Chemistry and Math!

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

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

Accuracy

Accuracy and Precision

Percent Error!

Percent Error (absolute value) | A | x 100 = answer in % 0 = Observed value A = Actual value

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

Precision and Accuracy Practice 1. Measured Mass = 18.75 g 2. Theoretical mass = 22.46 g Answer = 16.52

Precision and Accuracy Practice 1. Measured Mass = 42.875 2. Theoretical mass =42.913 Answer = .09%

Precision and Accuracy Practice 1. Measured Mass =.8696 ug 2. Theoretical mass = 1. 345 ug Answer = 35.35

SI Units

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

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

(m)

Kilogram

Density, Volume and Mass

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

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

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

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

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

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

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

Measurement

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

Instrument Precision Platform Balance +/- 0.1 gram Analytical Balance +/- 0.0001 gram 10 ml grad. cylinder +/- 0.1 ml 50 ml burette +/- 0.01 ml

Significant Digits

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: 1.234

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)

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

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

Significant Digits Rules All nonzero digits are significant Example: 375.42 (five significant digits) 22.3 (three significant digits)

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

Significant Digits Rules Zeros between nonzero digits are significant Example: 7008 (four significant digits) 1,400,002 (seven significant digits) 1230.0 (five significant digits)

Significant Digits Rules Leading zeroes or place holders are not significant. Example: 0.00025 (two significant digits) 0.0002500 (four significant digits)

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

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.

Rule Review When determining if the zero(s) are significant or not. Are they telling you how small the number is? (not-significant) 0.0005 - 1 significant digit Are they telling you that the measurement scale is for large objects? (not –significant) 155,000 – 3 significant digits

Significant Digits Practice 9.370 grams (four significant digits) 63,000.00 grams (seven significant digits) 705.06 ml (five significant digits)

Significant Digits Practice 9,000 grams (one significant digits) 0.0034 grams (two significant digits) 5,000.06 ml (six significant digits)

Significant digits in calculations In multiplication and division the answer must contain the fewest significant figures. Example 4.38 meters x 3.1 meters = 13.578 or 14 m2 2.85 cm x 7.2 cm = 20.52 or 21 cm2

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 + 3.1 meters = 7.48 or 7.5 m 2.85 cm + 7.2 cm = 10.05 or 10.1 cm

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

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.

Rule Review When determining if the zero(s) are significant or not. Are they telling you how small the number is? (not-significant) 0.0005 - 1 significant digit Are they telling you that the measurement scale is for large objects? (not –significant) 155,000 – 3 significant digits

Scientific Notation

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

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

Scientific Notation It is a number expressed between 1 and 10 multiplied by an exponential factor (raised to some power) Example: 0.0000006 = 6 x 10-7 33400000000000000000000 = 3.34 x 1022

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

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

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 .00001 = 1.00 x 10-5

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

Reverse Number Line 3 2 1 0 -1 -2 -3

Scientific Notation Problems! 5.30 x 10-3 Answer: 0.00530 7.5 x 105 Answer: 750,000.0

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

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

Reverse Number Line 3 2 1 0 -1 -2 -3

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

Scientific Notation in Mathematical functions 1.00 x 102 + 1.00 x 103 1.00 x 102 + 10.00 x 102 11.0 x 102 or 1.10 x 103

Scientific Notation in Mathematical functions 1.00 x 102 - 1.00 x 103 1.00 x 102 - 10.00 x 102 - 9.00 x 102

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

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

Practice

Scientific Notation in Mathematical functions 2.00 x 103 + 3.00 x 102 2.00 x 103 + 0.30 x 103 Answer: 2.30 x 103

Scientific Notation in Mathematical functions 5.00 x 104 - 11.00 x 103 5.00 x 104 - 1.10 x 104 Answer: 3.90 x 104

Scientific Notation Problems! (3.55 x 104 ) x (3.55 x 103 ) (3.55 x 3.55 ) x (104 + 103 ) Answer: 12.60 x 107 or 1.26 x 108

Scientific Notation Problems! (6.22 x 10-2 ) / (8.4 x 10-4 ) (6.22 / 8.4 ) (10-2 - 10-4 ) Answer: 0.74 x 102 or 7.40 x 101

Scientific Notation Problems! (6.22 x 10-2 ) + (8.40 x 10-4 )

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

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

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

Perform the following operations 2.00 x 10-3 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 10-4 ) / (5.42 x 10-7 ) 5.00 x 104 - 8.00 x 105 3.00 x 102 - 6.00 x 104 4.00 x 102 + 2.00 x 104 2.00 x 102 + 3.00 x 103

Perform the following operations 3.00 x 10-3 x 1.00 x 10-4 5.00 x 105 x 7.00 x 107 (9.22 x 102 ) / (7.41 x 104 ) (8.22 x 10-4 ) / (5.42 x 10-7 ) 7.00 x 104 - 2.00 x 105 5.00 x 102 - 6.00 x 104 5.00 x 102 + 2.00 x 104 4.00 x 102 + 3.00 x 103 B 3.00 x 10-4 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 10- 5 ) / (2.42 x 10-6 ) 4.00 x 103 - 8.00 x 105 3.00 x 103 - 6.00 x 104 4.00 x 105 + 2.00 x 104 2.00 x 104 + 3.00 x 103

Conversion factors

Conversion Factors Ratio between measurements and their units 3 feet = 1 yard 1 gram = 1,000.00 mg 1000.00 ug - 1 mg.

Dimensional Analysis

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

Dimensional Analysis (grid system)

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

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

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

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

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

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

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

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

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

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

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

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

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

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 1 1 Km 200 s 200s 1000 m

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) .

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 10-5 Km/s2

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)

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 106 1 oz AU 28.35 g 1000 kg ore 1 $ 400 1 oz 10g AU

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 106 1 oz AU 28.35 g 1000 kg ore 1 $ 400 1 oz 10g AU 7.09 x 106 kg ore

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

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

End Module 2

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

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

Density, Volume and Mass Problem: 1. Density = 14.4 grams/mL 2. Mass = ? Grams 3. Volume = 6.2 mL Answer = 89.28 grams

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

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

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

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

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