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 1.1—Observations & Measurements

4. Taking Observations Qualitative descriptions Color Texture
Formation of solids, liquids, gases
Heat changes
Anything else you observe

5. Clear versus Colorless
Colorless does not describe transparency
Words to describe transparency
Clear
Cloudy
Opaque
See-through
Parts are see-through with solid “cloud” in it
Cannot be seen through at all
You can be clear & colored
You need to describe the color of the solution & the cloud if it’s cloudy
(examples: blue solution & white cloud or colorless solution and blue solid)

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 the following in terms of transparency words & colors
Whole Milk
Opaque & white
Water
Clear & Colorless

8. Gathering Data Quantitative measurements
International System of Units (SI Units) are used
Quantity
Unit
Instrument used
Mass (how much stuff is there)
Kilogram (kg)
Balance
Volume (how much space it takes up)
Liters (L)
Graduated cylinder
Temperature (how fast the particles are moving)
Kelvin (K) or Celsius (°C)
Thermometer
Length
Meters (m)
Meter stick
Time
Seconds (sec)
stopwatch
Energy
Joules (J)
(Measured indirectly)

9. Measurement tool for Mass

10. Measurement Tool for Temperature

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 it’s in-between lines
Write down a “0” if it’s on the line
5 mL 10 15 20
25 mL
5 mL 10 15 20
25 mL
Remember:
Always read liquid levels from the bottom of the meniscus (the bubble at the top)
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 it’s in-between lines
Write down a “0” if it’s on the line
5 mL 10 15 20
25 mL
5 mL 10 15 20
25 mL
Example:
Read the measurements
It’s in-between the 10 & 11 line
10.5 mL
It’s on the 12 line
12.0 mL

13. Measurement Tool for Volume

14. Measurement Tool for Length
1.5 cm
1.95 cm

15. Uncertainty in Measurement
Example:
Read the measurements 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

16. Uncertainty in Measurement
Example:
Read the measurements
It’s right on the 6.9 line
6.90 1 2 3 4 5 6 7 8
It’s between the 3.8 & 3.9 line
3.85 1 2 3 4 5 6 7 8

17. HINT:Uncertainty in Measurement
Choose the right instrument
If you need to measure out 5 mL, don’t choose the graduated cylinder that can hold 100 mL. Use the 10 or 25 mL cylinder
The smaller the measurement, the more an error matters—use extra caution with small quantities
If you’re measuring 5 mL & you’re off by 1 mL, that’s a 20% error
If you’re measuring 100 mL & you’re off by 1 mL, that’s only a 1% error

18. Describe each group’s data as not precise, precise or accurate
Gathering Data
Multiple trials help ensure that you’re results weren’t a one-time fluke!
Precise—getting consistent data (close to one another)
Accurate—getting the “correct” or “accepted” answer consistently
Example:
Describe each group’s data as not precise, precise or accurate
Correct value

19. Precise & Accurate Data
Precise, but not accurate
Correct value
Example:
Describe each group’s data as not precise, precise or accurate
Precise & Accurate
Correct value
Not precise
Correct value

20. Can you be accurate without precise?
This group had one value that was almost right on…but can we say they were accurate?
Correct value
No…they weren’t consistently correct. It was by random chance that they had a result close to the correct answer.

21. Can you be accurate without precise?
This group had one value that was almost right on…but can we say they were accurate?
Correct value

22. You Try! Accepted Value = bulls-eye
*not accurate but precise *accurate & precise *not precise nor accurate

23. 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 g.
Group 1
Group 2
Group 3
Group 4
1.01 g g g
2.05 g
1.03 g g g
0.23 g
0.99 g g g
0.75 g
Average g

24. Percent Error A calculation designed to determine accuracy
% Error = |Accepted - Experimental| x 100
|Accepted|

25. 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 –1.50|x 100
1.87
= 20%

26. Section 1.2—Converting Units

27. Converting Units
Often, a measurement is more convenient in one unit but is needed in another unit for calculations.
Dimensional Analysis is a method for converting unit

28. Equivalents
Dimensional Analysis uses equivalents…called Conversion Factors
1 foot = 12 inches or 4 quarters = 1 dollar
What happens if you put one on top of the other?
1 foot
12 inches
4 quarters
1 dollar

29. Equivalents
Dimensional Analysis uses equivalents called conversion factors…what are they?
1 foot = 12 inches
What happens if you put one on top of the other?
When you put two things that are equal on top & on bottom, they cancel out and equal 1
1 foot
12 inches
= 1

30. Dimensional Analysis
Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement!
27 inches  1
= 27 inches

31. Dimensional Analysis
Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement!
27 inches  1
= 27 inches
1 foot
12 inches
27 inches 
= 2.25 feet

32. Dimensional Analysis
Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement!
Same physical meaning…it’s the same length either way!
27 inches  1
= 27 inches
1 foot
12 inches
27 inches 
= 2.25 feet
Remember…this equals “1”

33. Canceling
Anything unit that is identical on the top and the bottom of an expression will cancel
When canceling units…just cancel the units…
1 foot
12 inches
27 inches 

34. Common Equivalents = = = = = = = 1 ft 12 in 1 in 2.54 cm 1 min 60 s
1 hr =
3600 s
1 quart (qt) =
0.946 L
4 pints =
1 quart =
1 pound (lb)
454 g

35. Steps for using Dimensional Analysis1
Write down your given information
Write down an answer blank and the desired unit on the right side of the problem space 2
Use conversion factors to cancel unwanted unit and get desired unit. 3
Calculate the answer…multiply across the top & divide across the bottom of the expression 4

36. How many grams are equal to 1.25 pounds?
Example #1 1
Write down your given information
Example:
How many grams are equal to 1.25 pounds?
1.25 lb

37. How many grams are equal to 1.25 pounds?
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 1.25 pounds?
1.25 lb
= ________ g

38. How many grams are equal to 1.25 pounds?
Example #1
Use equivalents to cancel unwanted unit and get desired unit. 3
Example:
How many grams are equal to 1.25 pounds?
454 g
1.25 lb 
= ________ g 1 lb
Put the unit on bottom that you want to cancel out!
The equivalent with these 2 units is: 1 lb = 454 g
A tip is to arrange the units first and then fill in numbers later!

39. How many grams are equal to 1.25 pounds?
Example #1
Calculate the answer…multiply across the top & divide across the bottom of the expression 4
Example:
How many grams are equal to 1.25 pounds?
454 g 
568
1.25 lb
= ________ g 1 lb
Enter into the calculator: 1.25  454  1

40. Metric Prefixes Metric prefixes can be used to form
conversion factors as well
First, you must know the common metric
prefixes used in chemistry

41. Metric Prefixes = = = = = =
tera- (T) =
1,000,000,000,000
giga- (G) =
1,000,000,000
mega- (M) =
1,000,000
BASE UNITS: These prefixes work with any base unit, such as grams (g), liters (L), meters (m), seconds (s), etc.
kilo- (K) =
1000
hecto- (h) =
100
deka- (da) = 10
Base (1)  =
deci- (d)
0.1 =
centi- (c)
0.01 =
milli- (m)
0.001 =
micro- (μ) =
nano (n)
pico (p) =

42. Converting with the Metric System By Moving a Decimal Point
From Kilo to Milli: Locate the known prefix and the one you need to convert to on the chart. Move the direction and the number of places it takes to go from the known to the other.
If using the other prefixes, remember that there is a difference of 1000 or 3 places between each.

43. Examples 150 ml Convert 15 cl into ml Convert 6000 mm into Km
Convert 1.6 Dag into dg
Convert 3.4 nm into m
150 ml
.006 Km
160 dg m

44. Metric Activity: Answers
5 pm
4 x10-9 m & 4 nm
1 x 10-6 m
4 x m
10 mm & 1 cm 1m
5 km & 5 x 103
1Mm
1Gm

45. 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

46. 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

47. Metric Volume Units
To find the volume of a cube, measure each side and calculate: length  width  height
height
width
length
But most chemicals aren’t 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

48. How many grams are equal to 127.0 mg?
Example #2: Using D.A.
Example:
How many grams are equal to mg?
127.0 mg
= ________ g
You want to convert between mg & g
1 g = 1000 mg my way
1 mg = g the other way

49. How many grams are equal to 127.0 mg?
Example #2
Example:
How many grams are equal to mg? 1 g
127.0 mg 
0.1270
= ________ g
1000 mg
Enter into the calculator:   1
You may be able to do this in your head…but practice the technique on the more simple problems so that you’ll be a dimensional analysis pro for the more difficult problems (like stoichiometry)!

50. Multi-step problems
There isn’t always an equivalent that goes directly from where you are to where you want to go!
With multi-step problems, it’s often best to plug in units first, then go back and do numbers.

51. How many kilograms are equal to 345 cg?
Example #3
Example:
How many kilograms are equal to 345 cg?
345 cg
= _______ kg
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”

52. How many kilograms are equal to 345 cg?
Example #3
Example:
How many kilograms are equal to 345 cg? g kg
345 cg  
= _______ kg cg g
Go to the base unit
Go from the base unit

53. How many kilograms are equal to 345 cg?
Example #3
Example:
How many kilograms are equal to 345 cg? 1 g 1 kg
345 cg  
= _______ kg
100 cg
1000 g
100 cg = 1 g
1000 g = 1 kg
Remember—the # goes with the base unit & the “1” with the prefix!

54. How many kilograms are equal to 345 cg?
Example #3
Example:
How many kilograms are equal to 345 cg? 1 g 1 kg
345 cg  
= _______ kg
100 cg
1000 g
Enter into the calculator: (345  1 x 1)  (100 x 1000)

55. 0.250 kg is equal to how many grams?
You Try! #1
Example:
0.250 kg is equal to how many grams?

56. 0.250 kg is equal to how many grams?
You Try! #1
Example:
0.250 kg is equal to how many grams?
1000 g
0.250 kg 
= ______ g
250. 1 kg
1 kg = 1000 g
Enter into the calculator:  1000  1

57. You Try! #2
Example:
How many mL is equal to 2.78 L?

58. You Try! #2  1000 mL 2.78 L = ______ mL 1 L 2780 1 mL = 0.001 L
Example:
How many mL is equal to 2.78 L?
1000 mL
2.78 L 
= ______ mL
2780 1 L
1 mL = L
Enter into the calculator: 2.78  1000  1

59. 147 cm3 is equal to how many liters?
You Try! #3
Example:
147 cm3 is equal to how many liters?

60. 147 cm3 is equal to how many liters?
You Try! #3
Example:
147 cm3 is equal to how many liters?
Remember—cm3 is a volume unit, not a length like meters! 1 mL 1 L
147 cm3  
= _______ L
0.147 1
cm3
1000 mL
There isn’t one direct equivalent
1 cm3 = 1 mL
1 L = 1000 mL or .001L = 1mL
Enter into the calculator: 147  1   1  1

61. How many milligrams are equal to 0.275 kg?
Let’s Practice #4
Example:
How many milligrams are equal to kg?

62. How many milligrams are equal to 0.275 kg?
Let’s Practice #4
Example:
How many milligrams are equal to kg?
1000 g
1000 mg
0.275 kg  
= _______ mg
275,000 1 kg 1 g
There isn’t one direct equivalent
1 kg = 1000 g
1 g = 1000mg or 1 mg = g
Enter into the calculator:  1000  1000  1

63. Section 1.3—Significant Digits

64. 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
1.00 g
3.0 mL
= g/mL
how can the answer be known to and infinite number of decimal places?
If the actual measurements were only taken to 1 or 2 decimal places…
It can’t!

65. Significant Digits
A significant digit is anything that you measured in the lab—it 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

66. Significant Digit Rules1
All measured numbers are significant 2
All non-zero numbers are significant 3
Middle zeros are always significant
Trailing zeros are significant if there’s a decimal place 4 5
Leading zeros are never significant

67. All the fuss about zeros
Middle zeros are important…we know that’s 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 it’s indicating how precise the measurement was.
125.0 mL
125.0 is between 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 precision…therefore they are not significant m
m is the same as 127 mm

68. 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

69. 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

70. 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

71. 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
240.
370.0
Example:
Count the number of significant figures in each number

72. 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
240.
370.0
3 significant digits
Example:
Count the number of significant figures in each number
3 significant digits
4 significant digits
4 significant digits

73. Importance of Trailing Zeros
Just because the zero isn’t “significant” doesn’t mean it’s not important and you don’t have to write it!
“250 m” is not the same thing as “25 m” just because the zero isn’t significant
The zero not being significant just tells us that it’s a broader range…the 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

74. Count the number of significant figures in each number
Let’s Practice
1020 m g
100.0 m
10240 mL g
Example:
Count the number of significant figures in each number

75. Count the number of significant figures in each number
Let’s Practice
1020 m g
100.0 m
10240 mL 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

76. 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!

77. 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.
( )/2.0 = _______

78. 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 g g g
This answer assumes the missing digit in the problem is a zero…but we really don’t have any idea what it is

79. 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 g g
3 decimal places
Lowest is “2”
2 decimal places g
Answer is rounded to 2 decimal places
16.75 g

80. 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 mL mL
8.008 mL
This answer assumes the missing digit in the problem is a zero…but we really don’t have any idea what it is

81. 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 mL mL
2 decimal places
Lowest is “2”
3 decimal places
8.008 mL
Answer is rounded to 2 decimal places
8.01 mL

82. 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
= g/mL

83. 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
= g/mL
Answer is rounded to 2 sig digs
2 significant digits
3.8 g/mL

84. 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

85. 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

86. Compute & write the answer with the correct number of sig digs
Let’s Practice #1
Example:
Compute & write the answer with the correct number of sig digs
0.045 g g

87. Compute & write the answer with the correct number of sig digs
Let’s Practice #1
Example:
Compute & write the answer with the correct number of sig digs
0.045 g 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!

88. Compute & write the answer with the correct number of sig digs
Let’s Practice #2
Example:
Compute & write the answer with the correct number of sig digs
2.5 g/mL
 23.5 mL

89. Compute & write the answer with the correct number of sig digs
Let’s 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!

90. Compute & write the answer with the correct number of sig digs
Let’s Practice #3
Example:
Compute & write the answer with the correct number of sig digs
1.000 g
2.34 mL

91. Compute & write the answer with the correct number of sig digs
Let’s 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
= g/mL
Answer is rounded to 3 sig digs
3 significant digits
0.427 g/mL
Multiplication & Division use number of significant digits!

92. Compute & write the answer with the correct number of sig digs
Let’s Practice #4
Example:
Compute & write the answer with the correct number of sig digs
1.704 m
 2.75 m

93. Compute & write the answer with the correct number of sig digs
Let’s 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!

94. Section 1.4—Scientific Notation

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

96. 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 (>1) has a positive exponent & a number that began small (<1) has a negative exponent

97. Write the following numbers in scientific notation.
Example #1 m g g m
Example:
Write the following numbers in scientific notation.

98. Write the following numbers in scientific notation.
Example #1 4 m g g m
 10 m
Example:
Write the following numbers in scientific notation. -5
 10 g 2
 10 m -7
7.532  10 m
The decimal is moved to follow the first non-zero number
The power of 10 is the number of times it’s moved

99. Write the following numbers in scientific notation.
Example #1 4 m g g m
 10 m
Example:
Write the following numbers in scientific notation. -5
 10 g 2
 10 m -7
7.532  10 m
Large original numbers have positive exponents
Tiny original numbers have negative exponents

100. 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

101. Write out the following numbers.
Example #2
1.37  104 m
2.875  102 g
8.755  10-5 g
7.005 10-3 m
Example:
Write out the following numbers.

102. Write out the following numbers.
Example #2
1.37  104 m
2.875  102 g
8.755  10-5 g
7.005 10-3 m
13700 m
Example:
Write out the following numbers.
287.5 g m m
Move the decimal “the power of ten” times
Positive powers = big numbers. Negative powers = tiny numbers

103. Scientific Notation & Significant Digits
Scientific Notation is more than just a short hand.
Sometimes there isn’t a way to write a number with the needed number of significant digits
…unless you use scientific notation!

104. Take a look at this… Write 120004.25 m with 3 significant digits
Remember…120 isn’t the same as ! Just because those zero’s aren’t significant doesn’t mean they don’t have to be there! This answer isn’t correct!

105. Let’s Practice 0.0007650 g with 2 sig figs 120009.2 m with 3 sig figs
mL with 4 sig figs
g with 3 sig figs
Example:
Write the following numbers in scientific notation.
1.34 × 10-3 g
2.009  10-4 mL
3.987  105 g
2.897  103 m
Example:
Write out the following numbers

106. Let’s Practice 0.0007650 g with 2 sig figs 7.7 × 10-4 g
m with 3 sig figs
mL with 4 sig figs
g with 3 sig figs
7.7 × 10-4 g
Example:
Write the following numbers in scientific notation.
1.20 × 105 g
2.391 × 105 g
7.80 × 10-6 g
1.34 × 10-3 g
2.009  10-4 mL
3.987  105 g
2.897  103 m g
Example:
Write out the following numbers mL g
2897 m