1. Chemistry and Math!

2. Precision and Accuracy!
Accuracy- How close a measurement is to the accepted reference or theoretical value.

3. Precision and Accuracy!
Precision - How close a measurement is to subsequent measurements

4. Accuracy

5. Accuracy and Precision

6. Percent Error!

7. Percent Error (absolute value)
| A | x = answer in %
0 = Observed value
A = Actual value

8. Precision and Accuracy Practice
1. Measured Mass = 3.80 g
2. Theoretical mass = 3.92 g
Answer = 3.06%

9. Precision and Accuracy Practice
1. Measured Mass = g
2. Theoretical mass = g
Answer = 16.52

10. Precision and Accuracy Practice
1. Measured Mass =
2. Theoretical mass =42.913
Answer = .09%

11. Precision and Accuracy Practice
1. Measured Mass =.8696 ug
2. Theoretical mass = ug
Answer = 35.35

12. SI Units

13. SI Units
Measurement system in which different size units are related to each other by multiples of 10

14. System International or SI Units
Name given to the old metric system
Consists of seven base units

15. (m)

16. Kilogram

17. Density, Volume and Mass

18. Density, Volume and Mass
Density - the concentration of matter
Weight - gravitational pull exerted on a substance
Mass - the amount of matter
Volume -the amount matter will displace or fill up a container

19. Density Measurement A solid is measured in grams/cm3
A liquid is measured in grams/mL
A gas is measured in grams /Liter

20. Density, Volume and Mass
Volume = Mass
Density
Mass = (Volume) (Density)
Density = Mass Volume

21. Density, Volume and Mass
Volume = mL
Mass = Grams
Density = Grams/ml
(1 ml = 1 cm3 )

22. Density, Volume and Mass
Problem:
1. Density = 11.3 grams/mL
2. Mass = 51 grams
3. Volume of Displacement ?
Answer = 4.51 mL

23. Percent Yield
Total amount of product produced in a reaction as compared to the theoretical yield.
amount produced
theoretical yield x 100

24. Percent Yield
Total amount produced is 100 grams, the theoretical yield is 125 grams.
100 grams
125 grams x 100
80% yield

25. Measurement

26. Instrument Precision
Determined by the sensitivity of the instrument being used.
Determined by the accuracy of the individual using the measurement instrument.

27. Instrument Precision Platform Balance +/- 0.1 gram
Analytical Balance +/ gram
10 ml grad. cylinder +/- 0.1 ml
50 ml burette +/ ml

28. Significant Digits

29. Significant Digits The precision of the measurement used in chemistry.
Indicates all the numbers that are known with certainty plus one that is estimated.
Example:

30. Significant Digits Rules
Only apply to measurement
Numbers that DO NOT apply:
One dozen (counted number)
Thirty kids (counted number)
12 inches = 1 foot (Definition)
60 seconds - 1 minute (Definition)

31. Why Significant Digits ?
10th of a gram
1000th of a gram

32. Why Significant Digits ?
100,000 kilograms
10th of a gram

33. Significant Digits Rules
All nonzero digits are significant
Example:
(five significant digits)
22.3 (three significant digits)

34. Significant Digits Rules
Zeros after the decimal point are significant
Example:
32.0 (three significant digits)
2.003 (four significant digits)

35. Significant Digits Rules
Zeros between nonzero digits are significant
Example:
7008 (four significant digits)
1,400,002 (seven significant digits)
(five significant digits)

36. Significant Digits Rules
Leading zeroes or place holders are not significant.
Example:
(two significant digits)
(four significant digits)

37. Significant Digits Rules
Zeroes at the end before the decimal are not significant.
Example:
25,000 (two significant digits)
13,800 (three significant digits)

38. Rule Review Only apply to measurement
All nonzero digits are significant
Include zeros between nonzero digits
All other zeroes are significant unless they are place holders. This includes a measurement having a decimal point.

39. Rule Review When determining if the zero(s) are significant or not.
Are they telling you how small the number is? (not-significant)
significant digit
Are they telling you that the measurement scale is for large objects? (not –significant)
155,000 – 3 significant digits

40. Significant Digits Practice
9.370 grams
(four significant digits)
63, grams
(seven significant digits) ml
(five significant digits)

41. Significant Digits Practice
9,000 grams
(one significant digits)
grams
(two significant digits)
5, ml
(six significant digits)

42. Significant digits in calculations
In multiplication and division the answer must contain the fewest significant figures.
Example
4.38 meters x 3.1 meters = or 14 m2
2.85 cm x 7.2 cm = or 21 cm2

43. Significant digits in calculations
In addition and subtraction the result must have the same number of decimal places as the one with the fewest decimal places.
Example
4.38 meters meters = or 7.5 m
2.85 cm cm = or cm

44. QUIZ You have conducted an experiment combining Fluorine gas with Lithium metal. The expected combination should yield 10 grams of Lithium Chloride.
Determine the percent error for each of the two experiments.
Determine the density of each amount given below (A or B) if the mass is correct and the displacement equals 5 mL
Write out the number of significant digits for the four problems on the board
A B
13 grams 17 grams
16 grams 14 grams

45. Rule Review Only apply to measurement
All nonzero digits are significant
Include zeros between nonzero digits
All other zeroes are significant unless they are place holders. This includes a measurement having a decimal point.

46. Rule Review When determining if the zero(s) are significant or not.
Are they telling you how small the number is? (not-significant)
significant digit
Are they telling you that the measurement scale is for large objects? (not –significant)
155,000 – 3 significant digits

47. Scientific Notation

48. Scientific Notation
A mathematical process for writing very large numbers in an exponential factor so the number is more manageable.

49. Scientific Notation
A mathematical process for writing very large numbers in an exponential factor so the number is more manageable.

50. Scientific Notation
It is a number expressed between 1 and 10 multiplied by an exponential factor (raised to some power)
Example:
= 6 x 10-7 =
3.34 x 1022

51. Why Scientific Notation?
Easier to read and write very large and small numbers
Clearly displays the number of significant digits
Easier to work with in multiplication and division

52. Scientific Notation Equivalents
1 = 1.00 x 100 (all whole numbers)
10 = 1.00 x 101
100 = 1.00 x 102
1,000 = 1.00 x 103
10,000 = 1.00 x 104
100,000 = 1.00 x 105

53. Scientific Notation Equivalents
.1 = 1.00 x 10-1
.01 = 1.00 x 10-2
.001 = 1.00 x 10-3
.0001 = 1.00 x 10-4
= 1.00 x 10-5

54. Proper Notation Format
In chemistry ALL answers in Scientific Notation MUST be in proper notation format:
One whole number
Two decimal places
1.00 x 104

55. Reverse Number Line

56. Scientific Notation Problems!
5.30 x 10-3
Answer:
7.5 x 105
Answer: 750,000.0

57. Scientific Notation Problems!
3.63 x 104
Answer: 36,300.00
32.5 x 108
Answer: 3,250,000,000.00

58. Scientific Notation Problems!
0.078
Answer: 7.80 x 10-2
78,000.00
Answer: 7.80 x 104
0.0078
Answer: 7.80 x 10-3

59. Reverse Number Line

60. Scientific Notation in Mathematical functions
Rules of Function
In addition and subtraction the exponents must be equal
In multiplication the exponents are added
In division the exponents are subtracted

61. Scientific Notation in Mathematical functions
1.00 x x 103
1.00 x x 102
11.0 x 102 or
1.10 x 103

62. Scientific Notation in Mathematical functions
1.00 x x 103
1.00 x x 102
x 102

63. Scientific Notation in Mathematical functions
(1.00 x 102) x ( 1.00 x 103)
(1.00 x 1.00) ( )
1.00 x 105

64. Scientific Notation in Mathematical functions
(1.00 x 102) / ( 1.00 x 103)
(1.00 / 1.00) ( )
1.00 x 10-1

65. Practice

66. Scientific Notation in Mathematical functions
2.00 x x 102
2.00 x x 103
Answer: x 103

67. Scientific Notation in Mathematical functions
5.00 x x 103
5.00 x x 104
Answer: x 104

68. Scientific Notation Problems!
(3.55 x 104 ) x (3.55 x 103 )
(3.55 x 3.55 ) x ( )
Answer: x or
1.26 x 108

69. Scientific Notation Problems!
(6.22 x ) / (8.4 x 10-4 )
(6.22 / 8.4 ) ( )
Answer: 0.74 x or
7.40 x 101

70. Scientific Notation Problems!
(6.22 x ) + (8.40 x 10-4 )

71. Scientific Notation Problems!
(3.55 x 104 ) - (3.55 x 103 )

72. Scientific Notation in Mathematical functions
(2.0 x 106) / ( 1.0 x 103)

73. Scientific Notation in Mathematical functions
(3.0 x 104) x ( 1.0 x 107)

74. Perform the following operations
2.00 x x 3.00 x 10-4
2.00 x 105 x 3.00 x 107
(6.22 x 102 ) / (8.41 x 104 )
(4.22 x ) / (5.42 x 10-7 )
5.00 x x 105
3.00 x x 104
4.00 x x 104
2.00 x x 103

75. Perform the following operations
3.00 x x 1.00 x 10-4
5.00 x x 7.00 x 107
(9.22 x 102 ) / (7.41 x 104 )
(8.22 x ) / (5.42 x 10-7 )
7.00 x x 105
5.00 x x 104
5.00 x x 104
4.00 x x 103 B
3.00 x x 3.00 x 10-5
7.00 x 104 x 3.00 x 107
(9.11 x 103 ) / (7.41 x 105 )
(7.32 x ) / (2.42 x 10-6 )
4.00 x x 105
3.00 x x 104
4.00 x x 104
2.00 x x 103

76. Conversion factors

77. Conversion Factors Ratio between measurements and their units
3 feet = 1 yard
1 gram = 1, mg
ug - 1 mg.

78. Dimensional Analysis

79. Dimensional Analysis Method of managing multiple levels of conversion
Used to organize solutions to physics and chemistry problems

80. Dimensional Analysis (grid system)

81. Dimensional Analysis (definition)
100 cm 1 m
1 m cm

82. Dimensional Analysis
2 meters = X mm
1000 mm = 1 m

83. Dimensional Analysis (ratio system)
2 meters = X mm
1000 mm = 1 m
x =

84. Dimensional Analysis
2 mm = x Km
1000 mm = 1 m
1000 m = 1 Km

85. Dimensional Analysis 1.2 x 104 mm = x Km 1.00 x 103 mm = 1 m
1.00 x 103 m = 1 Km

86. Compound Calculations
Utilize derived formulas to determine the resulting calculations.
Utilize dimensional analysis to determine the appropriate units

87. Compound Calculations
Example
What is the area of a rectangular that is 10.3m long and 3.7m wide. Provide the answer in cm2.
Area = length x width
100cm = 1 m

88. Dimensional Analysis Area = length x width
What is the area of a rectangular that is 10.3m long and 3.7m wide. Provide the answer in cm2.
Area = length x width

89. Dimensional Analysis Area = length x width
What is the area of a rectangular that is 10.3m long and 3.7m wide. Provide the answer in cm2.
Area = length x width

90. Dimensional Analysis Practice
Example
What is the average speed of an object that travels 1856 meters in 900 seconds. Provide the answer in Kilometers.
Average speed = distance / time
1000 m = 1 Km

91. Average speed = distance / time
Dimensional Analysis
What is the average speed of an object that travels 1856 meters in 900 seconds. Provide the answer in Kilometers.
Average speed = distance / time

92. Average speed = distance / time
Dimensional Analysis
What is the average speed of an object that travels 1856 meters in 900 seconds. Provide the answer in Kilometers.
Average speed = distance / time

93. Dimensional Analysis Practice
Example
What is the average acceleration of an object that travels 956 meters in 200 seconds. Provide the answer in Kilometers.
Average speed = distance / time
Acceleration = Average speed / time

94. Dimensional Analysis Practice
What is the average acceleration of an object that travels 956 meters in 200 seconds. Provide the answer in Kilometers.
956 m Km
200 s s 1000 m

95. Dimensional Analysis Practice
What is the average acceleration of an object that travels 9.56 x 102 meters in 2.00 x 102 seconds. Provide the answer in Kilometers (1.00 x 103 meters = 1 kilometer) .

96. Dimensional Analysis Practice
What is the average acceleration of an object that travels 9.56 x 102 meters in 2.00 x 102 seconds. Provide the answer in Kilometers.
2.39 x Km/s2

97. Complex Compound Calculations Example
A specific type of ore contains 10 grams of gold per 1000 kg. of ore. If gold is worth $400 an ounce, what mass of ore must be mined to obtain $ 1,000,000?
(28.35 grams = 1 ounce)

98. Dimensional Analysis Example
A specific type of ore contains 10 grams of gold per 1000 kg. of ore. If gold is worth $400 an ounce, what mass of ore must be mined to obtain $ 1,000,000?
(28.35 grams = 1 ounce)
$1 x oz AU g kg ore $ oz g AU

99. Dimensional Analysis Example
A specific type of ore contains 10 grams of gold per 1000 kg. of ore. If gold is worth $400 an ounce, what mass of ore must be mined to obtain $ 1,000,000?
(28.35 grams = 1 ounce)
$1 x oz AU g kg ore $ oz g AU
7.09 x 106 kg ore

100. A
What is the average speed of an object that travels 2.03 x 102 meters in 1.20 x 103 seconds. Provide the answer in Kilometers. speed = dist / time 1000 meters = 1 kilometer . B
What is the average speed of an object that travels 3.09 x 104 meters in 2.31 x 103 seconds. Provide the answer in Kilometers. speed = dist / time 1000 meters = 1 kilometer

101. Perform the following operation using Dimensional Analysis and Scientific notation.
What is the average speed of an object that travels 2.03 x 102 meters in 1.20 x 103 seconds. Provide the answer in Kilometers. speed = dist / time 1000 meters = 1 kilometer B
What is the average speed of an object that travels 3.09 x 104 meters in 2.31 x 103 seconds. Provide the answer in Kilometers. speed = dist / time 1000 meters = 1 kilometer

102. End Module 2

103. A B 13 grams 17 grams 14 grams 12 grams 16 grams 13 grams
QUIZ You have conducted an experiment combining Chlorine gas with Sodium metal. The expected combination should yield 15 grams of Sodium Chloride. Determine the percent error for each of your three experiments and the overall average of the total experiments conducted.
A B
13 grams 17 grams
14 grams 12 grams
16 grams 13 grams

104. A B 13 grams 17 grams 14 grams 12 grams 16 grams 13 grams
QUIZ You have conducted an experiment combining Chlorine gas with Sodium metal. The expected combination should yield 15 grams of Sodium Chloride. Determine the percent error for each of your three experiments and the overall average of the total experiments conducted.
A B
13 grams 17 grams
14 grams 12 grams
16 grams 13 grams

105. Density, Volume and Mass
Problem:
1. Density = 14.4 grams/mL
2. Mass = ? Grams
3. Volume = 6.2 mL
Answer = grams

106. Density, Volume and Mass
Problem:
1. Density = ? Grams/mL
2. Mass = 35 grams
3. Volume = 5.4 mL
Answer = 6.48 grams/mL

107. Test Review Properties of Matter Division of Matter States of Matter
Percent Error
Significant Digits
Scientific Notation
Density
Bridge Unit Analysis

108. Dimensional Analysis Practice
Example
What is the average acceleration of an object that travels 852 meters in 145 seconds. Provide the answer in Kilometers per minute
Average speed = distance / time
Acceleration = Average speed / time

109. Determining Conversion Factors
Ratio and proportions
24 hours = 1 day ~ 12 hours = Y days
1 x 12 = 24 x Y
12 = 24Y
Y = 12/24
Y = .5 days

110. Determining Conversion Factors
Ratio and proportions
3 feet = 1 yard ~ 2 feet = Y yards
1 x 2 = 3 x Y
2 = 3Y
Y = 2/3
Y = .67 yards