Chapter%201:%20Scientists

1
Chapter 1 Scientists Tools
2
Chemistry is an Experimental Science

• This chapter will introduce the following tools
  that scientists use to do chemistry
• Section 1.1 Observations Measurements
• Section 1.2 Converting Units
• Section 1.3 Significant Digits
• Section 1.4 Scientific Notation

3
Section 1.1Observations Measurements
4
Collecting Data by Making Observations
5
Qualitative Data Common Mistake Clear vs
Colorless

• Colorless does not describe transparency
• Words to describe transparency

Clear
Opaque
Cloudy
Parts are see-through with solid cloud in it
See-through
Cannot be seen through at all

• You can be clear colored
• You can be cloudy colored

6
Clear versus Colorless
Cherry Kool-ade
Example Describe the following in terms of
transparency words colors
Whole Milk
Water
7
Clear versus Colorless
Cherry Kool-ade
Clear red
Example Describe using the terms of transparency
color
Whole Milk
Opaque white
Water
Clear Colorless
8
Types of Quantitative Data
Quantity
Common Unit
Instrument used
Mass (how much stuff is there)
Balance
gram (g)
Graduated cylinder
milliLiters (mL)
Volume (how much space it takes up)
Temperature (how fast the particles are moving)
Celsius (C)
Thermometer
Length
Meters (m)
Meter stick
Time
Seconds (sec)
stopwatch
Energy
Joules (J)
(Measured indirectly calorimeter)
9
Measuring Volume

• Each instrument has different calibrations.
• Beaker A 10 ml calibrations
• Volume 28 mL
• Graduated Cylinder B 1 ml calibrations
• Volume 28.3 mL
• Buret C 0.1 calibrations
• Volume 28.32 mL
• The more lines, the more precise the instrument.
• Always record the numbers you definitely can read
  off the instrument, plus an estimated digit.

10
Use the bottom of the meniscus to record the
volume of the liquid.
36.5 ml
?
11
Uncertainty in Measurement

• Every measurement has a degree of uncertainty
• The last decimal you write down is an estimate
• Write down a 5 if its in-between lines
• Write down a 0 if its on the line

Remember Always read liquid levels from the
bottom of the meniscus
Example Read the measurements
12
Uncertainty in Measurement

• Every measurement has a degree of uncertainty
• The last decimal you write down is an estimate
• Write down a 5 if its in-between lines
• Write down a 0 if its on the line

Example Read the measurements
Its in-between the 10 11 line 10.5 mL
Its on the 12 line 12.0 mL
13
Measuring Length
14
Measurement Tool for Length
1.5 cm
1.95 cm
15
Uncertainty in Measurement
Example Read the measurements
16
Uncertainty in Measurement
Example Read the measurements
Its right on the 6.9 line 6.90
Its between the 3.8 3.9 line 3.85
17
Measurement Tool for Temperature
What is the measurement of thermometer B seen to
the right?
18
Measurement Tool for Mass

• Always read exactly what the balance says
• Do not add any additional numbers!

19
HINTUncertainty in Measurement

• Choose the right instrument
• If you need to measure out 5 mL, dont choose the
  graduated cylinder that can hold 100 mL. Use the
  10 or 25 mL cylinder
• The smaller the measurement, the more an error
  mattersuse extra caution with small quantities
• If youre measuring 5 mL youre off by 1 mL,
  thats a 20 error
• If youre measuring 100 mL youre off by 1 mL,
  thats only a 1 error

20
Section 1.2Accuracy, Precision Significant
Digits
21
Gathering Data

• Multiple trials help ensure that youre results
  werent a one-time fluke!
• Precisegetting consistent data (close to one
  another)
• Accurategetting the correct or accepted
  answer consistently

Example Describe each groups data as not
precise, precise or accurate
22
Precise Accurate Data
Precise, but not accurate
Correct value
Example Describe each groups data as not
precise, precise or accurate
Precise Accurate
Correct value
Not precise
Correct value
23
Can you be accurate without precise?
This group had one value that was almost right
onbut can we say they were accurate?
Nothey werent consistently correct. It was by
random chance that they had a result close to the
correct answer.
24
Can you be accurate without precise?
This group had one value that was almost right
onbut can we say they were accurate?
25
You Try! Accepted Value bulls-eye
not accurate but precise accurate
precise not precise nor accurate
26
Example Below is a data table produced by three
groups of students who were measuring the mass of
a paper clip which had a known mass of 1.0004g.
  Group 1 Group 2 Group 3 Group 4
  1.01 g 2.863287 g 10.13251 g 2.05 g
  1.03 g 2.754158 g 10.13258 g 0.23 g
  0.99 g 2.186357 g 10.13255 g 0.75 g
Average 1.01 g 2.601267 g 10.13255 g 1.01 g
Group 1 has the most precise (all 3 measurements
are consistent with each other) accurate (the
average value of the 3 trials are closest to the
accepted value of 1.0004g) data.
27
Percent Error

• A calculation designed to determine accuracy
• Error Accepted - Experimental x 100
• Accepted

28
You Try!

• A student measured an unknown metal to be 1.50
  grams. The accepted value is 1.87 grams. What is
  the percent error?
• Error 1.87 1.50x 100
• 1.87
• 20 error

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Significant Digits

• A significant digit is anything that you measured
  in the labit has physical meaning
• The real purpose of significant digits is to
  know how many places to record in an answer from
  a calculation
• But before we can do this, we need to learn how
  to count significant digits in a measurement

30
Taking Using Measurements

• You learned in Section 1.2 how to take careful
  measurements
• Most of the time, you will need to complete
  calculations with those measurements to
  understand your results

0.3333333333333333333 g/mL
how can the answer be known to and infinite
number of decimal places?
If the actual measurements were only taken to 2
or 3 decimal places
It cant!
31
Significant Digit Rules
1
All measured numbers are significant
All non-zero numbers are significant
2
3
Middle zeros are always significant
Trailing zeros are significant if theres a
decimal place
4
5
Leading zeros are never significant
32
All the fuss about zeros
Middle zeros are importantwe know thats a zero
(as opposed to being 112.5)it was measured to be
a zero
102.5 g
The convention is that if there are ending zeros
with a decimal place, the zeros were measured and
its indicating how precise the measurement was.
125.0 mL
125.0 is between 124.9 and 125.1 125 is between
124 and 126
The leading zeros will dissapear if the units are
changed without affecting the physical meaning or
precisiontherefore they are not significant
0.0127 m
0.0127 m is the same as 127 mm
33
Sum it up into 2 Rules Oversimplification Rule
The 4 earlier rules can be summed up into 2
general rules
If there is no decimal point in the number, count
from the first non-zero number to the last
non-zero number
1
If there is a decimal point (anywhere in the
number), count from the first non-zero number to
the very end
2
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Examples of Summary Rule 1
If there is no decimal point in the number, count
from the first non-zero number to the last
non-zero number
1
124 20570 200 150
Example Count the number of significant figures
in each number
35
Examples of Summary Rule 1
If there is no decimal point in the number, count
from the first non-zero number to the last
non-zero number
1
124 20570 200 150
3 significant digits
Example Count the number of significant figures
in each number
4 significant digits
1 significant digit
2 significant digits
36
Examples of Summary Rule 2
If there is a decimal point (anywhere in the
number), count from the first non-zero number to
the very end
2
0.00240 240. 370.0 0.02020
Example Count the number of significant figures
in each number
37
Examples of Summary Rule 2
If there is a decimal point (anywhere in the
number), count from the first non-zero number to
the very end
2
0.00240 240. 370.0 0.02020
3 significant digits
Example Count the number of significant figures
in each number
3 significant digits
4 significant digits
4 significant digits
38
Importance of Trailing Zeros

• Just because the zero isnt significant doesnt
  mean its not important and you dont have to
  write it!

250 m is not the same thing as 25 m just
because the zero isnt significant The zero not
being significant just tells us that its a
broader rangethe real value of 250 m is
between 240 m 260 m. 250. m with the zero
being significant tells us the range is from 249
m to 251 m
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Lets Practice
1020 m 0.00205 g 100.0 m 10240 mL 10.320 g
Example Count the number of significant figures
in each number
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Lets Practice
1020 m 0.00205 g 100.0 m 10240 mL 10.320 g
3 significant digits
Example Count the number of significant figures
in each number
3 significant digits
4 significant digits
4 significant digits
5 significant digits
41
Rounding

• Go to the digit you want to round to
• Look to the right.
• If the number is less than 5, the digit you want
  to round to stays the same. Drop the rest of the
  digits
• If the number is greater than 5, the digit you
  want to round to moves up by one. Drop the rest
  of the digits.

1320 m (2) 0.00205 g (2) 752.4 m (3) 7.007 mL
(3) 10.350 g (3)
Example Round each number to number of sig figs
in the parentheses
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Rounding

• Go to the digit you want to round to
• Look to the right.
• If the number is less than 5, the digit you want
  to round to stays the same. Drop the rest of the
  digits
• If the number is greater than 5, the digit you
  want to round to moves up by one. Drop the rest
  of the digits.

1320 m 0.00205 g 752.4 m 7.007 mL 10.350 g
1300
Example Round each number to number of sig figs
in the parentheses
.0021
752
7.01
10.4
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Performing Calculations with Sig Figs
When recording a calculated answer, you can only
be as precise as your least precise measurement
Addition Subtraction Answer has least number
of decimal places as appears in the problem
1
Multiplication Division Answer has least
number of significant figures as appears in the
problem
2
Always complete the calculations first, and then
round at the end!
44
Always complete the calculations first, and then
round at the end!

• EXCEPTION When adding/subtracting and then
  multiplying/dividing, follow the rules for
  addition/subtraction first and then apply that
  number of sig figs to the multiplication/division
  rules.
• (6.350- 6.010) / 2.0 _______
• .340 / 2.0
• 3 s.f. / 2 s.f. .17

45
Addition Subtraction Example 1
Addition Subtraction Answer has least number
of decimal places as appears in the problem
1
Example Compute write the answer with the
correct number of sig digs
15.502 g 1.25 g
16.752 g
This answer assumes the missing digit in the
problem is a zerobut we really dont have any
idea what it is
46
Addition Subtraction Example 1
Addition Subtraction Answer has least number
of decimal places as appears in the problem
1
Example Compute write the answer with the
correct number of sig digs
15.502 g 1.25 g
3 decimal places
Lowest is 2
2 decimal places
16.752 g
Answer is rounded to 2 decimal places
16.75 g
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Addition Subtraction Example 2
Addition Subtraction Answer has least number
of decimal places as appears in the problem
1
Example Compute write the answer with the
correct number of sig digs
10.25 mL - 2.242 mL
8.008 mL
This answer assumes the missing digit in the
problem is a zerobut we really dont have any
idea what it is
48
Addition Subtraction Example 2
Addition Subtraction Answer has least number
of decimal places as appears in the problem
1
Example Compute write the answer with the
correct number of sig digs
10.25 mL - 2.242 mL
2 decimal places
Lowest is 2
3 decimal places
8.008 mL
Answer is rounded to 2 decimal places
8.01 mL
49
Multiplication Division Example 1
Multiplication Division Answer has least
number of significant figures as appears in the
problem
2
Example Compute write the answer with the
correct number of sig digs
10.25 g 2.7 mL
3.796296296 g/mL
50
Multiplication Division Example 1
Multiplication Division Answer has least
number of significant figures as appears in the
problem
2
Example Compute write the answer with the
correct number of sig digs
4 significant digits
Lowest is 2
10.25 g 2.7 mL
3.796296296 g/mL
Answer is rounded to 2 sig digs
2 significant digits
3.8 g/mL
51
Multiplication Division Example 2
Multiplication Division Answer has least
number of significant figures as appears in the
problem
2
Example Compute write the answer with the
correct number of sig digs
1.704 g/mL ? 2.75 mL
4.686 g
52
Multiplication Division Example 2
Multiplication Division Answer has least
number of significant figures as appears in the
problem
2
Example Compute write the answer with the
correct number of sig digs
1.704 g/mL ? 2.75 mL
4 significant dig
Lowest is 3
3 significant dig
4.686 g
Answer is rounded to 3 significant digits
4.69 g
53
Lets Practice 1
Example Compute write the answer with the
correct number of sig digs
0.045 g 1.2 g
54
Lets Practice 1
Example Compute write the answer with the
correct number of sig digs
0.045 g 1.2 g
3 decimal places
Lowest is 1
1 decimal place
1.245 g
Answer is rounded to 1 decimal place
1.2 g
Addition Subtraction use number of decimal
places!
55
Lets Practice 2
Example Compute write the answer with the
correct number of sig digs
2.5 g/mL ? 23.5 mL
56
Lets Practice 2
Example Compute write the answer with the
correct number of sig digs
2.5 g/mL ? 23.5 mL
2 significant dig
Lowest is 2
3 significant dig
58.75 g
Answer is rounded to 2 significant digits
59 g
Multiplication Division use number of
significant digits!
57
Lets Practice 3
Example Compute write the answer with the
correct number of sig digs
1.000 g 2.34 mL
58
Lets Practice 3
Example Compute write the answer with the
correct number of sig digs
4 significant digits
Lowest is 3
1.000 g 2.34 mL
0.42735 g/mL
Answer is rounded to 3 sig digs
3 significant digits
0.427 g/mL
Multiplication Division use number of
significant digits!
59
Lets Practice 4
Example Compute write the answer with the
correct number of sig digs
1.704 m ? 2.75 m
60
Lets Practice 4
Example Compute write the answer with the
correct number of sig digs
1.704 m ? 2.75 m
4 significant dig
Lowest is 3
3 significant dig
4.686 g
Answer is rounded to 3 significant digits
4.69 m2
Multiplication Division use number of
significant digits!
61
Multi Step Calculations
62
Section 1.3Metric System Dimensional Analysis
63
The Metric System

• Universal system of measurements
• Based on the powers of ten
• Only the US and Myanmar do not use this system

64
Metric Prefixes

• Used in the metric system to describe smaller
  or larger amounts of base units

The Great Magistrate King Henry Died by drinking
chocolate milk Monday near paris T G
M K H D b d
c m µ n
p 1 x 1012 1 x 109 1 x 106
1000 100 10 1 .1
.01 .001 1 x 10-6 1
x 10-9 1 x 10-12

• Base Units have a value of 1
• Examples are Liters (L) meters (m) grams
  (g) seconds (s)
• Place a prefix in front of a base unit to make a
  larger or smaller
• number Example ks kilosecond
• mm millimeter
• cg centigram
• m meter

65
Converting with the Metric System Using the
Ladder Method

• Determine the starting point.
• Count the jumps to your endpoint.
• Move the decimal the same number of jumps in the
  same direction
• If using the other prefixes, remember that there
  is a difference of 1000 or 3 places between each.
• T G M K H D
  b d c m µ
  n p
• EXAMPLE 4 km ______ m

4000
66
ExamplesT G M K H
D b d c m µ
n p
150 ml

• Convert 15 cl into ml
• Convert 6000 mm into Km
• Convert 1.6 Dag into dg
• Convert 3.4 nm into m

.006 Km
160 dg
.0000000034 m
67
A Different Way to Convert between Units

• Dimensional Analysis is another method
• It uses equivalents called conversion factors to
  make the exchange

68
Conversion Factors

• Change the Equivalents to Conversion Factors

1 foot 12 inches or 4 quarters 1 dollar

• What happens if you put one on top of the other?
  You create a ratio equal to 1

4 quarters 1 dollar
69
Common Equivalents

12 in
1 ft

1 in
2.54 cm

1 min
60 s

3600 s
1 hr

0.946 L
1 quart (qt)

4 pints
1 quart

1 pound (lb)
454 g
70
Steps for using Dimensional Analysis
1
Write down your given information
2
Determine what you want.
Use or create a conversion factor to compare what
you have to what you want
3
4
Set up the math so that the given unit is on the
bottom of the conversion factor
5
Calculate the answer. Multiply across the top.
Multiply across the bottom of the expression.
Divide the bottom by the top
71
Example 1
1
Write down your given information
Example How many yards are in 52 feet?
52 ft
72
Example 1
Determine what you want.
2
Example How many yards are in 52 feet?
________ yds
52 ft
73
Example 1
Use or create a conversion factor to compare what
you have to what you want
3 4
Example How many yards are in 52 feet?
1
yd
?
________ yds
52 ft
3
ft
Put the unit on bottom that you want to cancel
out!
The equivalent with these 2 units is 3 ft 1
yd A tip is to arrange the units first and then
fill in numbers later!
74
Example 1
Calculate the answer. Multiply across the top.
Multiply across the bottom of the expression.
Divide the bottom by the top
5
Example How many yards are in 52 feet?
1
yd
17.33
?
________ yd
52 ft
3
ft
Enter into the calculator 52 ? 1 ? 3
75
Example 2
1
Write down your given information
Example How many grams are equal to 127.0 mg?
127.0 mg
76
Example 1
Write down an answer blank and the desired unit
on the right side of the problem space
2
Example How many grams are equal to 127.0 mg?
________ g
127.0 mg
77
Example 1
Use or create a conversion factor to compare what
you have to what you want
3 4
Example How many grams are equal to 127.0 mg?
1
g
?
________ g
127.0mg
mg
1000
Put the unit on bottom that you want to cancel
out!
The equivalent with these 2 units is 1 g 1000
mg A tip is to arrange the units first and then
fill in numbers later!
78
Example 1
Calculate the answer. Multiply across the top.
Multiply across the bottom of the expression.
Divide the bottom by the top
5
Example How many grams are equal to 127.0 mg?
1
g
.127
?
________ g
127.0 mg
mg
1000
Enter into the calculator 127 ? 1 ? 1000
79
Metric Conversion Factors

• Many students get confused where to put the
  number shown in the previous chart
• Select which unit is greater.
• Make that unit 1 and then determine how many
  smaller units are in the bigger unit.

Example Write a correct equivalent between kg
and g
1 kg 1000 g my way
OR .001Kg 1 g the other way
80
Try More Metric Equivalents
Example Write a correct equivalent between mL
and L
There are two options 1 L 1000 ml my
way 0.001 L 1 mL the other way
Example Write a correct equivalent between cm
and mm
There are two options 1 cm 10 mm
my way .1cm 1mm the other way
81
Multi-step problems

• There isnt always an equivalent that goes
  directly from where you are to where you want to
  go!
• With multi-step problems, its often best to plug
  in units first, then go back and do numbers.

82
Example 3
Example How many kilograms are equal to 345 cg?
_______ kg
345 cg
There is no direct equivalent between cg
kg With metric units, you can always get to the
base unit from any prefix! And you can always get
to any prefix from the base unit! You can go from
cg to g Then you can go from g to kg
83
Example 3
Example How many kilograms are equal to 345 cg?
g
kg
?
?
_______ kg
345 cg
cg
g
Go to the base unit
Go from the base unit
84
Example 3
Example How many kilograms are equal to 345 cg?
1
g
kg
1
?
?
_______ kg
345 cg
cg
100
1000
g
100 cg 1 g 1000 g 1 kg
Rememberthe goes with the base unit the 1
with the prefix!
85
Example 3
Example How many kilograms are equal to 345 cg?
g
kg
1
1
?
0.00345
?
_______ kg
345 cg
100
cg
1000
g
Enter into the calculator (345 ? 1 x 1) ? (100 x
1000)

86
You Try! 1
Example 0.250 kg is equal to how many grams?
87
You Try! 1
Example 0.250 kg is equal to how many grams?
1000
g
?
250.
______ g
0.250 kg
1
kg
1 kg 1000 g
Enter into the calculator 0.250 ? 1000 ? 1
88
Last One! NOT in YOUR NOTES
Example How many mL is equal to 2.78 L?
89
Example How many mL is equal to 2.78 L?
mL
1000
?
2780
______ mL
2.78 L
L
1
1 mL 0.001 L
Enter into the calculator 2.78 ? 1000 ? 1
90
Metric Volume Units

• To find the volume of a cube, measure each side
  and calculate length ? width ? height

• But most chemicals arent nice, neat cubes!
• Therefore, they defined 1 milliliter as equal to
  1 cm3 (the volume of a cube with 1 cm as each
  side measurement)

1 cm3
1 mL
91
You Try! 3
Example 147 cm3 is equal to how many liters?
92
You Try! 3
Example 147 cm3 is equal to how many liters?
Remembercm3 is a volume unit, not a length like
meters!
mL
1
1
L
?
?
0.147
_______ L
147 cm3
1
cm3
mL
1000
There isnt one direct equivalent 1 cm3 1 mL 1
L 1000 mL or .001L 1mL
Enter into the calculator 147 ? 1 ? 0.001 ? 1 ? 1
93
Section 1.4Scientific Notation
94
Scientific Notation

• Scientific Notation is a form of writing very
  large or very small numbers that youve probably
  used in science or math class before
• Scientific notation uses powers of 10 to shorten
  the writing of a number.

95
Writing in Scientific Notation

• The decimal point is put behind the first
  non-zero number
• The power of 10 is the number of times it moved
  to get there
• A number that began large (gt1) has a positive
  exponent a number that began small (lt1) has a
  negative exponent

96
Example 1
Example Write the following numbers in
scientific notation.
240,000 m 0.0000048 g
97
Example 1
5
240,000 m 0.0000048
2.4 ? 10 m
Example Write the following numbers in
scientific notation.
-6
6.5423 ? 10 g
The decimal is moved to follow the first non-zero
number The power of 10 is the number of times
its moved
98
Reading Scientific Notation

• A positive power of ten means you need to make
  the number bigger and a negative power of ten
  means you need to make the number smaller
• Move the decimal place to make the number bigger
  or smaller the number of times of the power of ten

99
Example 2
Example Write out the following numbers.
5.3 ? 107 m
53000000 m
100
Example 3
1.23 x 108
123000000 0.000987 0.000000045 480000000000 0.0000
0612
Example Write out the following numbers in
scientific notation.
9.87 x 10-4
4.5 x 10-8
4.8 x 1011
6.12 x 10-6
101
Example 3
.0000000034
3.4 ? 10-9 m 1.12 ? 105 m 2.347 ? 107 g 8.9 ?
10-3 g 7.23 ?10-12 m
Example Write out the following numbers in
ordinary notation.
112000
23470000
.0089
.00000000000723
102
HONORS ONLY Scientific Notation Significant
Digits

• Scientific Notation is more than just a short
  hand.
• Sometimes there isnt a way to write a number
  with the needed number of significant digits

unless you use scientific notation!
103
How to enter scientific notation numbers into the
calculator

• 1. Punch the digit number into your calculator.
• 2. Push EE or EXP button. (Do not use the
  x(times) button.
• 3. Enter the exponent number. Use the /-
  button to change its sign.

Example Multiply 6.0 x105 times 4.0 x103 on
your calculator. Your answer is
240000000 or 2.4 x 109