Transcript Chapter 02_post

Chemistry 103
Chapter 2
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General Course structure
Learning Tools
Atoms ---> Compounds ---> Chemical Reactions
Chapter 2 – Slide 2
Outline
• Mathematics of Chemistry (Measurements)
–
–
–
–
–
–
Units
Significant Figures (Sig Figs)
Calculations & Sig Figs
Scientific Notation
Dimensional Analysis
Density
Chapter 2 – Slide 3
• Importance of Units
• Job Offer: Annual Salary = 1,000,000.
Chapter 2 – Slide 4
Measurements
Two components –
Numerical component
and
Dimensional component
Chapter 2 – Slide 5
Everyday Measurements
You make a measurement every time you
• Measure your height.
• Read your watch.
• Take your temperature.
• Weigh a cantaloupe.
Chapter 2 – Slide 6
Units and Measurements
• Scientists make many kinds of measurements
– The determination of the dimensions, capacity, quantity or extent
of something
– Length, Mass, Volume, Density
• All measurements are made relative to a standard
• All measurements have uncertainty
Chapter 2 – Slide 7
Systems of Measurement
• English System
– Common measurements
– Pints, quarts, gallons, miles, etc.
• Metric System
– Units in the metric system consist of a base unit
plus a prefix.
Chapter 2 – Slide 8
Measurement in Chemistry
In chemistry we
•
•
•
•
Measure quantities.
Do experiments.
Calculate results.
Use numbers to report
measurements.
• Compare results to
standards.
Copyright © 2008 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Chapter 2 – Slide 9
Length Measurement
Length
• Is measured using a
meter stick.
• Has the unit of meter
(m) in the metric (SI)
system.
Copyright © 2008 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Chapter 2 – Slide 10
Inches and Centimeters
The unit of an inch is
equal to exactly 2.54
centimeters in the
metric system.
1 in. = 2.54 cm
Copyright © 2008 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Chapter 2 – Slide 11
Volume Measurement
Volume
• Is the space occupied by
a substance.
• Has the unit liter (L) in
metric system.
1 L = 1.057 qt
• Uses the unit m3(cubic
meter) in the SI system.
• Is measured using a
graduated cylinder.
Copyright © 2008 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Chapter 2 – Slide 12
Mass Measurement
The mass of an object
• Is the quantity of material
it contains.
• Is measured on a balance.
• Has the unit gram(g) in
the metric system.
• Has the unit kilogram(kg)
in the SI system.
Copyright © 2008 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Chapter 2 – Slide 13
Temperature Measurement
The temperature of a substance
• Indicates how hot or cold it is.
• Is measured on the Celsius
(C) scale in the metric
system.
• On this thermometer
temperature is 18ºC or 64ºF.
• In the SI system uses the
Kelvin (K) scale.
Copyright © 2008 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Chapter 2 – Slide 14
Units in the Metric System
In the metric (SI) system, one unit is used for each
type of measurement:
Measurement
length
volume
mass
time
temperature
Metric
meter (m)
liter (L)
gram (g)
second (s)
Celsius (C)
SI
meter (m)
cubic meter (m3)
kilogram (kg)
second (s)
Kelvin (K)
Chapter 2 – Slide 15
Metric Base Units
Chapter 2 – Slide 16
Learning Check
For each of the following, indicate whether the
unit describes A) length, B) mass, or C) volume.
Chapter 2 – Slide 17
Learning Check
Identify the measurement with an SI unit.
1. John’s height is
2. The race was won in
3. The mass of a lemon is
4. The temperature is
Chapter 2 – Slide 18
Measured vs Exact numbers
Chapter 2 – Slide 19
Exact (Defined) and
Inexact (Measured) Numbers
• Exact numbers
– Have no uncertainty associated with them
– They are known exactly because they are defined or counted
– Example: 12 inches = 1 foot
• Measured numbers
– Have some uncertainty associated with them
– Example: all measurements
Chapter 2 – Slide 20
Accuracy vs. Precision
Accuracy
How closely a
measurement comes to
the true, accepted
value
Precision
How closely
measurements of the
same quantities come
to each other
Chapter 2 – Slide 21
Significant Figures
Chapter 2 – Slide 22
Significant Figures
Digits in any measurement are known with certainty,
plus one digit that is uncertain.
Measured numbers convey
*Magnitude
*Uncertainty
*Units
Chapter 2 – Slide 23
The Calculator Problem
7.8
3.8
Calculator Answer: 2.05263……
Is this a realistic answer?
Is it 2, 2.0, 2.1, 2.05, 2.06, 2.052,
2.053, 2.0526, etc.? Which is it?
Answer must reflect uncertainty
expressed in original measurements.
Using Significant Figures.
We will come back to this later.
Chapter 2 – Slide 24
Rules for Significant Figures
It’s ALL about the ZEROs
Chapter 2 – Slide 25
Rules for Sig Figs
• All non-zero numbers in a measurement
are significant.
4573
4573 has 4 sig figs
Chapter 2 – Slide 26
Rules for Sig Figs
• All zeros between sig figs are significant.
23007
23007 has 5 sig figs
Chapter 2 – Slide 27
Rules for Sig Figs
• In a number less than 1, zeros used to fix the
position of the decimal are not significant.
0.00021
0.00021 has 2 sig figs
Chapter 2 – Slide 28
Rules for Sig Figs
• When a number has a decimal point, zeros to
the right of the last nonzero digit are
significant
0.0002100
0.0002100 has 4 sig figs
Chapter 2 – Slide 29
Rules for Sig Figs
• When a number without a decimal point
explicitly shown ends in one or more zeros,
we consider these zeros not to be significant.
If some of the zeros are significant, bar
notation is used.
_
820000 meters - 3 sig figs 820000
Chapter 2 – Slide 30
Practice Identifying Sig Figs
Chapter 2 – Slide 31
Significant Figures
How many assuming all numbers are measured?
a). 75924
b). 30.002
c). 0.004320
d). 0.000002
e). 46,000
Chapter 2 – Slide 32
Measured Numbers
A measuring tool
• Is used to determine a
quantity such as height
or the mass of an object.
• Provides numbers for a
measurement called
measured numbers.
Copyright © 2008 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Chapter 2 – Slide 33
Reading a Meter Stick
. l2. . . . l . . . . l3 . . . . l . . . . l4. . cm
• The markings on the meter stick at the
end of the orange line are read as
The first digit
2
plus the second digit 2.7
• The last digit is obtained by estimating.
• The end of the line might be estimated
between 2.7–2.8 as about half-way (0.5)
which gives a reported length of 2.75 cm
Chapter 2 – Slide 34
Known + Estimated Digits
In the length reported as 2.75 cm,
• The digits 2 and 7 are certain (known)
• The final digit 5 was estimated (uncertain)
• All three digits (2.75) are significant including
the estimated digit
Chapter 2 – Slide 35
Learning Check
. l8. . . . l . . . . l9. . . . l . . . . l10. . cm
What is the length of the red line?
1) 9.0 cm
2) 9.03 cm
3) 9.04 cm
Chapter 2 – Slide 36
Solution
. l8. . . . l . . . . l9. . . . l . . . . l10. . cm
The length of the red line could be reported as
2) 9.03 cm
or
3) 9.04 cm
The estimated digit may be slightly different.
Both readings are acceptable.
Chapter 2 – Slide 37
Zero as a Measured Number
. l3. . . . l . . . . l4. . . . l . . . . l5. . cm
• For this measurement, the first and second known
digits are 4.5.
• Because the line ends on a mark, the estimated digit
in the hundredths place is 0.
• This measurement is reported as 4.50 cm.
Chapter 2 – Slide 38
Significant Figures
in Measured Numbers
Significant figures
• Obtained from a measurement include
all of the known digits plus the
estimated digit.
• Reported in a measurement depend on
the measuring tool.
Chapter 2 – Slide 39
Rounding off Numbers
• The number of significant figures in
measurements affects any calculations done
with these measurements
– Your calculated answer can only be as certain
as the numbers used in the calculation
Chapter 2 – Slide 40
Calculator: Friend or Foe?
• Sometimes, the calculator will show
more (or fewer) significant digits
than it should
– If the first digit to be deleted is 4 or less,
simply drop it and all the following
digits
– If the first digit to be deleted is 5 or
greater, that digit and all that follow are
dropped and the last retained digit is
increased by one
Chapter 2 – Slide 41
Sig Fig Rounding Example:
• Round the following measured number to
4 sig figs:
• 82.56702
Chapter 2 – Slide 42
Adding Significant Zeros
• Sometimes a calculated answer requires more significant
digits. Then one or more zeros are added.
Calculated Answer
Zeros Added to
Give 3 Significant Figures
4
1.5
0.2
12
Chapter 2 – Slide 43
Practice Rounding Numbers
Chapter 2 – Slide 44
Significant Figures
Round each to 3 sig figs
Chapter 2 – Slide 45
Multiplication and Division
When multiplying or dividing, use
• The same number of significant figures in your final
answer as the measurement with the fewest significant
figures.
• Rounding rules to obtain the correct number of significant
figures.
Example:
110.5
4 SF
x 0.048 = 5.304
2 SF
calculator
= 5.3 (rounded)
2 SF
Chapter 2 – Slide 46
Addition and Subtraction
When adding or subtracting, use
• The same number of decimal places in your final answer as
the measurement with the fewest decimal places.
• Use rounding rules to adjust the number of digits in the
answer.
25.2
+ 1.34
26.54
26.5
one decimal place
two decimal places
calculated answer
answer with one decimal place
Chapter 2 – Slide 47
Math operations with Sig Figs
Chapter 2 – Slide 48
Report Answer with Correct
Number of Sig Figs
A) 124.54 x 2.2 =
273.98800
B) 3420. + 2400. + 1095 = 6915.0000
C) 3420 + 2400 + 1095 = 6915.0000
D) 98.5564 =
45.68
2.1575394
Chapter 2 – Slide 49
When Math Operations Are
Mixed
If you have both addition/subtraction and
multiplication/division in a formula,
-carry out the operations in parenthesis first, and
round according to the rules for that type of operation.
-complete the calculation by rounding according to
the rules for the final type of operation.
Chapter 2 – Slide 50
When Math Operations Are
Mixed
_____5.681g_____
(52.15ml - 32.4ml)
=
-carry out the operations in parenthesis first, and
round according to the rules for that type of operation.
Chapter 2 – Slide 51
When Math Operations Are
Mixed
_____5.681g_____
(52.15ml - 32.4ml)
=
5.681g
19.8ml
-carry out the operations in parenthesis first, and
round according to the rules for that type of operation.
Chapter 2 – Slide 52
Mixed Operations and
Significant Figures
• What is the result (to the correct number of significant
figures) of the following calculations? Assume all
numbers are measured.
(23 - 21) x (24.4 - 23.1)
(298 - 270) x (322)
Chapter 2 – Slide 53
Back To The Calculator Problem
7.8
3.8
Calculator Answer: 2.05263……
Is this a realistic answer?
Is it 2, 2.0, 2.1, 2.05, 2.06, 2.052,
2.053, 2.0526, etc.? Which is it?
Answer must reflect uncertainty
expressed in original measurements.
Chapter 2 – Slide 54
Scientific Notation
Scientific notation
• Is used to write very large
or very small numbers
• The width of a human hair,
0.000 008 m is written as:
8 x 10-6 m
• A large number such as
2 500 000 s is written as:
2.5 x 106 s
Copyright © 2005 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Chapter 2 – Slide 55
Scientific Notation
• A number in scientific notation contains a coefficient
• (1 or greater, less than 10) and a power of 10.
150
0.000735
coefficient
power of ten
coefficient
power of ten
1.5
x
102
7.35
x
10-4
• To write a number in scientific notation, the decimal point is
moved after the first non zero digit.
• The spaces moved are shown as a power of ten.
52 000 = 5.2 x 104
0.00378 = 3.78 x 10-3
4 spaces left
3 spaces right
Chapter 2 – Slide 56
Some Powers of Ten
Chapter 2 – Slide 57
Comparing Numbers in Standard
and Scientific Notation
Standard Format
Diameter of Earth
12 800 000 m
Mass of a human
68 kg
Length of a pox virus
0.000 03 cm
Scientific Notation
Chapter 2 – Slide 58
Comparing Numbers in Standard
and Scientific Notation
Standard Format
Diameter of Earth
12 800 000 m
Mass of a human
68 kg
Length of a pox virus
0.000 03 cm
Scientific Notation
1.28 x 107 m (3 sig figs)
6.8 x 101 kg
(2 sig figs)
3 x 10-5 cm
(1 sig fig)
NOTE: The Coefficient identifies or indicates the number of significant
figures in the measurement.
Chapter 2 – Slide 59
Dimensional Analysis
Defining Conversion Factors
Conversion Factors
• Conversion factors
A ratio that specifies how one unit of measurement is
related to another
• Creating conversion factors from equalities
12 in.= 1 ft
1 L = 1000 mL
12 in
1 ft
 1 or
=1
1 ft
12 in
1L
1000 mL
 1 or
=1
1000 mL
1L
Chapter 2 – Slide 61
Dimensional Analysis
How many seconds are in 2 minutes?
? seconds = 2 minutes
60 seconds = 1 minute
? seconds = 2 minutes x 60 seconds =
1 minute
120 seconds (exactly)
Chapter 2 – Slide 62
Dimensional Analysis
If we assume there are exactly 365 days in a
year, how many seconds are in one year?
? seconds = 1 year
Chapter 2 – Slide 63
Dimensional Analysis
• A problem solving method in which the units
(associated with numbers) are used as a guide in
setting up the calculations.
 desired unit 
  Answer in desired units
Measuremen t in given unit x 
 given unit 
Conversion Factor
Chapter 2 – Slide 64
Exact vs Measured Relationships
• Metric to Metric – exact
• English to English – exact
• Metric to English –
typically measured
(must consider sig figs)
Chapter 2 – Slide 65
English to Metric Conversion
Factors
Chapter 2 – Slide 66
Dimensional Analysis
What is 165 lb in kg?
? kg = 165 lb
STEP 1 Given: 165 lb Need: kg
STEP 2 Plan
STEP 3 Equalities/Factors
1 kg = 2.205 lb
2.205 lb and
1 kg
1 kg
2.205 lb
STEP 4 Set Up Problem
Chapter 2 – Slide 67
Learning Check
• If a ski pole is 3.0 feet in length, how long
is the ski pole in mm?
(1000mm = 1m, 12 inches=1ft, 1m=39.37inches)
Chapter 2 – Slide 68
Learning Check
• If a ski pole is 3.0 feet in length, how long
is the ski pole in mm?
(1000mm = 1m, 12 inches=1ft, 1m=39.37inches)
3.0 feet
mm?
Plan
Chapter 2 – Slide 69
Learning Check
• If a bucket contains 4.65L of water. How
many gallons of water is this?
(1 gallon = 4qts, 1L = 1.057qt)
Chapter 2 – Slide 70
Dimensional Analysis
If Jules Vern expressed the title of his famous
book, “Twenty Thousand Leagues Under the Sea”
in feet, what would the title be?
(1mile = 5280ft, 1 League = 3.450miles)
Chapter 2 – Slide 71
Converting from squared units to squared
units or cubed units to cubed units
• Warning: This type of conversions give many
students difficulties!!!!!
• The one thing you have to remember:
– What does it mean to say that a unit is squared or
cubed?
– m2 = m x m;
s3 = s x s x s
• When there are squared or cubed units, you have
multiple units to cancel out!
Chapter 2 – Slide 72
Examples
• Convert 127.4 cm3 to m3.
(100cm = 1m)
• Convert .572 miles2 to km2.
(1km = .621miles)
Chapter 2 – Slide 73
Displacement volume for a stock engine in a
1984 Corvette is specified at 350 in3. What
is the displacement in L?
Chapter 2 – Slide 74
Percent Factor in a Problem
If the thickness of the skin fold at
the waist indicates an 11% body
fat, how much fat is in a person
with a mass of 86 kg?
percent factor
86 kg mass x
11 kg fat
100 kg mass
= 9.5 kg fat
Copyright © 2005 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Chapter 2 – Slide 75
Even MORE Practice
with Conversion Factors
• A lean hamburger is 22% fat by weight. How
many grams of fat are in 0.25 lb of the
hamburger? (1lb = 453.6g)
Chapter 2 – Slide 76
Density
• A ratio of the mass of an object divided by its volume
Density = Mass/Volume
• Typical units = g/mL (NOTE: 1mL=1cm3)
• We have an unknown metal with a mass of 59.24 g and a
volume of 6.64 mL. What is its density?
Chapter 2 – Slide 77
Density
• A ratio of the mass of an object divided by its volume
Density = Mass/Volume
• Typical units = g/mL (NOTE: 1mL=1cm3)
• We have an unknown metal with a mass of 59.24 g and a
volume of 6.64 mL. What is its density?
Density = 59.24g
6.64mL
= 8.92g/mL
Chapter 2 – Slide 78
Densities of Common Substances
Is Density a Physical or a Chemical Property?
Chapter 2 – Slide 79
Measuring Density in Lab
Chapter 2 – Slide 80
Learning Check
What is the density (g/cm3) of 48.0 g of a metal if the level
of water in a graduated cylinder rises from 25.0 mL to 33.0
mL after the metal is added?
A) 0.17 g/cm3
B) 6.0 g/cm3
C) 380 g/cm3
25.0 mL
33.0 mL
object
Chapter 2 – Slide 81
Sink or Float
• Ice floats in water
because the
density of ice is
less than the
density of water.
• Aluminum sinks
because its density
is greater than the
density of water.
Copyright © 2005 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Chapter 2 – Slide 82
Learning Check
Which diagram correctly represents the liquid layers in
the cylinder? Karo (K) syrup (1.4 g/mL), vegetable (V)
oil (0.91 g/mL,) water (W) (1.0 g/mL)
A
B
C
V
W
K
W
K
V
K
V
W
Chapter 2 – Slide 83
Learning Check
Osmium is a very dense metal. What is its density in
g/cm3 if 50.0 g of osmium has a volume of 2.22 cm3?
a) 2.25 g/cm3
b) 22.5 g/cm3 c) 111 g/cm3
Chapter 2 – Slide 84
Density as a Conversion Factor
Density can be written as an equality.
• For a substance with a density of 3.8 g/mL, the equality is:
3.8 g = 1 mL
• From this equality, two conversion factors can be written for
density.
Conversion
factors
3.8 g
1 mL
and
1 mL
3.8 g
Chapter 2 – Slide 85
Density Example
• You have been given 150.g of ethyl alcohol which
has a density of 0.785g/mL. Will this quantity fit
into a 150mL beaker?
Chapter 2 – Slide 86
DENSITY PRACTICE
Chapter 2 – Slide 87
Learning Check
The density of octane, a component of gasoline, is
0.702 g/mL. What is the mass, in kg, of 875 mL of
octane?
A) 0.614 kg
B) 614 kg
C) 1.25 kg
Chapter 2 – Slide 88
Temperature
Temperature
• Is a measure of how hot or cold an object is
compared to another object
• Indicates that heat flows from the object with a
higher temperature to the object with a lower
temperature
• Is measured using a thermometer
Copyright © 2005 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Chapter 2 – Slide 89
Temperature Scales
Chapter 2 – Slide 90
Solving a Temperature Problem
A person with hypothermia has a
body temperature of 34.8°C. What is
that temperature in °F?
TF
= 1.8 TC + 32
TF = 1.8 (34.8°C)
exact tenths
= 62.6 + 32°
= 94.6°F
tenths
+ 32°
exact
Copyright © 2005 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Chapter 2 – Slide 91
Converting between
Temperature Scales
• ***Conversions between Celsius and Kelvin
(Temperature in K) = (temperature in oC) + 273
(temperature in oC) = (temperature in K) – 273
• Conversions between Celsius and Fahrenheit
oF
= 9/5 (oC) + 32
oC = 5/9(oF – 32)
9/5 = 1.8/1
or 1.8 (oC) + 32
or 1/1.8 (oF – 32)
or 5/9 = 1/1.8
Chapter 2 – Slide 92