Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Matters and Measurement Edward Wen, PhD Chemistry is about Everyday experience Photo credit: itsnicethat.com • Why Cookies tastes different from Cookie Dough? • Why Baking Powder or Baking Soda? • Why using Aluminum Foil, not Paper Towel? • What if the Temperature is set too high? 2 Chapter Outline • • • • • • Classification of matters Measurement, Metric system (SI) Scientific Notation Significant figures Conversion factor Density 3 In Your Room • Everything you can see, touch, smell or taste in your room is made of matter. • Chemists study the differences in matter and how that relates to the structure of matter. 4 What is Matter? • Matter: anything that occupies space and has mass • Matter is actually composed of a lot of tiny little pieces: Atoms and Molecules 5 Atoms and Molecules • Atoms: the tiny particles that make up all matter. Helium gas (for blimp) is made up of Helium atoms. • Molecules: In most substances, the atoms are joined together in units. Liquid water is made up of water molecules (2 Hydrogen atoms + 1 Oxygen atoms) 6 Physical States of Matters • Matter can be classified as solid, liquid or gas based on what properties it exhibits State Shape Volume Compress Flow Solid Fixed Fixed No No Liquid Indef. Fixed No Yes Gas Indef. Indef. Yes Yes 7 Why different States of a Matter? Structure Determines Properties • the atoms or molecules have different structures in solids, liquid and gases 8 Solids • Particles in a solid: packed close together and are fixed in position though they may vibrate Incompressible retaining their shape and volume Unable to flow 9 Liquids • Particles are closely packed, but they have some ability to move around Incompressible Able to flow, yet not to escape and expand to fill the container (not “antigravity”) 10 Gases • The particles have complete freedom from each other (not sticky to each other) • The particles are constantly flying around, bumping into each other and the container • There is a lot of empty space between the particles (low density) Compressible Able to flow and Fill space (“antigravity”) 11 Classifying Matter: Sugar, Copper, Coke, Gasoline/Water 12 Classification of Matter •Matter Pure Substance •Constant Composition Mixture •Variable Composition •Homogeneous 13 Pure substance Matter that is composed of only one kind of piece. Solid: Salt, Sugar, Dry ice, Copper, Diamond Liquid: Propane, distilled water (or Deionized water, DI water) Gas: Helium gas (GOODYEAR blimp) 14 Classifying Pure Substances: Elements and Compounds Elements: Substances which can not be broken down into simpler substances by chemical reactions. (A,B) Compounds: Most substances are chemical combinations of elements. (C) • Examples: Pure sugar, pure water can be broken down into elements Properties of the compound not related to the properties of the elements that compose it 15 Elements • Example: Diamond (pure carbon), helium gas. • 116 known, 91 are found in nature others are man-made • Abundance = percentage found in nature Hydrogen: most abundant in the universe Oxygen: most abundant element (by mass) on earth and in the human body Silicon: abundant on earth surface • every sample of an element is made up of lots of identical atoms 16 Compounds • Composed of elements in fixed percentages water is 89% O & 11% H • billions of known compounds • Organic (sugar, glycerol) or inorganic (table salt) • same elements can form more than one different compound water and hydrogen peroxide contain just hydrogen and oxygen carbohydrates all contain just C, H & O (sugar, starch, glucose) 17 Mixture Matter that is composed of different kinds of pieces. Different samples may have the same pieces in different percentages. (D) Examples: Solid: Flour, Brass (Copper and Zinc), Rock Liquid: Salt water, soda, Gasoline Gas: air 18 Classification of Mixtures • Homogeneous = composition is uniform throughout appears to be one thing every piece of a sample has identical properties, though another sample with the same components may have different properties solutions (homogeneous mixtures): Air; Tap water • Heterogeneous = matter that is nonuniform throughout contains regions with different properties than other regions: gasoline mixed with water; Italian salad dressing 19 What is a Measurement? • Quantitative observation • comparison to an agreed upon standard Every measurement has a number and a unit: • 77 Fahrenheit: Room temperature • 7.5 pounds: Average newborn body weight in the US: • 55 ± 0.5 grams: amount of sugar in one can of Coca Cola UNIT: what standard you are comparing your object to the number tells you 1. what multiple of the standard the object measures 2. the uncertainty in the measurement (±) 20 Some Standard Units in the Metric System Quantity Measured Name of Unit Abbreviation Mass gram g Length meter m Volume liter L Time seconds s Temperature Kelvin K 21 Related Units in the SI System All units in the SI system are related to the standard unit by a power of 10 (exactly!) • 1 kg = 103 g • 1 km = 103 m • 1 m = 102 cm • The power of 10 is indicated by a prefix • The prefixes are always the same, regardless of the standard unit 22 Prefixes Used to Modify Standard Unit • kilo = 1000 times base unit = 103 1 kg = 1000 g = 103 g • deci = 0.1 times the base unit = 10-1 1 dL = 0.1 L = 10-1 L; 1 L = 10 dL • centi = 0.01 times the base unit = 10-2 1 cm = 0.01 m = 10-2 m; 1 m = 100 cm • milli = 0.001 times the base unit = 10-3 1 mg = 0.001 g = 10-3 g; 1 g = 1000 mg • micro = 10-6 times the base unit 1 m = 10-6 m; 106 m = 1 m • nano = 10-9 times the base unit 1 nL = 10-9L; 109 nL = 1 L 23 Common Prefixes in the SI System Prefix Symbol Decimal Equivalent Power of 10 1,000,000 Base 106 1,000 Base 103 mega- M kilo- k deci- d 0.1 Base 10-1 centi- c 0.01 Base 10-2 milli- m 0.001 Base 10-3 micro- or mc 0.000 001 Base 10-6 nano- n 0.000 000 001 Base 10-9 24 Standard Unit vs. Prefixes Using meter as example: 1 km = 1000 m = 103 m 1g = 10 dm = 100 cm = 1000 mm = 1,000,000 m = 1,000,000,000 nm = 102 cm = 103 mm = 106 m = 109 nm 25 Length • Two-dimensional distance an object covers • SI unit: METER (abbreviation as m) About 3½ inches longer than a yard 1 m = 10-7 the distance from the North Pole to the Equator • Commonly use centimeters (cm) 1 m = 100 cm = 1.094 yard 1 cm = 0.01 m = 10 mm 1 inch = 2.54 cm (exactly) 26 Mass • Amount of matter present in an object • SI unit: kilogram (kg) about 2 lbs. 3 oz. • Commonly measure mass in grams (g) or milligrams (mg) 1 kg = 2.2046 pounds (1 lbs. = 0.45359) 1 g = 1000 mg = 103 mg 1 g = 0.001 kg = 10-3 kg 27 Volume • Amount of three-dimensional space occupied • SI unit = cubic meter (m3) • Commonly measure solid volume in cubic centimeters (cm3) 1 m3 = 106 cm3 1 cm3 = 10-6 m3 = 0.000001 m3 • Commonly measure liquid or gas volume in milliliters (mL) 1 gallon (gal) = 3.78 L = 3.78 103 mL 1 L = 1 dm3 = 1000 mL = 103 mL 1 mL = 1 cm3 = 1 cc (cubic centimeter) 28 Common Everyday Units and Their EXACT Conversions 11 cm 1 inch (in) 1 mile 1 foot 1 yard = = = = 2.54 cm 5280 feet (ft) 12 in 3 ft 29 Common Units and Their Equivalents Mass 1 kilogram (km) = 2.205 pounds (lb) 1 pound (lb) = 453.59 grams (g) 1 ounce (oz) = 28.35 (g) Volume 1 liter (L) = 1.057 quarts (qt) 1 U.S. gallon (gal) = 3.785 liters (L) 30 Units • Always write every number with its associated unit • Always include units in your calculations you can do the same kind of operations on units as you can with numbers • cm × cm = cm2 • cm + cm = cm • cm ÷ cm = 1 using units as a guide to problem solving 31 Conversion Factor • Relationships to Convert one unit of measurement to another: US dollar Canadian dollar, dollar cent • Conversion Factors: Relationships between two units Both parts of the conversion factor have the same number of significant figures • Conversion factors generated from equivalence statements e.g. 1 inch = 2.54 cm can give or 2 .54 cm 1in 1in 2.54cm 32 How to Use Conversion Factor • Arrange conversion factors so starting unit cancels Arrange conversion factor so starting unit is on the bottom of the conversion factor unit 1 x unit 2 unit 1 = unit 2 Conversion Factor 33 We have been using the Conversion Factor ALL THE TIME! • How are we converting #cents into #dollars? Why? From 1 dollar = 100 cents 45,000 cents x 1 dollar dollar = 450 dollars 100 cents cents Conversion Factor 34 Convert 325 mg to grams Given: 325 mg Find: ? g Conv. Fact. 1 mg = 10-3 g Soln. Map: mg g 0.325 g 35 Practice: How to set up Conversion? • To convert 5.00 inches to cm, from 1 in = 2.54 cm (exact), which one of the two conversion factors should be used? 1 in 2.54 cm or 2.54 cm 1 in 36 Practice: Conversion among Units • 500 mg = ? g ?g 500mg ? mg 0 .5 g • 3.78 L = ? mL ? mL 3.78L ?L 3780mL • 1.2 nm = ? m ?m 1.2nm ? nm * 8.0 in = ? m ? cm ? m 8.0in ? in ? cm 1.2 10 9 nm 0.203m 37 Scientific Notation Very Large vs. Very Small numbers: •The sun’s diameter is 1,392,000,000 m; •An atom’s diameter is 0.000 000 000 3 m Scientific Notation: 1.392 x 109 m & 3 x 10-10 m the sun’s diameter is 1,392,000,000 m an atom’s average diameter is 0.000 000 000 3 m Scientific Notation (SN) Power of 10 (Math language): • 10 x 10 = 100 100 = 102 (2nd power of 10) • 10 x 10 x 10 = 1,000 1,000 = 103 (3rd power of 10) each Decimal Place in our number system represents a different power of 10 • 24 = 2.4 x 101 = 2.4 x 10 • 1,000,000,000 (1 billion) = 109 • 0.0000000001 (1/10 billionth ) = 10-10 Easily comparable by looking at the power of 10 39 Exponents 10Y exponent 1.23 x 10-8 decimal part exponent part 1.23 x 105 > 4.56 x 102 4.56 x 10-2 > 7.89 x 10-5 7.89 x 1010 > 1.23 x 1010 • when the exponent on 10 (Y) is positive, the number is that many powers of 10 larger sun’s diameter = 1.392 x 109 m = 1,392,000,000 m • when Y is negative, the number is that many powers of 10 smaller avg. atom’s diameter = 3 x 10-10 m = 0.0000000003 m 40 Writing Numbers in SN Big numbers: 12,340,000 1.234 x 107 Small numbers: 0.0000234 2.34 x 10-5 41 Writing a Number in Standard Form 1.234 x 10-6 • since exponent is -6, move the decimal point to the left 6 places if you run out of digits, add zeros 000 001.234 0.000 001 234 If the exponent > 1, add trailing zeros: 1.234 x 1010 1.2340000000 12,340,000,000 42 Scientific calculators 43 Inputting Scientific Notation into a Calculator -1.23 x 10-3 • input decimal part of the number if negative press +/- key • (–) on some • press EXP key EE on some (maybe 2nd function) • input exponent on 10 press +/- key to change exponent to negative Input 1.23 1.23 Press +/- -1.23 Press EXP -1.23 00 Input 3 -1.23 03 Press +/- -1.23 -03 44 Significant Figures (Sig. Fig.) Definition: The non-place-holding digits in a reported measurement some zero’s in a written number are only there to help you locate the decimal point 12.3 cm has 3 sig. figs. and its range is 12.2 to 12.4 cm 0.1230 cm What is Sig. Fig. for? has 4 sig. figs. the range of values to expect for and its range is repeated measurements 0.1229 to 0.1231 cm the more significant figures there are in a measurement, the smaller the range of values is 45 Counting Significant Figures 1. All non-zero digits are significant 1.5 : 2 Sig. Fig.s 2. Interior zeros are significant 1.05 : 3 Sig. Fig.s 3. Trailing zeros after a decimal point are significant 1.050 : 4 Sig. Fig.s. Leading zeros are NOT significant 0.001050 : 4 Sig. Fig.s Place-holding zero’s = SN : 1.050 x 10-3 46 Counting Significant Figures (Contd) 4. Exact numbers has infinite () number of significant figures: example: 1 pound = 16 ounces 1 kilogram = 1,000 grams = 1,000,000 milligrams 1 water molecule contains 2 hydrogen atoms 5. Zeros at the end of a number without a written decimal point are ambiguous and should be avoided by using scientific notation. Example: 150. has 3 sig. fig 150 is ambiguous number 1.50 x 102 has 3 sig. fig. 47 Example–Counting Sig. Fig. in a Number How many significant figures are in each of the following numbers? 2 Sig. Fig. – leading zeros not sig. 4 Sig. Figs – trailing & interior zeros sig. 2 sig. Figs, all digits sig. 27 3 Sig. Figs – only decimal parts count 2.97 × 105 sig. 1 m = 1000 mm both 1 and 1000 are exact numbers. unlimited sig. figs. 0.0035 1.080 48 Practice: How many Significant figures vs. Decimal places? • 2.2 cm 2 sig. Figs; 1 decimal place 3 sig. Figs; • 2.50 cm 2 decimal places 49 Sig. Fig. in Multiplication/Division; Rounding vs. Zeroing • When multiplying or dividing measurements with Sig. Fig., the result has the same number of significant figures as the measurement with the fewest number of significant figures Rounding • 5.02 × 89,665 × 0.10 = 45.0118 = 45 3 SF 5 SF 2 SF 2 SF • 5.892 ÷ 4 SF 6.10 3 SF = 0.96590 = 0.966 3 SF 50 Sig. Fig. in Multiplication/Division: Scientific notation • Occasionally, scientific notation is needed to present results with proper significant figures. 5.89 × 6,103 = 35946.67 = 3.59 × 104 51 Example: Determine the Correct Number of Sig. Fig. 1. 1.01 × 0.12 × 53.51 ÷ 96 = 0.067556 = 0.068 3 SF 2 SF 4 SF 2 SF 2. 56.55 × 0.920 ÷ 34.684 = 1.5 4 SF. 3 SF. 6 SF. result should have 2 Sig. Fig. = 1.50 result should have 3 Sig. Fig. 52 Sig. Fig. in Addition/Subtraction • when adding or subtracting measurements with significant figures, the result has the same number of decimal places as the measurement with the fewest number of decimal places 5.74 + 2 dp 4.865 3 dp 0.823 3 dp 3.965 3 dp + 2.651 = 9.214 = 9.21 3 dp = 0.9 2 dp = 0.900 3 dp 53 Example: Determine the Correct Number of Significant Figures 1. 0.987 + 125.1 – 1.22 = 124.867 = 124.9 3 dp 1 dp 2 dp result should have 1 dp 2. 0.764 – 3.449 – 5.315 = -8 = -8.000 3 dp 3 dp 3 dp result should have 3 dp 54 Sig. Fig. in Combined Calculations • Do and/or , then + and/or 3.489 – 5 .67 × 2.3 3 dp 3 Sig. Fig. 2 Sig. Fig. = 3.489 – 3 dp 13 0 dp = -9.511 = -10 0 dp (2 sig. fig.) • Parentheses (): Do calculation in () first, then the rest 3.489 × (5.67 – 2.3) 2 dp 1 dp = 3.489 × 4 Sig. Fig. 3.4 = 11.8628 2 Sig. Fig. 2 Sig. Fig. = 12 55 Practice: Calculation with Proper Significant Figures a. 12.99 + 2.09 x 1.921 = 12.99 + 4.01 = 17.00 b. 2.00 x 3.5 - 1.000 = 7.0 – 1.000 = 6.0 2.54 12.46 c. 3.75 15.00/3.75 = 4.00 d. (0.0025 6.7) 8.8 6.7 8.8 = 59 56 How to solve Unit Conversion Problems 1) Write down Given Amount and Unit 2) Write down what you want to Find and Unit 3) Write down needed Conversion Factors or Equations 4) Design a Solution Map for the Problem order Conversions to cancel previous units or arrange Equation so Find amount is isolated. Example: from Equation A = b c to solve for b 57 Solution Map for Unit Conversion 4) Apply the Steps in the Solution Map check that units cancel properly multiply terms across the top and divide by each bottom term Example: 2.54 g 12.46 g 15.00g 2 1 . 9 g / cm 3.1cm 2.5cm 7.75cm 2 5) Check the Answer to see if its Reasonable correct size and unit 58 Example: Unit Conversion Alternative Route: Convert 7.8 km to miles km m cm Given: 7.8 km Find: ? mi Conv. Fact. 1 mi = 5280 ft 1 foot = 12 in 1 in = 2.54 cm (exact) Soln. Map: km mi in ft mi 60 Alternative Route: Convert 7.8 km to miles Given: 7.8 km Find: ? mi Conv. Fact. 1 mi = 5280 ft 1 foot = 12 in 1 in = 2.54 cm (exact) Soln. Map: km mi • Apply the Solution Map: 1000 m 100 cm 1 in 1 ft 1 mi 7.8 km mi 1 km 1m 2.54 cm 12 in 5280 ft = 4.84692 mi • Sig. Figs. & Round: = 4.8 mi 61 Temperature • Temperature is a measure of the average kinetic energy of the molecules in a sample • Not all molecules have in a sample the same amount of kinetic energy • a higher temperature means a larger average kinetic energy 62 Fahrenheit Temperature Scale Two reference points: • Freezing point of concentrated saltwater (0°F) • Average body temperature (100°F) more accurate measure now set average body temperature at 98.6°F • Room temperature is about 75°F 63 Celsius Temperature Scale Two reference points: • Freezing point of distilled water (0°C) • Boiling point of distilled water (100°C) more reproducible standards most commonly used in science • Room temperature is about 25°C 64 Fahrenheit vs. Celsius • a Celsius degree is 1.8 times larger than a Fahrenheit degree • the standard used for 0° on the Fahrenheit scale is a lower temperature than the standard used for 0° on the Celsius scale F - 32 C 1.8 F 1.8 C 32 65 The Kelvin Temperature Scale • both the Celsius and Fahrenheit scales have “-” numbers • Kelvin scale is an absolute scale, meaning it measures the actual temperature of an object • 0 K is called Absolute Zero: all molecular motion would stop, theoretically the lowest temperature in the universe 0 K = -273°C = -459°F Absolute Zero is a theoretical value 66 Kelvin vs. Celsius • the size of a “degree” on the Kelvin scale is the same as on the Celsius scale though technically, call the divisions on the Kelvin as kelvins, not degrees that makes 1 K 1.8 times larger than 1°F • the 0 standard on the Kelvin scale is a much lower temperature than on the Celsius scale K C 273 67 Ext remes of Temperature On the Earth, • Lowest temperature recorded: -89.2°C (-128.6 °F, 184 K) • Highest air temperature recorded: ~60°C (140 F) In science lab, • the highest temperature: 4 x 1012 K (?) • the lowest temperature: ~10-10 K (?) 68 Conversion Between Fahrenheit and Kelvin Temperature Scales Convert 104°F into Celsius and Kelvin Information Given: 104 F Find: ? °C, ? K Eq’ns: K 273 C 1.8 C 32 F • Fahrenheit to Celsius: = 40 °C (keep 2 significant figures) Celsius to Kelvin: = 313 K 70 Mass & Volume M ass Density Mass & Volume: V olum e • two main characteristics of matter • even though mass and volume are individual properties - for a given type of matter they are related to each other! Density (ratio of mass vs. volume): for a certain matter, its density is one of the characteristic to distinguish from one another 71 M ass Density V olum e Unit for density • Solids = g/cm3 1 cm3 = 1 mL • Liquids = g/mL: Density of water = 1.00 g/mL • Gases = g/L: Density of Air ~ 1.3 g/L Volume of a solid can be determined by water displacement • Density : solids > liquids >>> gases except ice and dry wood are less dense than liquid water! 72 Density of Common Matters 73 Density • Temperature affects the density: Heating objects causes objects to expand, density The Lava Lamp: heating/cooling • In a heterogeneous mixture, the denser object sinks Why do hot air balloons rise? The “Gold Rush”: Extracting gold particle from sand Density of gasoline changes over the day! 74 Density and Volume Styrofoam vs. Quarter: Both of these items have a mass of 23 grams, but they have very different volumes; therefore, their densities are different as well. 75 Density and Buoyancy • • • • Average density of human body = 1.0 g/cm3 Average density of sea water = 1.03 g/mL Density of mercury, liquid metal, = 13.6 g/mL Density of copper penny = 8.9 g/cm3 76 Density of Body and Body Fat Density of fat tissue < Density of Muscle/Bones Estimate the mass percentage of body fat: 4.57 Body fat% 4.142 100% 3 Density ( g / cm ) Average body fat%: Female 28%, Male 22% 77 M Using Density in Calculations D V Mass Density Volume • Both sides multiplied by Volume Solution Maps: m, V D M a ss D en sity V olu m e m V, D • Both sides divided by Density Mass Volume Density m, D V 78 Application of Density A man gives a woman an engagement ring and tells her that it is made of platinum (Pt). Critical thinking : test to determine the ring’s density before giving him an answer about marriage. Data: She places the ring on a balance and finds it has a mass of 5.84 grams. She then finds that the ring displaces 0.556 cm3 of water. Density Pt = 21.4 g/cm3 79 Test results Given: Mass = 5.84 grams Volume = 0.556 cm3 Density Pt = 21.4 g/cm3 Find: Density in grams/cm3 m D V 5.84 g 0.556 cm 3 g 10.5 cm 3 80 Density as a Conversion Factor • Between mass and volume!! Density H2O = 1 g/mL \ • 1 g H2O 1 mL H2O Density lead = 11.3 g/cm3 • 11.3 g lead 1 cm3 lead 1.00 g 1 mL or 1 mL 1.00 g 11.3 g 1 mL or 1 mL 11.3 g • How much does 4.0 cm3 of Lead weigh? 4.0 cm3 Pb x 11.3 g Pb 1 cm3 Pb = 45 g Pb 81 Measurement and Problem Solving Density as a Conversion Factor • The gasoline in an automobile gas tank has a mass of 60.0 kg and a density of 0.752 g/cm3. What is the volume? • Given: 60.0 kg • Find: Volume in L • Conversion Factors: 0.752 grams/cm3 1000 grams = 1 kg 82 Measurement and Problem Solving Density as a Conversion Factor • kg g cm3 3 1000 g 1 cm 4 3 60.0 kg 7.98 10 cm 1 kg 0.752 g 83 Example: A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm3? Information: Given: m = 5.59 x 104 g Find: density, g/cm3 Solution Map: m,VD Equation: D m V Volume = 57.2 L = 5.72 x 104 cm3 m 5.59 x 104 g D 4 3 V 5.72 x 10 cm = 0.977 g/cm3 84 Practice: Calculation involving Density 1. The density of air at room temperature and sea level is 1.29 g/L. Calculate the mass of air in a 5.0-gal bottle (1 gal = 3.78 L). KEY: 24 g (2SF) 2. A driver filled 15.60 kg of gasoline into his car. If the density of gasoline is 0.788 g/mL, what is the volume of gasoline in liters? KEY: 19.8 L (3SF) 85 About Challenging Problems 1.99+: Proper dosage of a drug is 3.5 mg/kg of body weight. Calculate the milligrams of this drug for a 138-lb individual? (1 lb = 454 g). KEY: 2.2×102 mg (2SF) 1.103: 100. mg ibuprofen/5 mL Motrin. Calculate the grams of ibuprofen in 1.5 teaspoons of Motrin. (1 teaspoon = 5.0 mL) KEY: 0.15 g (2SF) 86