precise but not
accurate
Precise AND
accurate
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Types of Error
•
Random Error (Indeterminate Error) measurement has an equal probability of being
high or low.
Systematic Error (Determinate Error) - Occurs
in the same direction each time (high or low),
often resulting from poor technique or incorrect
calibration. This can result in measurements that
are precise, but not accurate.
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Uncertainty in Measurement
•
A digit that must be estimated is called
uncertain. A measurement always has some
degree of uncertainty.
 Measurements are performed with
instruments
 No instrument can read to an infinite
number of decimal places
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Nature of Measurement
Measurement - quantitative observation
consisting of 2 parts
•
Part 1 - number
Part 2 - scale (unit)
Examples:
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20 grams
34.5 mL
45.0 m
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Significant figures or significant digits
• Digits that are not beyond accuracy of
measuring device
• The certain digits and the estimated
digit of a measurement
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Rules
•
•
•
•
•
•
•
245
0.04
0.040
1000
10.00
0.0301
103
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•
•
•
•
•
•
•
3
1
2
1
4
3
3
significant
significant
significant
significant
significant
significant
significant
digits
digit
digits
digit
digit
digit
digit
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Rules for Counting Significant
Figures - Details
•
Nonzero integers always count as
significant figures.
3456 has
4 sig figs.
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Rules for Counting Significant
Figures - Details
•
Zeros
- Leading zeros do not count as
significant figures.
– 0.0486 has
3 sig figs.
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Rules for Counting Significant
Figures - Details
•
Zeros
Captive zeros always count as
significant figures.
– 16.07 has
4 sig figs.
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Rules for Counting Significant
Figures - Details
•
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 Counting Significant
Figures - Details
•
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?
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1.0070 m 
5 sig figs
17.10 kg 
4 sig figs
100,890 L 
5 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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Rules for Significant Figures in
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 #2
Calculation
Calculator says:
Answer
3.24 m + 7.0 m
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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Rules for Significant Figures in
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 #3
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
100.0 g ÷ 23.7 cm3
4.219409283 g/cm3 4.22 g/cm3
23 m2
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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Why do we use scientific notation?
• To express very small and very large
numbers
• To indicate the precision of the number
• Use it to avoid
with sig digs
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Scientific Notation
In science, we deal with some very
LARGE numbers:
1 mole = 602000000000000000000000
In science, we deal with some very
SMALL numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
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.
2 500 000 000
9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
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2.5 x
9
10
The exponent is the
number of places we
moved the decimal.
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0.0000579
1 2 3 4 5
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
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5.79 x
-5
10
The exponent is negative
because the number we
started with was less
than 1.
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Review:
Scientific notation expresses a
number in the form:
M x
1  M  10
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n
10
n is an
integer
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SI measurement
• Le Système international
d'unités
• The only countries that
have not officially adopted
SI are Liberia (in western
Africa) and Myanmar
(a.k.a. Burma, in SE Asia),
but now these are
reportedly using metric
regularly
• Metrication is a process
that does not happen all at
once, but is rather a
process that happens over
time.
• Among countries with nonmetric usage, the U.S. is
the only country
significantly holding out.
The U.S. officially adopted
SI in 1866.
Information from U.S.
Metric Association
The Fundamental SI Units
(le Système International, SI)
Physical Quantity
Mass
Name
kilogram
Abbreviation
kg
Length
meter
m
Time
second
s
Temperature
Kelvin
K
Electric Current
Ampere
A
mole
mol
candela
cd
Amount of Substance
Luminous Intensity
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Standards of Measurement
When we measure, we use a measuring
tool to compare some dimension of an
object to a standard.
For example, at one time the standard
for length was the king’s foot. What
are some problems with this
standard?
Derived SI units
Physical quantity
Name
Volume
cubic meter
Pressure
pascal
Energy
joule
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Abbreviation
m3
Pa
J
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Metric System
• System used in science
• Decimal system
• Measurements are related by factors of
10
• Has one standard unit for each type of
measurement
• Prefixes are attached in front of
standard unit
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Metric Prefixes
• Kilo- means 1000 of that unit
– 1 kilometer (km) = 1000 meters (m)
• Centi- means 1/100 of that unit
– 1 meter (m) = 100 centimeters (cm)
– 1 dollar = 100 cents
• Milli- means 1/1000 of that unit
– 1 Liter (L) = 1000 milliliters (mL)
SI Prefixes Common to Chemistry
Prefix
Mega
Kilo
Deci
Centi
Milli
Micro
Nano
Pico
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Unit Abbr.
M
k
d
c
m

n
p
Exponent
106
103
10-1
10-2
10-3
10-6
10-9
10-12
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Metric Prefixes
Metric Prefixes
Conversion Factors
Fractions in which the numerator and denominator
are EQUAL quantities expressed in different units
Example:
1 in. = 2.54 cm
Factors: 1 in.
2.54 cm
and
2.54 cm
1 in.
Learning Check
Write conversion factors that relate each of
the following pairs of units:
1. Liters and mL
2. Hours and minutes
3. Meters and kilometers
How many minutes are in 2.5 hours?
Conversion factor
2.5 hr x
60 min
1 hr
= 150 min
cancel
By using dimensional analysis / factor-label method, the UNITS
ensure that you have the conversion right side up, and the UNITS
are calculated as well as the numbers!
Steps to Problem Solving
1. Write down the given amount. Don’t forget the units!
2. Multiply by a fraction.
3. Use the fraction as a conversion factor. Determine if the
top or the bottom should be the same unit as the given
so that it will cancel.
4. Put a unit on the opposite side that will be the new unit.
If you don’t know a conversion between those units
directly, use one that you do know that is a step toward
the one you want at the end.
5. Insert the numbers on the conversion so that the top and
the bottom amounts are EQUAL, but in different units.
6. Multiply and divide the units (Cancel).
7. If the units are not the ones you want for your answer,
make more conversions until you reach that point.
8. Multiply and divide the numbers. Don’t forget “Please
Excuse My Dear Aunt Sally”! (order of operations)
Learning Check
A rattlesnake is 2.44 m long. How long
is the snake in cm?
a) 2440 cm
b) 244 cm
c) 24.4 cm
Solution
A rattlesnake is 2.44 m long. How long
is the snake in cm?
b) 244 cm
2.44 m x 100 cm
1m
= 244 cm
Learning Check
How many seconds are in 1.4 days?
Unit plan: days
seconds
hr
1.4 days x 24 hr
1 day
x
min
??
Wait a minute!
What is wrong with the following setup?
1.4 day x 1 day
24 hr
x
60 min
1 hr
x 60 sec
1 min
Dealing with Two Units
If your pace on a treadmill is 65 meters per
minute, how many seconds will it take for
you to walk a distance of 8450 feet?
What about Square and Cubic units?
• Use the conversion factors you already
know, but when you square or cube the
unit, don’t forget to cube the number
also!
• Best way: Square or cube the ENITRE
conversion factor
• Example: Convert 4.3 cm3 to mm3
4.3 cm3 10 mm
(
1 cm
3
)
=
4.3 cm3 103 mm3
13 cm3
= 4300 mm3
Learning Check
• A Nalgene water
bottle holds 1000
cm3 of dihydrogen
monoxide (DHMO).
How many cubic
decimeters is that?
Solution
1000 cm3
(
1 dm 3
10 cm
)
= 1 dm3
So, a dm3 is the same as a Liter !
A cm3 is the same as a milliliter.
Temperature Scales
• Fahrenheit
• Celsius
• Kelvin
Anders Celsius
1701-1744
Lord Kelvin
(William Thomson)
1824-1907
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Temperature Scales
Boiling point of
water
Freezing point
of water
Fahrenheit
Celsius
Kelvin
212 ˚F
100 ˚C
373 K
180˚F
100˚C
32 ˚F
0 ˚C
Notice that 1 Kelvin = 1 degree Celsius
100 K
273 K
Calculations Using
Temperature
• Generally require temp’s in kelvins
• T (K) = t (˚C) + 273.15
• Body temp = 37 ˚C + 273 = 310 K
• Liquid nitrogen = -196 ˚C + 273 = 77 K
Fahrenheit Formula –
180°F
5°C
=
9°F
1°C
Zero point:
=
1.8°F
0°C = 32°F
°F
= 9/5 °C + 32
100°C
Celsius Formula –
Rearrange to find T°C
°F
=
°F - 32
°F - 32
9/5 °C + 32
=
=
9/5 °C ( +32 - 32)
9/5 °C
9/5
(°F - 32) * 5/9
9/5
= °C
Temperature Conversions –
A person with hypothermia has a body temperature of
29.1°C. What is the body temperature in °F?
°F
=
9/5 (29.1°C)
+ 32
=
52.4 + 32
=
84.4°F
Temperature measurements
Kelvin temperature scale is also called
absolute temperature scale
There is not negative Kelvin temperature
K=0C + 273.15
0F
= 32 + 9/5 0C
0C
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= 5/9 (0F –32)
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What is temperature?
• Measure of how hot or cold an object is
• Determines the direction of heat
transfer
• Heat moves from object with higher
temperature to object with lower
temperature
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Learning Check –
Pizza is baked at 455°F. What is that in °C?
1) 437 °C
2) 235°C
3) 221°C
Density: m/v
• Density tells you how much matter
there is in a given volume.
• Usually expressed in g/ml or g/cm3
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Densities of some common materials
Material
Density
g/cm3
Material
Density
g/L
Gold
Mercury
19.3
13.6
Chlorine
CO2
2.95
1.83
Lead
11.4
Ar
aluminum
2.70
Oxygen
Sugar
1.59
Air
Water
1.000
Nitrogen
Gasoline 0.66-0.69 Helium
Ethanol
0.789
Hydrogen
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1.66
1.33
1.20
1.17
0.166
.0084
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Intensive and Extensive properties
• Intensive properties do not depend on
amount of matter (density, boiling
point, melting point)
• Extensive properties do depend on
amount of matter(mass , volume,
energy content).
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Energy
• Capacity to do work
• Work causes an object to move (F x d)
• Potential Energy: Energy due to
position
• Kinetic Energy: Energy due to the
motion of the object
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The Joule
The unit of heat used in modern thermochemistry
is the Joule
1 kg  m
1 joule 1 newton  meter 
2
s
2
Non SI unit calorie
1Cal=1000cal
4.184J =1cal or 4.184kJ=Cal
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Law of conservation of energy
• Energy is neither created nor
destroyed; it only changes form
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Calorimetry
The amount of heat absorbed or released
during a physical or chemical change can be
measured…
…usually by the change in temperature of a
known quantity of water
1 calorie is the heat required to raise the
temperature of 1 gram of water by 1 C
1 BTU is the heat required to raise the
temperature of 1 pound of water by 1 F
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Calorimeter
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A Cheaper
Calorimeter
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Specific heat
• Amount of heat energy needed to warm
1 g of that substance by 1oC
• Units are J/goC or cal/goC
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Specific Heat Notes
• Specific heat – how well a substance
resist changing its temperature when it
absorbs or releases heat
• Water has high s – results in coastal
areas having milder climate than inland
areas (coastal water temp. is quite
stable which is favorable for marine
life).
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More Specific Heat
• Organisms are primarily water – thus
are able to resist more changes in their
own temperature than if they were
made of a liquid with a lower s
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Specific heats of some common
substances
Substance
Water
Iron
Aluminum
Ethanol
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(cal/g° C)
• 1.000
• 0.107
• 0.215
• 0.581
(J/g ° C)
4.184
0.449
0.901
2.43
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Calculations Involving Specific Heat
q  s  m  T
OR
q
s
m  T
s = Specific Heat Capacity
q = Heat lost or gained
T = Temperature change
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Principle of Heat Exchange
• The amount of heat lost by a substance
is equal to the amount of heat gained
by the substance to which it is
transferred.
• m x ∆t x s = m x ∆t x s
heat lost
heat gained
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How to calculate amount of heat ?
H= specific heat x mass x change in T
Example
Calculate the energy required to raise the temperature
of a 387.0g bar of iron metal from 25oC to 40oC. The
specific heat of iron is 0.449 J/goC
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