Transcript Measurement Number of Significant Figures

Welcome to CHEM 101: Survey
of General Chemistry
Prof. Abdi Mohamed
Contact Info: Page 1 of Syllabus
1
Chem 101, Welcome on Board!
Lecture 1 Outline

Introduction





Course Organization and Procedures
The Scientific Method
Measurement and Scientific Notation
Measured Numbers and Significant Figures
Problem Solving



Dimensional Analysis
Density Problems
Temperature Conversions
2
Course Organization and Procedure
 Meetings:
Tuesdays: AS 1519, Labs days
Thursdays: AS 1521, All lecture (Note, Different)
 Your Course Grade Will be Computed:
3 midterms (lowest dropped)
200 pts
33%
Cumulative Final
200 pts
33%
6 Quizzes (10 pts each, lowest dropped)
50 pts
8%
8 Home works (lowest dropped)
35 pts
6%
8 labs (10 pts each)
80 pts
13%
Group Presentation
20 pts
3%
Subjective Evaluation
15 pts
3%
3
Past Student Performance
 Grading Scale
Based on percent overall points (see syllabus,
page 4)… No curving
Fall CHE 101 Student Grades
50%
Percent Students
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
A RANGE
B RANGE
C RANGE
DFW
4
Lecture Format
 Active Learning: Get Engaged
Warm-up questions or quiz
~ 5–10 minutes
Short lecture
~ 15 minutes
Group activity
~ 10 minutes
Second Short lecture
~ 15 minutes
Active Learning (Individual/pair)
~ 10 minutes
 Why group work? Why active learning?
5
Comments from Prev. Quarters.
My Philosophy: Getting students engaged on course content
facilitates learning and provides opportunities to correct
misconceptions early on.
Research on learning: students need to be active for meaningful
learning to transpire.
 “It made me actually work with what I had just
learned instead of listening and not really paying
that good of attention. They really helped me.”
 “I learned this way the best.”
 Not for everyone …Some hate it! (~ 5 to 10%)
6
Feeling Towards Chemistry
 “Chemistry was my last pre-req class and I put it off
to the end because I thought I would be horrible at it
and that I would hate it.”
 “Chemistry is not for me.”
C’mon now! Key… Such feeling my inhibit your ability
to earn higher grade (FYI, my sister also hates
chemistry and my brother tells me, “You study chem
what?)
 “Neither of these turned out to be true.”
 “I enjoyed learning chemistry.”
7
What you don’t have to worry
about in this class …
 In the past, you may have memorized
formulas? Forget about that



All formulas will be available to you during
exams
You are allowed to bring your own 4 x 6” index
card to all the midterms
You are allowed to bring 8.5 x 11” sheet to the
final exam
 Applied knowledge, not memorization
8
The Scientific Method: Overview
Four Steps:
1. Observation
2. Hypothesis
3. Experiment
4. Theory
9
The Scientific Method: Overview
10
Everyday Scientific Thinking
Observation: The sound from a CD in a CD player skips.
Hypothesis 1: The CD player is faulty.
Hypothesis 2: The original CD has a defect.
Experiment 1: When I replace the CD with another one,
the sound from this second CD is OK.
Experiment 2: When I play the original CD in another
player, the sound still skips.
Theory:
My experimental results indicate the
original CD has a defect.
11
Example From My Own Research Work
Observation: Malaria parasites cannot convert folate compounds
(example folic acid) to their polyglutamate forms
Hypothesis 1: Parasites lack the enzyme that converts folates to
polyglutamate form
Hypothesis II: Compounds are not taken up by the parasites
(transport problem)
Experiment I: Assayed activity of the enzyme that carries out
folate polyglutamylation. Parasites readily
converted folic acid to its polyglutamate form
Theory:
Malaria parasites are able to convert folates to
their polyglutamate form
12
Measurement and Scientific Notation
Measurement gives us three things:
1) Value
2) Unit (dimension)
3) error (uncertainty)
In chemistry we




Measure quantities.
Do experiments.
Calculate results.
Use numbers to report
measurements.
Copyright © 2007 by Pearson Education, Inc.
Publishing as Benjamin Cummings
13
Stating Measurements
In every measurement, a number is followed by a
unit.
Observe the following examples of measurements:
Number and Unit
35 m
0.25 L
225 lb
3.4 hr
14
Units in the Metric System
In the metric and SI systems, 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)
15
Some Units You Should Know
The inside back cover of your text lists some useful
conversion factors. That page will be available to you during
exams, but it is good idea to be familiar with these units
anyway.
Length: 1 meter (m) = 100 centimeters (cm)
1 inch (in) = 2.54 cm (exact)
Volume: 1 liter (L) = 1000 milliliters (mL)
Mass:
1 kilogram (kg) = 1000 grams (g)
1 g = 1000 mg
1 kg = 2.20 Ib
16
Prefixes and Scale
You should definitely learn this inside out. Again, these
prefixes are given in the inside back cover of your text, which
should be available to you on exam dates.
17
The Scientific Notation
 A very large or a very small number can be expressed as a
number between 1 and 10 and power of 10
 Power of 10 can be either positive or negative.
coefficient power of ten
1.5 x 102
coefficient
power of ten
7.35
x 10-4
 To write a number in scientific notation, the decimal point is
placed after the first digit.
 The spaces moved are shown as a power of ten.
52 000. = 5.2 x 104
4 spaces left
0.00378 = 3.78 x 10-3
3 spaces right
18
Comparing Numbers in Scientific and
Standard formats
Here are some numbers written in standard format and in
scientific notation
Number in
Standard Format
Scientific Notation
Diameter of the Earth
12 800 000 m
1.28 x 107 m
Mass of a human
68 kg
6.8 x 101 kg
Length of a virus
0.000 03 cm
3 x 10-5 cm
19
Pause: Group Activity, On-the-Board
Problem Session
 Group activity: all groups work on problems on group
activity 1 worksheet, problems 1-3
 While working on the problems, ask if you have any
questions. I’m more than happy to help
20
Measured Numbers
 Two types of numbers:
1) Measured numbers: obtained by measuring quantities
2) Exact numbers: obtained by counting, defined numbers
Come up with examples involving measured number and exact
numbers:
Measured Numbers
Exact Numbers
21
Significant Figures (SF) in Calculations:
A Guided-Inquiry Exercise
 Study the following examples and determine the rules for
rounding off numbers. First, what does it mean to round a
number?
 5.304 becomes 5.3 when rounded
 110.548 becomes 110.5 when rounded
Okay, so what is the rule for rounding?
The rule is:
22
Determining Significant Figures
TABLE 1.4
Copyright © 2007 by Pearson Education, Inc.
Publishing as Benjamin Cummings
23
Counting Significant Figures
All non-zero numbers in a measured number are
significant.
Measurement
38.15 cm
5.6 ft
65.6 lb
122.55 m
Number of Significant
Figures
4
2
3
5
24
Sandwiched Zeros
Sandwiched zeros
 Occur between nonzero numbers.
 Are significant.
Measurement
50.8 mm
2001 min
0.0702 lb
0.40505 m
Number of Significant
Figures
3
4
3
5
25
Leading Zeros
Leading zeros
 Precede non-zero digits in a decimal number.
 Are not significant.
Measurement
0.008 mm
0.0156 oz
0.0042 lb
0.000262 mL
Number of Significant
Figures
1
3
2
3
26
Trailing Zeros
Trailing zeros
 Are zeros at the right end of number
 Are significant ONLY if the number contains decimal
 If the number has NO decimal, these are NOT SF
Measurement
25000 cm
2.00 kg
48 60.0 mL
25 005 000 g
480.
Number of Significant Figures
2
3
5
5
3
27
Significant Figures in Scientific Notation
In scientific notation
 All digits including zeros in the coefficient are
significant.
Scientific Notation
8 x 104 m
8.0 x 104 m
8.00 x 104 m
Number of Significant
Figures
1
2
3
28
Learning Check
State the number of significant figures in each of
the following measurements:
A. 0.030 m
B. 4.050 L
C. 0.0008 g
D. 2.80 m
Consult with someone sitting next to you.
29
Learning Check
A. Which answer(s) contains 3 significant figures?
1) 0.4760
2) 0.00476
3) 4.76 x 103
B. All the zeros are significant in
1) 0.00307
2) 25.300
3) 2.050 x 103
C. The number of significant figures in 5.80 x 102 is
1) one
2) two
3) three
30
Learning Check: You Decide
In which set(s) do both numbers contain the
same number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 4.00 x 102
3) 0.000015 and 150 000
31
Significant Figures (SF) in Calculations:
A Guided-Inquiry Exercise
 Look at the following example involving multiplication or
division:
M/D:
110.5
x
4 SF
0.048 = 5.304
2 SF
=
calculator
5.3 (rounded)
2 SF
How did you determine how many sig. figs our answer should have?
 Now, what about addition or subtraction: here is an example:
A/S:
110.5
+
0.048
=
110.5 (rounded)
How is sig. figs in final answer determined?
32
Pause: Think Aloud Pair Problem
Solving (TAPPS)
 Work with some one sitting next to you on ALE 1
worksheet, problems 1-5. YOU HAVE 5 MINUTES
 Alternative in answering the questions
 One of you solves one problem out-load, sharing your
thinking process as you solve the problem with your
partner; the other listens, giving you feedback as
necessary. Start with problem 1
 On the next problem, switch roles. The listener become
problem-solver and vice versa
33
Pause: Individual Learning Exercise
 Work on your own problems 6-10 of ALE 1. You have
5 minutes. Go.
 Now, check your answers with someone sitting next
to you. Reconcile any differences you may have
34
Problem Solving: Dimensional Analysis
 Trick is to identify correct equivalent statement(s)
1m
1 lb
=
2.20 lb =
=
1000 mm
16 oz
1 kg
 Obtain fraction from equality; write as numerator and
denominator (ratio)
 Ratio can be inverted to give two conversion factors for
each equality
1 in.
And 2.54 cm
2.54 cm
1 in.
 Correct conversion factor cancels some units and leaves
desired units
 When done check for SF and SENSE
35
Table 1.9: Some Common Equalities
Quick examples:
1) Convert 6 hours to second. (2) How many m in 524 cm?
36
Problem Solving: Density
Density
 Compares the mass of an object to its volume.
 Is the mass of a substance divided by its volume.
Density expression
D = mass
= g or g
volume
mL
cm3
= g/cm3
Note: 1 mL = 1 cm3
 Table 1.10 shows densities for common materials
37
Pause: Group Activity Exercise
 Group activity: all groups work on ALE 1 worksheet,
problems 11-18, skip # 15
 While working on the problems, ask if you have any
questions. I’m more than happy to help
38
Problem Solving: Temperature Conversions
Temperature scales
 Fahrenheit (oF)
Celsius (oC)
Kelvin (K)
 Have reference
points for the
boiling and
freezing points
of water.
39
Copyright © 2007 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Temperature Conversion Formulas
 On the Fahrenheit scale, there are 180°F between the
freezing and boiling points and on the Celsius scale,
there are 100°C, thus a ratio of 1.8oF/1oC
 Zero points are different
 Conversion Factors
TF
= 1.8 TC + 32
TC
= TK - 273
TF - 32
TC 
18
.
TK
= TC + 273
40
Pause: Individual/Group Learning Exercise
 Work on problems 4-9 on group activity on your own
first, then work as group on the same problems
 While working on the problems, ask if you have any
questions. I’m more than happy to help
41
Dimensional Analysis: An In-depth Look
 Write the initial and final units.
 Write a unit plan to convert the initial unit to the final
unit.
 Write equalities and conversion factors.
 Use conversion factors to cancel the initial unit and
provide the final unit.
Unit 1 x
Unit 2
= Unit 2
Unit 1
Initial x
Conversion = Final
unit
factor
unit
42
Setting up a Problem
How many minutes are 2.5 hours?
Initial unit
=
2.5 hr
Final unit
=
? min
Plan
=
hr
min
Setup problem to cancel hours (hr).
Initial
Conversion
Final
unit
factor
unit
2.5 hr x 60 min = 150 min (2 SF)
1 hr
Copyright © 2007 by Pearson Education, Inc.
Publishing as Benjamin Cummings
43
Pause: TAPPS Exercise
A rattlesnake is 2.44 m long. How many centimeters
long is the snake?
1) 2440 cm
2) 244 cm
3) 24.4 cm
44
Using Two or More Factors
 Often, two or more conversion factors are required
to obtain the unit needed for the answer.
Unit 1
Unit 2
Unit 3
 Additional conversion factors are placed in the
setup to cancel each preceding unit
Initial unit x factor 1 x factor 2 = Final unit
Unit 1
x Unit 2
x Unit 3
= Unit 3
Unit 1
Unit 2
45
Example: Problem Solving
How many minutes are in 1.4 days?
Initial unit: 1.4 days
Factor 1
Factor 2
Plan:
days
hr
min
46
Check the Unit Cancellation
 Be sure to check your unit cancellation in the setup.
 The units in the conversion factors must cancel to
give the correct unit for the answer.
What is wrong with the following setup?
1.4 day x 1 day x 1 hr
24 hr
60 min
Units =
day2/min is not the unit needed
Units don’t cancel properly.
47
Pause Group Work
A bucket contains 4.65 L of water. How many
gallons of water is that?
Unit plan:
L
Equalities:
1.06 qt = 1 L
1 gal = 4 qt
qt
gallon
48
More Group Work
If a ski pole is 3.0 feet in length, how long is the
ski pole in mm?
49
Individual Learning Check
If your pace on a treadmill is 65 meters per minute,
how many minutes will it take for you to walk a
distance of 7500 feet?
50