Chemistry Atoms First Julia Burdge Jason Overby Chapter

Chemistry: Atoms First Julia Burdge & Jason Overby Chapter 1 Chemistry: The Science of Change Homework: 5, 9, 15, 17, 23, 25, 27, 31, 37, 29, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77 and 79 Kent L. Mc. Corkle Cosumnes River College Sacramento, CA Copyright (c) The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 1

1 Chemistry: The Science of Change 1. 1 The Study of Chemistry 1. 5 Uncertainty in Measurement Chemistry You May Already Know Significant Figures The Scientific Method Calculations with Measured Numbers 1. 2 Classification of Matter Accuracy and Precision States of Matter 1. 6 Using Units and Solving Problems Mixtures Conversion Factors 1. 3 The Properties of Matter Dimensional Analysis Physical Properties Tracking Units Chemical Properties Extensive and Intensive Properties 1. 4 Scientific Measurement SI Base Units Mass Temperature Derived Units: Volume and Density

1. 1 The Study of Chemistry is the study of matter and the changes that matter undergoes. Matter is anything that has mass and occupies space.

The Study of Chemistry Scientists follow a set of guidelines known as the scientific method: • gather data via observations and experiments • identify patterns or trends in the collected data • summarize their findings with a law • formulate a hypothesis • with time a hypothesis may evolve into a theory

1. 2 Classification of Matter Chemists classify matter as either a substance or a mixture of substances. A substance is a form of matter that has definite composition and distinct properties. Ø Examples: salt (sodium chloride), iron, water, mercury, carbon dioxide, and oxygen Substances differ from one another in composition and may be identified by appearance, smell, taste, and other properties. A mixture is a physical combination of two or more substances. A homogeneous mixture is uniform throughout. Ø Also called a solution. Ø Examples: seawater, apple juice A heterogeneous mixture is not uniform throughout. Ø Examples: trail mix, chicken noodle soup

Classification of Matter All substances can, in principle, exist as a solid, liquid or gas. We can convert a substance from one state to another without changing the identity of the substance.

Classification of Matter Solidsparticles Solid do not conform are held closely to the shape together of their in an ordered fashion. container. Liquidsparticles Liquid do conform are close to together the shapebut of are theirnot held rigidly in position. container. Gasesparticles Gas assume have both the significant shape and volume separation of from container. their each other and move freely.

Classification of Matter A mixture can be separated by physical means into its components without changing the identities of the components.

1. 3 The Properties of Matter There are two general types of properties of matter: 1) Quantitative properties are measured and expressed with a number. 2) Qualitative properties do not require measurement and are usually based on observation.

The Properties of Matter A physical property is one that can be observed and measured without changing the identity of the substance. Ø Examples: color, melting point, boiling point A physical change is one in which the state of matter changes, but the identity of the matter does not change. Ø Examples: changes of state (melting, freezing, condensation)

The Properties of Matter A chemical property is one a substance exhibits as it interacts with another substance. Ø Examples: flammability, corrosiveness A chemical change is one that results in a change of composition; the original substances no longer exist. Ø Examples: digestion, combustion, oxidation

The Properties of Matter An extensive property depends on the amount of matter. Ø Examples: mass, volume An intensive property does not depend on the amount of matter. Ø Examples: temperature, density

1. 4 Scientific Measurement Properties that can be measured are called quantitative properties. A measured quantity must always include a unit. The English system has units such as the foot, gallon, pound, etc. The metric system includes units such as the meter, liter, kilogram, etc.

SI Base Units The revised metric system is called the International System of Units (abbreviated SI Units) and was designed for universal use by scientists. There are seven SI base units

Units in Measurements Factor Prefix Symbol 1 x 106 Mega M 1 x 103 Kilo k the base units grams (g) meters (m) Moles (mol) volume (L) 1 x 10 -2 centi c 1 x 10 -3 milli m 1 x 10 -6 micro m 1 x 10 -9 nano n 1 x 10 -12 pico p Taylor 2010

Mass is a measure of the amount of matter in an object or sample. Because gravity varies from location to location, the weight of an object varies depending on where it is measured. But mass doesn’t change. The SI base unit of mass is the kilogram (kg), but in chemistry the smaller gram (g) is often used. 1 kg = 1000 g = 1× 103 g Atomic mass unit (amu) is used to express the masses of atoms and other similar sized objects. 1 amu = 1. 6605378× 10 -24 g

Temperature There are two temperature scales used in chemistry: The Celsius scale (°C) Ø Freezing point (pure water): 0°C Ø Boiling point (pure water): 100°C The Kelvin scale (K) Ø The “absolute” scale Ø Lowest possible temperature: 0 K (absolute zero) K = °C + 273. 15

Worked Example 1. 1 Normal human body temperature can range over the course of a day from about 36°C in the early morning to about 37°C in the afternoon. Express these two temperatures and the range that they span using the Kelvin scale. Strategy Use K = °C + 273. 15 to convert temperatures from Celsius to Kelvin. Solution 36°C + 273 = 309 K 37°C + 273 = 310 K What range do they span? Depending on the precision required, the conversion from °C to K is often simply done by adding 273, rather than 273. 15. 310 K - 309 K = 1 K Think About It Remember that converting a temperature from °C to K is different from converting a range or difference in temperature from °C to K.

Temperature The Fahrenheit scale is common in the United States. Ø Freezing point (pure water): 32°C Ø Boiling point (pure water): 212°C There are 180 degrees between freezing and boiling in Fahrenheit (212°F-32°F) but only 100 degrees in Celsius (100°C-0°C). Ø The size of a degree on the Fahrenheit scale is only of a degree on the Celsius scale. Temp in °F = ( ×temp in °C ) + 32°F

Worked Example 1. 2 A body temperature above 39°C constitutes a high fever. Convert this temperature to the Fahrenheit scale. Strategy We are given a temperature and asked to convert it to degrees Fahrenheit. We will use the equation below: Temp in °F = ( × temp in °C ) + 32°F Solution Temp in °F = ( × 39°C ) + 32°F Temp in °F = 102°F Think About It Knowing that normal body temperature on the Fahrenheit scale is approximately 98. 6°F, 102°F seems like a reasonable answer.

Taking Measurements While Erlenmeyer flasks and beakers have volume markings, those Markings are only approximations and should NEVER be used for taking measurement readings Taylor 2010

Taking Measurements Graduated cylinders are moderately accurate and are primarily what we use in the laboratory for measuring volumes of liquids Taylor 2010

Taking Measurements Burettes, Pipettes and volumetric flasks are the most accurate way to make solutions and to measure volumes. However, they tend to be more difficult to use than graduated cylinders. Taylor 2010

Taking Measurements You want to read the volume of solution at the meniscus and you may need to get down to eye level with the graduated cylinder to read the meniscus properly. Taylor 2010

Uncertainty in Measurement An inexact number must be reported so as to indicate its uncertainty. Significant figures are the meaningful digits in a reported number. The last digit in a measured number is referred to as the uncertain digit. When using the top ruler to measure the memory card, we could estimate 2. 5 cm. We are certain about the 2, but we are not certain about the 5. The uncertainty is generally considered to be + 1 in the last digit. 2. 5 + 0. 1 cm

Uncertainty in Measurement When using the bottom ruler to measure the memory card, we might record 2. 45 cm. Again, we estimate one more digit than we are certain of. 2. 45 + 0. 01 cm

Taking Measurements Which piece of glassware would you use to get the most accurate measured value? or Beaker Graduated cylinder Taylor 2010

Taking Measurements Let’s consider the significant figure value we would obtain? What is our certain measured value? What is our estimated value ? 13 10 Taylor 2010

Taking Measurements Let’s consider the significant figure value we would obtain? What is our certain measured value? What is our estimated value ? 13. 51 13. 5 Taylor 2010

Taking Measurements Which piece of glassware would you use to get the most accurate measured value? or Beaker Graduated cylinder Taylor 2010

Significant Figures • Why? – To show the certainty in a measured value – To indicate the margin of error when measuring • How? – Report all known values – Estimate one value past what’s given Taylor 2010

Significant Figures Rules • Any digit that is not zero is significant 1. 234 kg 4 significant figures • Zeros between nonzero digits are significant 606 m 3 significant figures • Zeros to the left of the first nonzero digit are not significant 0. 08 L 1 significant figure • If a number is greater than 1, then all zeros to the right of the decimal point are significant 2. 0 mg 2 significant figures • If a number is less than 1, then only the zeros that are at the end and in the middle of the number are significant 0. 00420 g 3 significant figures Taylor 2010

Significant Figures Rules • Any number that has zeros after the digits and no decimal point according to Tro may have an infinite number of significant figures • However, there is considerable number of scientists who believe that zeros that come after the digits when a decimal point is not present are considered to be NOT significant • For example the number 54, 000 would have infinite or 2 significant figures where as 54, 000. would have 5 Taylor 2010

Significant Figures How many significant figures are in each of the following measurements? 24 m. L 2 significant figures 3001 g 4 significant figures 0. 0320 m 3 3 significant figures 6. 4 x 104 molecules 2 significant figures 560 kg 2 significant figures Taylor 2010

Significant Figures How many significant figures are there in 1. 3070 g? A. 6 B. 5 C. 4 Ans: B D. 3 E. 2 Taylor 2010

Worked Example 1. 4 Determine the number of significant figures in the following measurements: (a) 443 cm, (b) 15. 03 g, (c) 0. 0356 kg, (d) 3. 000× 10 -7 L, (e) 50 m. L, (f) 0. 9550 m. Strategy Zeros are significant between nonzero digits or after a nonzero digit with a decimal. Zeros may or may not be significant if they appear to the right of a nonzero digit without a decimal. Solution (a) 443 cm 3 S. F. (c) 0. 0356 kg 3 S. F. (e) 50 m. L 1 or 2, ambiguous (b) 15. 03 g 4 S. F. (d) 3. 000 x 10 -7 L 4 S. F. (f) 0. 9550 m 4 S. F. Think About It Be sure that you have identified zeros correctly as either significant or not significant. They are significant in (b) and (d); they are not significant in (c); it is not possible to tell in (e); and the number in (f) contains one zero that is significant, and one that is not.

Significant Figures Addition and Subtraction of Significant Figures The answer cannot have more digits to the right of the decimal point than any of the original numbers. 89. 332 +1. 1 90. 432 3. 70 -2. 9133 0. 7867 one significant figure after decimal point round off to 90. 4 two significant figures after decimal point round off to 0. 79 Taylor 2010

Significant Figures Multiplication and Division of Significant Figures The number of significant figures in the result is set by the original number that has the smallest number of significant figures. 4. 51 x 3. 6666 = 16. 536366 = 16. 5 3 sig figs round to 3 sig figs 6. 8 ÷ 112. 04 = 0. 0606926 = 0. 061 2 sig figs round to 2 sig figs Taylor 2010

Significant Figures What are Exact Numbers? Numbers from definitions or numbers of objects are considered to have an infinite number of significant figures. The average of three measured lengths; 6. 64, 6. 68 and 6. 70? 6. 64 + 6. 68 + 6. 70 = 6. 67333 = 6. 673 = 7 3 Because 3 is an exact number Taylor 2010

Significant Figures After carrying out the following operations, how many significant figures are appropriate to show in the result? (13. 7 + 0. 027) ¸ 8. 221 A. 1 B. 2 Ans: C C. 3 D. 4 E. 5 Taylor 2010

Calculations with Measured Numbers In addition and subtraction, the answer cannot have more digits to the right of the decimal point than any of the original numbers. 102. 50 ← two digits after the decimal point + 0. 231 ← three digits after the decimal point 102. 731 ← round to two digits after the decimal point, 102. 73 143. 29 - 20. 1 123. 19 ← two digits after the decimal point ← one digit after the decimal point ← round to one digit after the decimal point, 123. 2

Worked Example 1. 5 Perform the following arithmetic operations and report the result to the proper number of significant figures: (a) 317. 5 m. L + 0. 675 m. L, (b) 47. 80 L – 2. 075 L, (c) 13. 5 g ÷ 45. 18 L, (d) 6. 25 cm x 1. 175 cm, (e) 5. 46 x 102 g + 4. 991 x 103 g Strategy Apply the rules for significant figures in calculations, and round each answer to the appropriate number of digits. Solution (a) 317. 5 m. L + 0. 675 m. L 318. 175 m. L (b) 47. 80 L - 2. 075 L 45. 725 L ← round to 318. 2 m. L ← round to 45. 73 L

Worked Example 1. 5 (cont. ) Perform the following arithmetic operations and report the result to the proper number of significant figures: (a) 317. 5 m. L + 0. 675 m. L, (b) 47. 80 L – 2. 075 L, (c) 13. 5 g ÷ 45. 18 L, (d) 6. 25 cm x 1. 175 cm, (e) 5. 46 x 102 g + 4. 991 x 103 g Strategy Apply the rules for significant figures in calculations, and round each answer to the appropriate number of digits. Solution (e) 5. 46 x 102 g + 49. 91 x 102 g 55. 37 x 102 g = 5. 537 x 103 g Think About It Changing the answer to correct scientific notation doesn’t change the number of significant figures, but in this case it changes the number of places past the decimal place.

Worked Example 1. 5 (cont. ) Perform the following arithmetic operations and report the result to the proper number of significant figures: (a) 317. 5 m. L + 0. 675 m. L, (b) 47. 80 L – 2. 075 L, (c) 13. 5 g ÷ 45. 18 L, (d) 6. 25 cm x 1. 175 cm, (e) 5. 46 x 102 g + 4. 991 x 103 g Strategy Apply the rules for significant figures in calculations, and round each answer to the appropriate number of digits. Solution 3 S. F. (c) 13. 5 g = 0. 298804781 g/L 45. 18 L ← round to 0. 299 g/L 4 S. F. (d) 6. 25 cm× 1. 175 cm = 7. 34375 cm 2 3 S. F. 4 S. F. ← round to 7. 34 cm 2

Worked Example 1. 6 An empty container with a volume of 9. 850 x 102 cm 3 is weighed and found to have a mass of 124. 6 g. The container is filled with a gas and reweighed. The mass of the container and the gas is 126. 5 g. Determine the density of the gas to the appropriate number of significant figures. Strategy This problem requires two steps: subtraction to determine the mass of the gas, and division to determine its density. Apply the corresponding rule regarding significant figures to each step. Solution 126. 5 g – 124. 6 g mass of gas = 1. 9 g density = ← one place past the decimal point (two sig figs) 1. 9 g = 0. 00193 g/cm 3 2 3 9. 850 x 10 cm ← round to 0. 0019 g/cm 3 Think About It In this case, although each of the three numbers we started with has four significant figures, the solution only has two significant figures.

Calculations with Measured Numbers In multiplication and division, the number of significant figures in the final product or quotient is determined by the original number that has the smallest number of significant figures. 1. 4× 8. 011 = 11. 2154 2 S. F. 4 S. F. ← fewest significant figures is 2, so round to 11 11. 57/305. 88 = 0. 0378252 4 S. F. 5 S. F. ← fewest significant figures is 4, so round to 0. 03783

Calculations with Measured Numbers Exact numbers can be considered to have an infinite number of significant figures and do not limit the number of significant figures in a result. Ø Example: Three pennies each have a mass of 2. 5 g. What is the total mass? 3× 2. 5 = 7. 5 g Exact (counting number) Inexact (measurement)

Scientific Notation Converting Numbers to Scientific Notation The number of atoms in 12 g of carbon: 602, 200, 000, 000 6. 022 x 1023 The mass of a single carbon atom in grams: 0. 00000000000199 1. 99 x 10 -23 N x 10 n N is a number between 1 and 10 n is a positive or negative integer Taylor 2010

Calculations with Measured Numbers In calculations with multiple steps, round at the end of the calculation to reduce any rounding errors. ØDo not round after each step. Compare the following: Rounding after each step Rounding at end 1) 3. 66× 8. 45 = 30. 9 2) 30. 9× 2. 11 = 65. 2 1) 3. 66× 8. 45 = 30. 93 2) 30. 93× 2. 11 = 65. 3 In general, keep at least one extra digit until the end of a multistep calculation.

Scientific Notation • Why? – To express large or small numbers in a simpler format – All numbers provided in scientific notation are significant • How? 568. 762 0. 00000772 move decimal left move decimal right n>0 n<0 568. 762 = 5. 68762 x 102 0. 00000772 = 7. 72 x 10 -6 Taylor 2010

Scientific Notation Addition and Subtraction Of numbers in Scientific notation 4. 31 x 104 + 3. 9 x 103 = 1. Write each quantity with the same exponent n 4. 31 x 104 + 0. 39 x 104 = 2. Combine N 1 and N 2 3. The exponent, n, remains the same 4. 70 x 104 Taylor 2010

Scientific Notation Multiplication and Division In Scientific Notation Multiplication Rules 1. Multiply N 1 and N 2 (4. 0 x 10 -5) x (7. 0 x 103) = (4. 0 x 7. 0) x (10 -5+3) = 2. Add exponents n 1 and n 2 3. Check to make sure N 3 is between 1 -10 Division Rules 1. Divide N 1 and N 2 28 x 10 -2 = 2. 8 x 10 -1 8. 5 x 104 ÷ 5. 0 x 109 = (8. 5 ÷ 5. 0) x 104 -9 = 2. Subtract exponents n 1 and n 2 3. Check to make sure N 3 is between 1 -10 1. 7 x 10 -5 Taylor 2010

Scientific Notation Put the following values into Scientific Notation 24 m. L 2. 4 x 101 m. L 3001 g 3. 001 x 103 g 0. 0320 m 3 3. 20 x 10 -2 m 3 640, 000 molecules 0. 0000091 kg 6. 4 x 108 molecules 9. 1 x 10 -12 kg Taylor 2010

Scientific Notation Do the following Mathematical Calculations using Scientific Notation 2. 4 x 104 + 3. 72 x 103 = 2. 8 x 104 4. 4 x 10 -5 ÷ 5. 92 x 102 = 7. 4 x 10 -8 7. 19 x 1015 X 8. 345 x 10 -5 = 6. 00 x 1011 5. 6 x 10 -4 - 3. 0 x 10 -3 = 5. 9 x 10 -4 Taylor 2010

Units in Measurements Hints for converting between units • Always write fractions on 2 lines • Always use scientific notation for your factor • Always go through the “base” • Always pair the base with the factor Remember these rules regarding working with numbers in Scientific Notation • When you multiply values with exponents, ADD the exponents • When you divide values with exponents, SUBTRACT the exponent of the denominator from the numerator • When you raise an exponent to a power, multiply the exponent by the power Taylor 2010

Scientific Notation and your Calculator Taylor 2010

Scientific Notation and your Calculator The scientific notation key Taylor 2010

Derived Units: Volume and Density There are many units (such as volume) that require units not included in the base SI units. The derived SI unit for volume is the meter cubed (m 3). A more practical unit for volume is the liter (L). Ø 1 dm 3 = 1 L Ø 1 cm 3 = 1 m. L

Derived Units: Volume and Density The density of a substance is the ratio of mass to volume. d = density m = mass V = volume SI-derived unit: kilogram per cubic meter (kg/m 3) Other common units: g/cm 3 (solids) g/m. L (liquids) g/L (gases)

Worked Example 1. 3 Ice cubes float in a glass of water because solid water is less dense than liquid water. (a) Calculate the density of ice given that, at 0°C, a cube that is 2. 0 cm on each side has a mass of 7. 36 g, and (b) determine the volume occupied by 23 g of ice at 0°C. Strategy (a) Determine density by dividing mass by volume, and (b) use the calculated density to determine the volume occupied by the given mass. Solution (a) A cube has three equal sides so the volume is (2. 0 cm)3, or 8. 0 cm 3 7. 36 g d= = 0. 92 g/cm 3 3 8. 0 cm (b) Rearranging d = m/V to solve for volume gives V = m/d 23 g V= = 25 cm 3 3 0. 92 g/cm Think About It For a sample with a density less than 1 g/cm 3, the number of cubic centimeters should be greater than the number of grams. In this case, 25 cm 3 > 23 g.

Units in Measurements Conversions to try: 1) 3. 72 mm 2 to Km 2 6) 5. 34 g/ L to pg/p. L 2) 3. 72 pmol to Mmol 7) 5. 34 KL to n. L 3) 3. 72 mol/ L to mmol/ m. L 8) 5. 34 ng to Mg 4) 3. 72 KL to m. L 9) 5. 34 pm to cm 5) 3. 72 ng/ mol to g/ mmol 10) 5. 34 g/cm 3 to Kg/m 3 Answers: 1) 3. 72 x 10 -12 Km 2 4) 3. 72 x 106 m. L 7) 5. 34 x 1012 n. L 10) 5. 34 x 103 Kg/m 3 2) 3. 72 x 10 -18 Mmol 5) 3. 72 x 10 -12 g/mmol 8) 5. 34 x 10 -15 Mg 3) 3. 72 mmol/ m. L 6) 5. 34 pg/p. L 9) 5. 34 x 10 -10 cm Taylor 2010

Problem Solving Dimensional Analysis • What is it? – a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value – also called Factor-Label Method or the Unit Factor Method • Why use it? – To describe the same or equivalent "amounts" of what we are interested in. For example, we know that 1 inch = 2. 54 centimeters Taylor 2010

Problem Solving 1. Determine which unit conversion factor(s) are needed 2. Carry units through calculation 3. If all units cancel except for the desired unit(s), then the problem was solved correctly How many m. L are in 1. 63 L? 1 L = 1000 m. L 1. 63 L x = 1630 m. L 1 L 2 1 L L 1. 63 L x = 0. 001630 1000 m. L Taylor 2010

Problem solving A rock climber estimates that the rock face is 155 ft high. The rope he brought is 65 m long. Is the rope long enough to reach the top? (1 ft = 0. 3048 m) To answer we need the unit conversion of 1 foot = 0. 3048 meters X = 65 m 1 foot 210 feet 0. 3048 m Taylor 2010

Problem Solving The speed limit is 55 miles/hr. What is the speed limit in standard SI units? To answer we need the unit conversion of 1 mi = 1. 6093 Km 1 Km = 1000 m 4 m 55 miles 1. 6093 Km 1000 m 8. 9 x 10 X = X 1 hr 1 mile 1 Km 1 hr Taylor 2010

Density Typicall the units are g/ m. L or g/ cm 3 density = mass volume d = m V A piece of platinum metal with a density of 21. 5 g/cm 3 has a volume of 4. 49 m. L. What is its mass? d = m V m = d x V = 21. 5 g/cm 3 x 4. 49 cm 3 = 96. 5 g Taylor 2010

Density A piece of metal with a mass of 114 g was placed into a graduated cylinder that contained 25. 00 m. L of water, raising the water level to 42. 50 m. L. What is the density of the metal? A. B. C. D. E. 0. 154 g/m. L 0. 592 g/m. L 2. 68 g/m. L 6. 51 g/m. L 7. 25 g/m. L Ans: D Taylor 2010

Density using density as a conversion factor what is the mass of a piece of metal with a volume of 15. 8 grams if the density of the metal is 2. 7 g/m. L? 1 The units of volume are either m. L, cm 3, or L. Given that the density is given in g/m. L, the volume of the piece of metal is most likely 15. 8 m. L (and not 15. 8 g). Assuming that is the case, you are trying to convert from m. L to grams, so the labels of the conversion factor must be grams on top and m. L on the bottom so that the m. L labels will cancel. The density tells us the numbers that go into the conversion factor: 2. 7 grams of Al has a volume of 1 m. L. So 15. 8 m. L x ( 2. 7 g / 1 m. L ) = _____ grams Taylor 2010

1. 6 Using Units and Solving Problems A conversion factor is a fraction in which the same quantity is expressed one way in the numerator and another way in the denominator. For example, 1 in = 2. 54 cm, may be written: 1 in 2. 54 cm or 2. 54 cm 1 in

Dimensional Analysis – Tracking Units The use of conversion factors in problem solving is called dimensional analysis or the factor-label method. Ø Example: Convert 12. 00 inches to meters. = 30. 48 cm 12. 00 in × The result contains 4 sig figs because the conversion, a definition, is exact. Which conversion factor will cancel inches and give us centimeters? 1 in 2. 54 cm or 2. 54 cm 1 in

Worked Example 1. 7 The Food and Drug Administration (FDA) recommends that dietary sodium intake be no more than 2400 mg per day. Strategy The necessary conversion factors are derived from the equalities 1 g = 1000 mg and 1 lb = 453. 6 g. 1 g 1000 mg or Solution 2400 mg × 1000 mg 1 g 1 g 1000 mg 1 lb 453. 6 g × 1 lb 453. 6 g or 453. 6 g 1 lb = 0. 005291 lb Think About It Make sure that the magnitude of the result is reasonable and that the units have canceled properly. If we had mistakenly multiplied by 1000 and 453. 6 instead of dividing by them, the result (2400 mg× 1000 mg/g× 453. 6 g/lb = 1. 089× 109 mg 2/lb) would be unreasonably large and the units would not have canceled properly.

Worked Example 1. 8 An average adult has 5. 2 L of blood. What is the volume of blood in cubic meters? Strategy 1 L = 1000 cm 3 and 1 cm = 1 x 10 -2 m. When a unit is raised to a power, the corresponding conversion factor must also be raised to that power in order for the units to cancel appropriately. Solution 5. 2 L × cm 3 1000 1 L × 10 -2 1 x m 1 cm 3 = 5. 2 x 10 -3 m 3 Think About It Based on the preceding conversion factors, 1 L = 1× 10 -3 m 3. Therefore, 5 L of blood would be equal to 5× 10 -3 m 3, which is close to the calculated answer.

Accuracy and Precision Accuracy tells us how close a measurement is to the true value. Good accuracy and good precision Precision tells us how close a series of replicate measurements are to one another. Poor accuracy but good precision Poor accuracy and poor precision

Accuracy and Precision Three students were asked to find the mass of an aspirin tablet. The true mass of the tablet is 0. 370 g. Student A: Results are precise but not accurate Student B: Results are neither precise nor accurate Student C: Results are both precise and accurate

1 Chapter Summary: Key Points The Scientific Method States of Matter Substances Mixtures Physical Properties Chemical Properties Extensive and Intensive Properties SI Base Units Mass Temperature Volume and Density Significant Figures