1. Chapter 2 $ ₤ ¥ L m kg ml mm μg + - * / yx
Chemistry 103
Chapter 2
$ ₤ ¥
L m kg ml mm μg
* / yx

2. General Course structure
Learning Tools
Atoms ---> Compounds ---> Chemical Reactions

3. Outline Mathematics of Chemistry (Measurements) Units
Significant Figures (Sig Figs)
Calculations & Sig Figs
Scientific Notation
Dimensional Analysis
Density

4. Importance of Units
Job Offer: Annual Salary = 1,000,000.

5. Measurements Two components – Numerical component and
Dimensional component

6. Everyday Measurements
You make a measurement every time you
Measure your height.
Read your watch.
Take your temperature.
Weigh a cantaloupe.

7. 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

8. 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.

9. Measurement in Chemistry
In chemistry we
Measure quantities.
Do experiments.
Calculate results.
Use numbers to report measurements.
Compare results to standards.
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10. Length Measurement Length Is measured using a meter stick.
Has the unit of meter (m) in the metric (SI) system.
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11. Inches and Centimeters
The unit of an inch is
equal to exactly 2.54
centimeters in the
metric system.
1 in. = 2.54 cm
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12. Volume Measurement Volume Is the space occupied by a substance.
Has the unit liter (L) in metric system.
1 L = qt
Uses the unit m3(cubic meter) in the SI system.
Is measured using a graduated cylinder.
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13. 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.
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14. 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.
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15. Units in the Metric System
In the metric (SI) system, one unit is used for each
type of measurement:
Measurement Metric SI
length meter (m) meter (m)
volume liter (L) cubic meter (m3)
mass gram (g) kilogram (kg)
time second (s) second (s)
temperature Celsius (C) Kelvin (K)

16. Metric Base Units

17. Learning Check
For each of the following, indicate whether the unit describes A) length, B) mass, or C) volume.

18. 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

19. Measured vs Exact numbers

20. 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

21. 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

22. Significant Figures

23. Measured numbers convey
Significant Figures
Digits in any measurement are known with certainty, plus one digit that is uncertain.
Measured numbers convey
*Magnitude
*Uncertainty
*Units

24. The Calculator Problem
7.8
3.8
Calculator Answer: ……
Is this a realistic answer?
Is it 2, 2.0, 2.1, 2.05, 2.06, 2.052, 2.053, , etc.? Which is it?
Answer must reflect uncertainty expressed in original measurements. Using Significant Figures.
We will come back to this later.

25. Rules for Significant Figures
It’s ALL about the ZEROs

26. Rules for Sig Figs
All non-zero numbers in a measurement are significant.
4573
4573 has 4 sig figs

27. Rules for Sig Figs All zeros between sig figs are significant. 23007
23007 has 5 sig figs

28. Rules for Sig Figs
In a number less than 1, zeros used to fix the position of the decimal are not significant.
has 2 sig figs

29. Rules for Sig Figs
When a number has a decimal point, zeros to the right of the last nonzero digit are significant
has 4 sig figs

30. Rules for Sig Figs _ 820000 meters - 3 sig figs 820000
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. _
meters sig figs

31. Practice Identifying Sig Figs

32. Significant Figures How many assuming all numbers are measured?

33. 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.
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34. Reading a Meter Stick
. l l l l l cm
The markings on the meter stick at the end of the orange line are read as
The first digit 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

35. 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

36. Learning Check . l8. . . . l . . . . l9. . . . l . . . . l10. . cm
What is the length of the red line?
1) cm
2) cm
3) cm

37. Solution
. l l l l l cm
The length of the red line could be reported as
2) cm
or 3) cm
The estimated digit may be slightly different. Both readings are acceptable.

38. Zero as a Measured Number
. l l l 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.

39. Significant Figures in Measured Numbers
Obtained from a measurement include all of the known digits plus the estimated digit.
Reported in a measurement depend on the measuring tool.

40. 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

41. 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

42. Sig Fig Rounding Example:
Round the following measured number to
4 sig figs:

43. 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

44. Practice Rounding Numbers

45. Significant Figures Round each to 3 sig figs

46. 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:
x = = (rounded)
4 SF SF calculator SF

47. 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.
one decimal place
two decimal places
26.54 calculated answer
answer with one decimal place

48. Math operations with Sig Figs

49. Report Answer with Correct Number of Sig Figs
A) x =
B) =
C) =
D) =
45.68

50. 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.

51. When Math Operations Are Mixed
_____5.681g_____ =
(52.15ml ml)
carry out the operations in parenthesis first, and round according to the rules for that type of operation.

52. When Math Operations Are Mixed
_____5.681g_____ = g
(52.15ml ml) ml
carry out the operations in parenthesis first, and round according to the rules for that type of operation.

53. 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.
( ) x ( )
( ) x (322)

54. Back To The Calculator Problem
7.8
3.8
Calculator Answer: ……
Is this a realistic answer?
Is it 2, 2.0, 2.1, 2.05, 2.06, 2.052, 2.053, , etc.? Which is it?
Answer must reflect uncertainty expressed in original measurements.

55. Scientific Notation Scientific notation
Is used to write very large or very small numbers
The width of a human hair, m is written as:
8 x 10-6 m
A large number such as
s is written as:
2.5 x 106 s
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56. Scientific Notation
A number in scientific notation contains a coefficient
(1 or greater, less than 10) and a power of 10.
coefficient power of ten coefficient power of ten
x x
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.
= x = x 10-3
4 spaces left spaces right

57. Some Powers of Ten

58. Comparing Numbers in Standard and Scientific Notation
Standard Format Scientific Notation
Diameter of Earth m
Mass of a human
68 kg
Length of a pox virus cm

59. Comparing Numbers in Standard and Scientific Notation
Standard Format Scientific Notation
Diameter of Earth
m x 107 m (3 sig figs)
Mass of a human
68 kg x 101 kg (2 sig figs)
Length of a pox virus
cm 3 x 10-5 cm (1 sig fig)
NOTE: The Coefficient identifies or indicates the number of significant figures in the measurement.

60. Defining Conversion Factors
Dimensional Analysis
Defining Conversion Factors

61. 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

62. 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)

63. Dimensional Analysis
If we assume there are exactly 365 days in a year, how many seconds are in one year?
? seconds = 1 year

64. Dimensional Analysis
A problem solving method in which the units (associated with numbers) are used as a guide in setting up the calculations.
Conversion Factor

65. Exact vs Measured Relationships
Metric to Metric – exact
English to English – exact
Metric to English –
typically measured
(must consider sig figs)

66. English to Metric Conversion Factors

67. Dimensional Analysis What is 165 lb in kg?
STEP 1 Given: 165 lb Need: kg
STEP 2 Plan
STEP 3 Equalities/Factors
1 kg = lb
2.205 lb and kg
1 kg lb
STEP 4 Set Up Problem
? kg = 165 lb

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)

69. 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

70. Learning Check
If a bucket contains 4.65L of water. How many gallons of water is this?
(1 gallon = 4qts, 1L = 1.057qt)

71. 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)

72. 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!

73. Examples Convert 127.4 cm3 to m3. (100cm = 1m)
Convert .572 miles2 to km2.
(1km = .621miles)

74. Displacement volume for a stock engine in a 1984 Corvette is specified at 350 in3. What is the displacement in L?

75. 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 kg fat
100 kg mass
= 9.5 kg fat
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76. 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)

77. Density Density = Mass/Volume
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 g and a volume of 6.64 mL. What is its density?

78. Density Density = Mass/Volume
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 g and a volume of 6.64 mL. What is its density?
Density = 59.24g = g/mL
6.64mL

79. Densities of Common Substances
Is Density a Physical or a Chemical Property?

80. Measuring Density in Lab

81. 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) g/cm B) 6.0 g/cm C) 380 g/cm3
25.0 mL mL
object

82. 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.
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83. 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 W K V V W K V W K

84. 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) g/cm b) g/cm c) g/cm3

85. 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 g and mL
factors 1 mL g

86. 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?

87. DENSITY PRACTICE

88. Learning Check
The density of octane, a component of gasoline, is g/mL. What is the mass, in kg, of 875 mL of octane?
A) kg B) 614 kg C) kg

89. 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
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90. Temperature Scales

91. 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 
TF = 1.8 (34.8°C) °
exact tenths exact
= °
= 94.6°F
tenths
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92. 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) or 1.8 (oC) + 32
oC = 5/9(oF – 32) or 1/1.8 (oF – 32)
9/5 = 1.8/ or 5/9 = 1/1.8