Measuring
Welcome
to Chemistry 1:
A college preparatory
course.
•
•
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Cellphone = NO!!!!
Webpage
Need to Buy
– Scientific Calculator
– Notebook or Binder
•
Safety Contract – Signed
•
Course Expectations
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–
HW & Review (HW Bonus Points)
Make up missed work
•
•
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Notes
Tests
Getting Extra Help
Shoes in Locker
Letters of recommendation
“Are you a student, or just a kid who comes to
school?”
1. Three specific things you must do to be
successful in this course.
2. Three things you must never do
(academically) in this course.
Measuring
Scientific Method
Hypothesis – testable, educated guess
Theory - repeatedly confirmed hypothesis that
has predictive power.
Law – Theory with NO known exceptions
Measuring
Hypothesis
Theory
Law
Measuring
Science changes!!!!!
Spotting Bad Science
Measuring
1. Based on Anecdotal Evidence
Anecdotal - From stories, not studies (no math)
2. Small Sample Size
3. Not published in Journals – not reviewed
or tested
4. Broad Claims
Example: The Water Cure
Measuring
Measuring
•
•
Estimated place – every measurement
must have ONE estimated place.
One place past the smallest marking
Measuring
Measuring
Measuring
Measuring
Measuring
Measuring
Measuring
Measuring
Measuring
Measuring
Measuring
Graphing
1. Label x and y axis including units
2. Mark Axis using a convenient scale
3. Title your graph “The Dependence of Y
on X”
4. Mark dots with a small circle
5. Draw “Best Fit” line or curve
Measuring
Graphing
•
Best Fit Line
a. Used ONLY for linear relationships.
b. Fits y = mx + b
m = slope
b = y-intercept
c. If graph is almost perfect line, same # dots
above and below
X = independent variable (you can control)
Y = dependent variable (can’t control)
Measuring
Measuring
Measuring
Graphing
•
Best Fit Curve
a. Used if points are clearly not linear.
b. Can be fit to higher order eqns:
y = mx2 + b
Measuring
Measuring
Graphing
Rectangle A = L X W
Triangle A = ½ B X H
Circle
A = r2
Irregular Shape?
Measuring
Measuring
Graphing Lab
•
•
•
•
Use centimeters
TWO decimal places, last one is the
estimated place
Write down the letter of your shape
See me for the actual value
Measuring
1. What do chemists study/do?
2. What professions/college majors require a
chemistry course?
3. Where is chemistry important in
business/industry?
4. What household products are “chemicals”?
5. Where in history was chemistry important?
Measuring
Scientific Notation
1. Descartes:1637 - “I think, therefore I
am”
2. Powers of 10
100 = 1
101 = 10
102 = 10 X 10 = 100
103 = 10 X 10 X 10 =1000
Measuring
Scientific Notation
200,000,000,000 stars (Andromeda):
2 X 100,000,000,000
2 X 1011 stars
Measuring
Scientific Notation
3. A Helium atom masses
0.000,000,000,000,000,000,000,006,645g
6.645 X 10-24 g
Measuring
Scientific Notation
340
378,400
0.00234
0.000 000 000 0918
5.6 X 105
6.12 X 10-3
2.6 X 10-7
4 x 102
Measuring
Scientific Notation
43
575,400
0.000723
0.000 000 0014
6.5 X 10-5
2.16 X 103
6.2 X 107
8 x 10-2
Measuring
Scientific Notation
There are ~900 students at
Dallas
9 X 102 =
90 X 101 =
3
=
0.9 X 10
Measuring
Scientific Notation
Write 4500 in scientific notation
with the following exponents:
X 103
X 102
X 105
X 104
Measuring
Scientific Notation
Write 4500 in scientific notation
with the following exponents:
4.5 X 103
45 X 102
0.045 X 105
0.45 X 104
Measuring
Scientific Notation
Examples:
(2.0 x 102) + (3.0 x 103) = 3.2 X 103
(6.0 X 103) ÷ (3.0 x 10-5)=2.0X108
(2.0 x 107) - (6.3 x 105) = 1.9X107
Measuring
Scientific Notation
(4.0 x 105) x (3.0 x 10-1)=
(6.0 x 108) ÷ (3.0 x 105)=
(8.4x 1012) ÷ (8.4 x 109)=
NOTE: 103 = 1 X 103
Measuring
Scientific Notation
(4.0 x 105) x (3.0 x 10-1)=1.2 X105
(6.0 x 108) ÷ (3.0 x 105)= 2 X 103
(8.4x 1012) ÷ (8.4 x 109)= 1 X 103
NOTE: 103 = 1 X 103
Measuring
Accuracy and Precision
• Accuracy – how close the average of a set of
measurements is to the accepted value (AAA)
• Precision – How close a set of measured values
are to one another (reproducibility)
• Always compare to a textbook value
Measuring
X
X
X
X X
X
X
X
X
X X
XX
X
X
X
Measuring
Percent Error
Percent Error – Measure of accuracy
% Error = Experimental – Accepted X 100
Accepted
NOTE: “Experimental” =average of all trials
Measuring
A student measures the density of a sample of
copper at 8.75 g/mL. The accepted value is
8.96 g/mL. Calculate the percent error.
Measuring
Error Analysis: Range
Range - Measure of precision
Range = highest trial – lowest trial
Measuring
Example 1
A student measures the density of a sample of
lead and does four trials (11.3, 10.5, 11.9,
10.8 g/cm3). Calculate the range and
comment on precision.
Measuring
Accuracy and Precision
Students did trials to measure the density of a
metal. The accepted density is 7.2 g/cm3.
Were they accurate or precise?
Set 1
Set 2
Set 3
7.21 7.25 7.18
6.40 7.90 7.30
6.45 6.52 6.48
Measuring
Significant Figures
1. Def - All of the measured values plus one
estimated place
2. Examples
6 cm
0.005 mm
1340 kg
6.0 cm
0.0050 mm
1340. kg
6.01 cm
0.00500 mm
1340.0 kg
Measuring
Numbers with a Decimal
How many sig figs? Also, write in sci.
notation:
3.44 cm
60.001 cm
430.0 cm
0.0032 cm
0.00320 cm
Measuring
Numbers without a Decimal
1. Often poor measurements
2. Examples: “Not left”
18,500 kg
120 ft
Measuring
Numbers without a Decimal
How many sig figs? Also, write in scientific
notation:
10,500 cm
240 cm
120,000 cm
4 cm
45 cm
How many significant figures are in the following?
Also, write the numbers in proper scientific
notation.
1508 cm
20.003 lb
300 ft
300.0 ft
0.00705 m
0.007050 m
1250
1250.
1250.0
Measuring
Significant Figures
Round the following to three sig figs:
32.45
32.449
0.0067530
0.003904
11,980
Round to four significant figures:
598,937
0.00053254
5.37286
0.39201
0.39205
How many significant figures?
0.00200
7450
8.40 X 1010
0.0020
144.0
9.000 X 10-5
Round to three significant figures:
54.649999
300.847
200.49
0.00056732
0.0045282
1.456 X 10-4
8.605 X 107
100.
200
Measuring
Significant Figures and Math
1. Math answers are only as good as the
worst measurement.
2. Example:
Determining the area of a room:
6.9 m by 10.478 m
3. Round AFTER you do the math.
Measuring
Significant Figures and Math
Addition/Subtraction Rule - Keep the
least number of decimal places.
Examples:
7.56
0.0327
0.375
– 0.00068
+ 14.2203
Measuring
Significant Figures and Math
Multiplication/Division Rule –
Answer contains the least # of
TOTAL significant figures
Examples
23.4 X 32.25 =
Measuring
Significant Figures and Math
11.688  4.0 =
7 cm X 7 cm =
4.68 X 1016  9.1 X 10-5 =
1. Multiple Operations – Round when you change
between add/sub and mult/div
2. Examples
(0.56 X 11.73) + 22.34 =
(6.5688) + 22.34 =
(6.6) + 22.34 = 28.9
(12.45 – 11.643) X 2.68 =
(0.807) X 2.68 =
0.81 X 2.68 = 2.1708 = 2.2
160 X 3.445 =
19.64 + 0.466 =
4.856 X 10102.0 X 102=
(16.44  2.33) + 22.3 =
(7.055793991) + 22.3
7.06 + 22.3 = 29.36 = 29.4
Measuring
Significant Figures and Math
160 X 3.445 = 550
19.64 + 0.466 = 20.11
4.856 X 10102.0 X 102 = 2.4 X 108
(16.44  2.33) + 22.3 = 29.4
Measuring
Warm-Up
19.64 - 14.465 =
320 X 0.04550 =
3.1415 X 1011 X 8.47 X 10-7=
(12.7 X 10.43) + 23.8 =
0.00320 X 10-4 (write in proper sci. not.)
Measuring
Absolute Numbers
Also called “exact” numbers
Have an infinite number of significant figures
Counting numbers and values in definitions.
Examples:
23 students
Diameter = 2r
1 km=1000m
5. NEVER use exact numbers for determining sf.
1.
2.
3.
4.
Measuring
Absolute numbers or measured values?
Y= X3
1 m = 100 cm
2.85 grams
1 cm = 10 mm
37 apples
50 people
400 people
Measuring
Absolute Numbers
If we divide 1.66 lbs of candy among 3
people, how much candy will each person
get?
(Ans: 0.553 lbs/person)
What is the diameter of a circle whose radius
is 3.835 m?
(Ans: 7.670 m)
Measuring
1. What is the diameter of a circle with a radius
of 2.567 cm?
2. If we buy 1.84 pounds of coffee and divide it
among three people, how much coffee will
each person get?
3. How many centimeters is 7.565 meters?
4. How would you divide 12.35 kg of candy
among eight children?
Measuring
Metric
Qualitative – data with no number
Quantitative – data with a number
Measuring
Metric
1. SI System – Le System International d’Unites
2. 1670 – Gabriel Mouton (French Vicar)
3. 1795 – Adopted by France
Measuring
Measuring
Metric
4. Base ten scale
1000 m
100 m
10 m
1m
1m
1m
1m
=
=
=
=
=
=
=
1 km (kilo)
1 hm (hecto)
1 dam (deca)
1m
10 dm (deci)
100 cm(centi)
1000 mm (milli)
Measuring
Measuring
Metric
Fundamental Units (MKS)
Length
meter
Mass
kilograms
Time
second
Derived Units
Volume
liter (dm3)
Energy
Joules (kg m2/s2)
Measuring
Metric
Factor Label method
55 cm = ? m
0.055 L = ? mL
0.00456 km = ? cm
550 cm2 = ? m2
25 miles/hr = ? m/s
a.
b.
c.
d.
e.
f.
g.
h.
129 hrs  Days
0.468 mkm
825 cm2  in2
0.00230 L  mL
0.468 m  mm
1245 cm  km
55.0 mi/hr  km/hr
55.0 mi/hr  m/min
129 hrs  Days
0.468 mkm
825 cm2  in2
0.00230 L  mL
0.468 m  mm
1245 cm  km
55 mi/hr  km/hr
55 mi/hr  m/min
5.38 days
0.000468
128 in2
2.30 mL
468 mm
0.01245 km
88.5 km/hr
1470 m/min
Measuring
Metric
1 km
1 hm
1 dam
1m
1 dm
1 cm
1 mm
=
=
=
=
=
=
=
103 m
102 m
101 m
1m
10-1
10-2
10-3 m
Convert using powers of ten
50 cm = ? m
5 mm = ? m
65 km = ? m
23.3 mL = ? L
0.0047 mm = ? m
0.876 L = ? mL
1.
2.
3.
4.
5.
6.
7.
Round to 3 sf:
0.0050460
Calculate using sf (10.345 – 8.23) X 54
65.0 m/s =? miles/hr
584 cm3 = ? in3
234 cm = ? Feet
3.00 X 108 m/s = miles/s
45.0 L/s = gallons/min
(1.00 inch = 2.54 cm)
(1.609 km = 1.00 mile)
(1.000 gallon = 3.785 L)
1.
2.
3.
4.
5.
6.
7.
0.00505
110
145 miles/hr
35.6 in3
7.68 Feet
3.00 X 108 m/s = 186 000 miles/s
713 gallons/min
(1.00 inch = 2.54 cm)
(1.609 km = 1.00 mile)
(1.000 gallon = 3.785 L)
Temperature
Measuring
Temperature
Absolute Zero
• All atomic and molecular motion stops
• Coldest possible temperature?
• Liquid Nitrogen = 77 K (-196 oC)
• Dry Ice = 216 K (-56.6 oC)
Measuring
Measuring
Measuring
Planck Temperature = 1.417 x 1032 K
(temperature of the Big Bang)
Measuring
Temperature
Conversion Formulas
F = 1.8 (oC) + 32
K = C + 273
C = K – 273
Measuring
Temperature
Ex:
24 oC
48oF
177 K
=
=
=
oF
oC
oC
Measuring
Temperature
102 oF
-10.0 oC
25 oC
177 K
310 oF
 oC
 oF
 K
 oF
 K
Measuring
Temperature
102 oF
-10.0 oC
25 oC
177 K
310 oF





39oC
14 oF
298 K
-141 oF
427 K
Measuring
Temperature
25 oC
50 oF
310 K
10 K
-15 oC
 oF
 K
 oC
 oC
 K
Measuring
Temperature
25 oC
50 oF
310 K
10 K
-15 oC





77 oF
283 K(10 oC)
37 oC
-263 oC
258 K
Measuring
Page 39
15 a) 0.77 b) 13.0
21 a) 5000 m
d) 100 yd
23 a) 7
c) 32
b) 1400 ft2
b) 12.7
c) 1.49
d) 326
c) 1.21 in2
Measuring
Page 40 (40-42, 53, 55, 57, 60)
42 a) 6.8 X 106
6800
6.8
b) 786
0.786
7.68X10-4
c) 4452
4.452
4.452 X 10-3
53) 384,300km
55) 0.376 qt
57) 114 g
60) 109 yd (10.9 yd)
Measuring
23 a)
b)
c)
42 a)
b)
c)
7
12.7
1.49
6.8 X 106
786
4452
6800
0.786
4.452
6.8
7.68X10-4
4.452 X 10-3
Measuring
Measuring
Sig Figs Review WS
1 a=4b=3 c=2 d=4 e=3
2a) 20.
e) 6.27
b) 960
f) 417
c) 55.2
g) 2.7
d) 5800
f=6
g=2
h=3
Measuring
B2) 3ft=1yd,
10 dm = 1 m
1.00 gal = 3.78 L
2.20 lb = 1.00 kg
B3) 15.5 miles
B4) $2.16, 9.72 oz
B5) 366 cm
B6) $8.94
Measuring
29
4.23 X 105
4.338 X 102
2.0 X 10-3
8.8 X 102
8 X 10-5
8.2 X 107
7.5 X 1013
1.06 X 10-6
Measuring
39
1.58 X 10-10
2.29 X 1010
3.69 X 10-6
3.15 X 1012
3. Most precise = 26.202, most acc = 26.8
Measuring
5. a) 2
b) 3
c) 3
d) 3
e) 4
f) 5
g) 2
h) 2
9. a) 120
b) 28
c) 38,000 d) 0.47
e) 56 f) 0.040 g) 1,600,000 h) 320
11.a) 0.667
b) 0.400 c) 0.625 d) 3.25
15. a) 0.77
b) 13.0
c) 32
d) 326
24. a) 120 cm2 b) 394 ft2 c) 2 cm d) 2.3 in
25. a) 5000 m b) 1400 ft2 d) 1.21 in2 d) 100 yd
27. a) 7
b) 12.7
c) 1.49
28.a) 1.57 X102 b)1.57X10-1 c) 3.00 X10-2
Measuring
d) 4.0 X107 e) 3.49 X10-2 f) 3.2 X 104
g) 3.2 X1010 h) 7.71 X10-4 i) 2.34 X 103
29. a) 4.23 X105 b) 4.338 X102 c) 2.0 X10-3
d) 8.8 X102 e) 8 X10-5 f) 8.20 X107
g) 7.5 X1013 h) 1.06 X10-6
32. a) 0.000475 b) 6550 c) 0.00788
d) 489,000 e) 4.75
f) 3.4
33.a) 0.064
b) 8340 c) 220
d) 0.00342
34. a) 4.89 X10-4
b) 4.56 X10-5 c) 7.8X 103
Measuring
d)5.71 X10-2 e) 4.975 X108 f) 3.0 X 10-2
35. a) 7.8X10-10 b) 7.2X10-1
c) 3.450X1019
d) 2.8X1010 e) 6.9X10-14
f) 2.3X103
39. a) 1.58 X10-10
c) 3.69 X10-6
43.a) 4.56 X1016
c) 1.7 X10-14
b) 2.29 X1010
d) 3.15 X1012
b) 5 X10-9
d) 1.26 X1012
Write in Sci Notation
Measuring
4 X 102
5 X 10-3
6 X 104
3.4 X 10-3
7.5 X 1012
6.457 X 10-2
5.6 X 10-5
4.5 X 102
Write the expanded number
0.000 05
2 000 000 000
0.144
150 000 000 000
0.000 000 244
300 000
0.00045
45 000
Calculate in Sci Not
a) 3 X 105
b) 2 X 103
c) 4.3 X 103
d) 6 X 107
e) 2.5 X 10-6
f) 1.664 X10-3
g) 3.0 X 104
h) 8 X 10-4
i) 1.6 X 101
j) 1.16 X 107
How many signif
figures?
Calculate using SF
a) 15.2
m) 91.0
b) 20.
n) 4.1
c) 6
o) 0.0075
d) 19.4
e) 15
f) 3.1
g) 1.23
h) 4.27
i) 0.0102
j) 50
k) 49
l) 49.0
Multiple operations & SF
a) 20.
b) 960
c) 55.2
d) 5800
Abs. # Calculations
a) 303 cm3
b) 756.3 cm
c) 1.544 kg/child
d) 0.65 m
e) 5.134 cm
f) 25.6 ml
g) 553 cm2
h) 0.613 kg/person
Metric Conversions
Measuring
a) 250 cm
m) 5.678292 km
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
57 cm
0.42 m
420 mm
46.7 m
72,000 ml
2.3 cm
8.955 g
8.68 X 10-6 kg
0.654 g
6,000 mL
1.2 dm
n)
o)
p)
q)
r)
s)
t)
u)
v)
w)
x)
0.088 L
19 mL
3.9 m
0.0234 L
45 mL
1.2 cm
0.072 g
0.0862 km
2470 cm
340 mL
4.8 cm
y) 0.0012 mL
z) 2.3 mL
Temperature
Conversions
Measuring
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
298 K
25 oC
226 K
-196 oC
62.2 oC
309 K
263 K
59 oC
127 oC
176 K
k)
l)
m)
n)
o)
p)
q)
5273 K
-271 oC
371 K
18.3 oC
239 K
33 oC
256 K
62.
lbs
g
kg
1.72
780.
0.780
2.17
985
0.985
16.0
7260
7.26
71. Longer, 10.9 yards
102.a) 310 K b) 408 K c) -68oC
d) -231 oF e) 311 K d) 248 K
Complete
the following chart (1.00 inch = 2.54 cm)
Measuring
inches
cm
m
4.75
824
0.537
How many Dekameters is 456 cm?
Convert 60oF to Celsius and Kelvin
Complete
the following chart (1.00 inch = 2.54 cm)
Measuring
inches
cm
m
4.75
12.1
0.121
324
824
8.24
21.1
53.7
0.537
How many Dekameters is 456 cm? 0.456 dam
Convert 60.0oF to Celsius and Kelvin 15.6oC, 289K
A
43
Measuring
G 400 (4 X 102)
B
5.5
H
35
C
306.9
I
30
D
2.21
J
25
E
7.7
K
40
F
10.88
L
165