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

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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. Copyright © by Pearson Education, Inc. Publishing as Benjamin Cummings

10 Length Measurement Length Is measured using a meter stick.
Has the unit of meter (m) in the metric (SI) system. Copyright © by Pearson Education, Inc. Publishing as Benjamin Cummings

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 Copyright © by Pearson Education, Inc. Publishing as Benjamin Cummings

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. Copyright © by Pearson Education, Inc. Publishing as Benjamin Cummings

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. Copyright © by Pearson Education, Inc. Publishing as Benjamin Cummings

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. Copyright © by Pearson Education, Inc. Publishing as Benjamin Cummings

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. Copyright © by Pearson Education, Inc. Publishing as Benjamin Cummings

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 Copyright © by Pearson Education, Inc. Publishing as Benjamin Cummings

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 Copyright © by Pearson Education, Inc. Publishing as Benjamin Cummings

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. Copyright © by Pearson Education, Inc. Publishing as Benjamin Cummings

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 Copyright © by Pearson Education, Inc. Publishing as Benjamin Cummings

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 Copyright © by Pearson Education, Inc. Publishing as Benjamin Cummings

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


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