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CHEM 1405: Introductory Chemistry Houston Community College Dr. Laura Jakubowski Chapter 2 – The Metric System Textbook “Introductory Chemistry: Concepts and Critical Thinking” Seventh Edition by Charles H. Corwin © 2014 Pearson Education, Inc. Basic Units and Symbols • Up until the 1800s, the English system was most commonly used for measurements • The metric system was later adopted, as it offers simplicity and basic units – the meter (m) for length, the gram (g) for mass, the liter (L) for volume, and the second (s) for time • Original metric references: © 2014 Pearson Education, Inc. 2 Metric Prefixes • The metric system is a decimal system, it uses a prefix to express a multiple or a fraction of a basic unit © 2014 Pearson Education, Inc. 3 The International System of Units (SI) • The metric system is sometimes referred to as the International System of measurement (symbol SI) • SI is similar to the metric system, but much more comprehensive length mass time temperature electric current light intensity amount of substance meter kilogram second Kelvin ampere candela mole m kg s K A cd mol © 2014 Pearson Education, Inc. 4 Metric Conversion Factors • A unit equation relates two quantities that are equal • For example, 1000 meters = 1 kilometer (1000 m = 1 km), also known as an exact equivalent • Further examples: • 1 kg = 1000 g • 1 s = 1,000,000,000 ns • 1 L = 1 × 106 µL • A unit factor is the ratio of two equivalent quantities, the numerator and denominator are equivalent – ratio can be inverted to reciprocal 1 m = 100 cm unit factors are: 1m 100 cm and 100 cm 1m © 2014 Pearson Education, Inc. 5 Metric-Metric Conversions • The unit analysis method is very effective for the problems found in introductory chemistry • Step 1: Write down the unit asked for in the answer • Step 2: Write down the given value related to the answer • Step 3: Apply unit factor(s) to convert the unit in the given value to the unit in the answer © 2014 Pearson Education, Inc. 6 Metric-Metric Conversions • Problem: find the mass in grams of a 325 mg aspirin tablet © 2014 Pearson Education, Inc. 7 Metric-Metric Conversions • Problem: find the mass in grams of a 325 mg aspirin tablet 325 mg unit factor × = g 1 g = 1000 mg 1g 1000 mg 325 mg × or 1g 1000 mg 1000 mg 1g = 0.325 g © 2014 Pearson Education, Inc. 8 Metric-Metric Conversions • The mass of Earth is 5.98 × 1024 kg. What is the mass in megagrams? © 2014 Pearson Education, Inc. 9 Metric-Metric Conversions • The mass of Earth is 5.98 × 1024 kg. What is the mass in megagrams? given value 5.98 × 1024 kg unit factor 1 × 5.98 × 1 kg 1000 g or 1000 g 1kg 1024 × unit factor 2 unit in answer 1 Mg 1,000,000 g or 1,000,000 g 1 Mg = ? Mg 1000 g 1 Mg kg × × = 5.98 × 1021 Mg 1kg 1,000,000 g © 2014 Pearson Education, Inc. 10 Metric-English Conversions • The United States is the last major world nation to formally adopt the metric system – and progress is slow to achieve full compliance • Therefore, the following conversions are useful to know: © 2014 Pearson Education, Inc. 11 Metric-English Conversions • A can of soda contains 12.0 fl oz (1 quart = 32 fluid ounces). What is the volume of soda in milliliters? • If a tennis ball weighs 2.0 oz (16 oz = 1 lb), what is the mass of the tennis ball in grams? © 2014 Pearson Education, Inc. 12 Metric-English Conversions • A can of soda contains 12.0 fl oz (1 quart = 32 fluid ounces). What is the volume of soda in milliliters? 12.0 fl oz × 1 qt 946 mL × = 355 mL 32 fl oz 1 qt • If a tennis ball weighs 2.0 oz (16 oz = 1 lb), what is the mass of the tennis ball in grams? 454 g 1 lb 2.0 oz × × = 57 g 1 lb 16 oz © 2014 Pearson Education, Inc. 13 Set Up the Following Conversion Equations a) An elephant weighs 5,100 kg. What is its mass in pounds? b) A television screen measures 42 in. What is the size of the screen in meters? c) Light travels through the universe at a velocity of 3.00 × 1010 cm/s. How many gigameters does light travel per second? 14 Set Up the Following Conversion Equations a) An elephant weighs 5,100 kg. What is its mass in pounds? 1000 g 1 lb 5,100 kg × × = 11,000 lb 1 kg 454 g b) A television screen measures 42 in. What is the size of the screen in meters? 1m 2.54 cm 42 in. × 1 in. × 100 cm = 1.1 m c) Light travels through the universe at a velocity of 3.00 × 1010 cm/s. How many gigameters does light travel per second? 3.00 × 1010 cm/s × 1m 1 Gm × = 0.300 Gm/s 9 100 cm 1 × 10 m 15 The Percent Concept • A percent (symbol %) expresses the amount of a single quantity compared to an entire sample • A dime is 10% of a dollar, and a quarter is 25% of a dollar one quantity × 100% = N% total sample • After 1971, 5 cent coins were composed of both nickel and copper. If a coin contains 3.80 g copper and 1.27 g nickel, what is the percent of copper in the coin? © 2014 Pearson Education, Inc. 16 The Percent Concept • A percent (symbol %) expresses the amount of a single quantity compared to an entire sample • A dime is 10% of a dollar, and a quarter is 25% of a dollar one quantity × 100% = N% total sample • After 1971, 5 cent coins were composed of both nickel and copper. If a coin contains 3.80 g copper and 1.27 g nickel, what is the percent of copper in the coin? 3.80 g = 0.750 × 100% = 75.0% (3.80 + 1.27) g © 2014 Pearson Education, Inc. 17 Percent Unit Factors • Percent can be expressed as parts per 100 parts, 10% and 25% correspond to 10 and 25 parts per 100 parts, respectively 10 100 25 • 25% corresponds to 100 • 10% corresponds to • The Moon contains 4.70% iron. What is the mass of iron in a lunar sample that weighs 235 g? © 2014 Pearson Education, Inc. 18 Percent Unit Factors • Percent can be expressed as parts per 100 parts, 10% and 25% correspond to 10 and 25 parts per 100 parts, respectively 10 100 25 • 25% corresponds to 100 • 10% corresponds to • The Moon contains 4.70% iron. What is the mass of iron in a lunar sample that weighs 235 g? 4.70 g iron 235 g sample × = 11.0 g iron 100 g sample © 2014 Pearson Education, Inc. 19 Volume by Calculation • Volume of a rectangular solid can be calculated if length (l), width (w), and thickness (t) are known t w l l × w × t = volume • If solid measures 3 cm by 2 cm by 1 cm: 3 cm × 2 cm × 1 cm = 6 cm3 • The unit cm3 is referred to as a cubic centimeter © 2014 Pearson Education, Inc. 20 Thickness Calculation • A sheet of aluminum foil measures 25.0 mm by 10.0 mm and the volume is 3.75 mm3. What is the thickness of the foil in mm? © 2014 Pearson Education, Inc. 21 Thickness Calculation • A sheet of aluminum foil measures 25.0 mm by 10.0 mm and the volume is 3.75 mm3. What is the thickness of the foil in mm? l × w × t = volume 25.0 mm × 10.0 mm × t = 3.75 mm3 (solve for t): 250. mm2 × t = 3.75 mm3 3.75 mm3 t= 250 mm2 t = 0.0150 mm © 2014 Pearson Education, Inc. 22 Volumes of Solids, Liquids, and Gases • A liter (L) is equivalent to the volume occupied by a cube, 10 cm per side • Calculated volume of a liter: 1 L = 10 cm × 10 cm × 10 cm = 1000 cm3 • Recall that 1 L = 1000 mL 1000 cm3 = 1 L = 1000 mL 1000 cm3 = 1000 mL • Therefore: 1 cm3 = 1 mL • Note – in medicine, a cm3 is often abbreviated as cc (cubic centimeter) © 2014 Pearson Education, Inc. 23 Metric-English Volume Conversion • An automobile engine has a volume displacement of 498 cm 3 in each cylinder, express the volume in cubic inches (in.3). • An SUV has a 244 in3 engine, express the engine volume in liters. © 2014 Pearson Education, Inc. 24 Metric-English Volume Conversion • An automobile engine has a volume displacement of 498 cm 3 in each cylinder, express the volume in cubic inches (in.3). 498 cm3 × 1 in. 1 in. 1 in. × × = 30.4 in.3 2.54 cm 2.54 cm 2.54 cm • An SUV has a 244 in3 engine, express the engine volume in liters. 244 in.3 × 1L 2.54 cm 2.54 cm 2.54 cm × × × = 4.00 L 3 1000 cm 1 in. 1 in. 1 in. © 2014 Pearson Education, Inc. 25 Set Up the Following Conversion Equations a) A patient receives an 850 cc (cm3) infusion of fluid. How many liters of fluid did the patient receive? b) A moon sample is found to contain 7.50% aluminum. What is the total mass of the lunar sample if the amount of aluminum is 5.25 g? c) A windowpane is 0.53 cm thick and 95 cm wide. How tall is the windowpane, assuming its volume is 12,600 cm3? 26 Set Up the Following Conversion Equations a) A patient receives an 850 cc (cm3) infusion of fluid. How many liters of fluid did the patient receive? 850 cm3 × 1L = 0.85 L 3 1000 cm b) A moon sample is found to contain 7.50% aluminum. What is the total mass of the lunar sample if the amount of aluminum is 5.25 g? 100 g sample 5.25 g aluminum × = 70.0 g sample 7.50 g aluminum c) A windowpane is 0.53 cm thick and 95 cm wide. How tall is the windowpane, assuming its volume is 12,600 cm3? l × 95 cm × 0.53 cm = 12,600 cm3 l = 250 cm 27 Volume of a Solid by Displacement • The volume of an irregular solid cannot be determined directly by multiplying its measurements • The volume can be determined indirectly by measuring the amount of water it displaces – called volume by displacement • The difference between the final water level and the initial water level in the graduated cylinder (10.5 mL) is equal to the volume of the solid piece of jade © 2014 Pearson Education, Inc. 28 Volume of a Gas by Displacement • The volume displacement method can also be used to determine the volume of a gas • Using a setup as seen, a sample is heated, produces a gas, and that gas displaces a certain volume of water • The volume of water displaced is equal to the volume of gas produced © 2014 Pearson Education, Inc. 29 The Density Concept • Which weighs more – a ton of feathers or a ton of bricks? They have the same mass, but very different volume! cnx.org 30 The Density Concept • The density (symbol d) expresses the concentration of its mass • Density is defined as the amount of mass per unit volume mass = density volume • Different units can be used to express density – for solids and liquids usually g/mL or g/cm3, and for gases usually g/L Substance: Density: 0.917 g/cm3 © 2014 Pearson Education, Inc. 1.00 g/cm3 11.3 g/cm3 22.5 g/cm3 31 The Density Concept • Identify the liquids and solids Choose from: • water • ethyl ether • chloroform • rubber • ice • aluminum L2 L3 © 2014 Pearson Education, Inc. 32 The Density Concept • Identify the liquids and solids Choose from: • water ethyl ether • ethyl ether • chloroform water • rubber L • ice • aluminum chloroform L 2 3 ice rubber aluminum © 2014 Pearson Education, Inc. 33 Density Calculations • If a platinum nugget has a mass of 214.50 g and a volume of 10.0 cm3, what is the density of the metal? • Carbon tetrachloride is a solvent used for degreasing electronic parts. If 25.0 mL of carbon tetrachloride has a mass of 39.75 g, what is the density of the liquid? © 2014 Pearson Education, Inc. 34 Density Calculations • If a platinum nugget has a mass of 214.50 g and a volume of 10.0 cm3, what is the density of the metal? mass = density volume 214.50 g = 21.5 g/cm3 3 10.0 cm • Carbon tetrachloride is a solvent used for degreasing electronic parts. If 25.0 mL of carbon tetrachloride has a mass of 39.75 g, what is the density of the liquid? 39.75 g = 1.59 g/mL 25.0 mL © 2014 Pearson Education, Inc. 35 Applying Density as a Unit Factor • The unit analysis method can be used to solve density problems • For example, the density of mercury is 13.6 g/mL, this can be expressed as: 13.6 g 1 mL or 1 mL 13.6 g • What is the volume in mL of 75.5 g of liquid mercury? • A 1.00-in cube of copper measures 2.54 cm on a side. What is the mass in grams of the copper cube (d of copper = 8.96 g/cm3)? © 2014 Pearson Education, Inc. 36 Applying Density as a Unit Factor • The unit analysis method can be used to solve density problems • For example, the density of mercury is 13.6 g/mL, this can be expressed as: 13.6 g 1 mL or 1 mL 13.6 g • What is the volume in mL of 75.5 g of liquid mercury? 75.5 g × 1 mL = 5.55 mL 13.6 g • A 1.00-in cube of copper measures 2.54 cm on a side. What is the mass in grams of the copper cube (d of copper = 8.96 g/cm3)? (2.54 cm)(2.54 cm)(2.54 cm) = 16.4 cm3 8.96 g × = 147 g 1 cm3 © 2014 Pearson Education, Inc. 37 Specific Gravity • The ratio of the density of a liquid to the density of water (at 4 °C) is called specific gravity (symbol sp gr) • Specific gravity is a unitless quantity density of object (g/mL) specific gravity = density of water (g/mL) • The density of water is 1.00 g/mL, therefore the specific gravity is 1.00 • Diagnostic medical testing often includes the specific gravity of body fluids • The specific gravity of urine may be 1.02 and of blood may be 1.06, meaning both are more dense than water © 2014 Pearson Education, Inc. 38 Temperature • Temperature is the average kinetic energy of individual particles in motion, and it is measured with a thermometer • Three temperature scales: Water Freezes Water Boils • Fahrenheit degree (symbol °F) • Celsius degree (symbol °C) • Kelvin unit (symbol K) • Lowest possible temperature is -273.15 °C, 0 K • No highest temperature, but the sun’s interior is ~10,000,000K © 2014 Pearson Education, Inc. 39 Temperature Conversions • 180 Fahrenheit units are equivalent to 100 Celsius units (212 °F - 32 °F) • The difference between the freezing point from °F to °C is 32 100 °C (°F - 32 °F) × = °C 180 °F 180 °F °C × 100 °C + 32 °F = °F • Celsius units are equivalent to Kelvin units, but the Kelvin scale is 273 units above the Celsius scale °C + 273 = K © 2014 Pearson Education, Inc. 40 Temperature Conversions • Normal body temperature is 98.6 °F. What is normal body temperature in degrees Celsius? • The temperature in Celsius of liquid nitrogen is -196 °C, what is the Kelvin temperature? © 2014 Pearson Education, Inc. 41 Temperature Conversions • Normal body temperature is 98.6 °F. What is normal body temperature in degrees Celsius? 100 °C (98.6 °F - 32 °F) × = °C 180 °F 66.6 °F × 100 °C = 37.0 °C 180 °F • The temperature in Celsius of liquid nitrogen is -196 °C, what is the Kelvin temperature? -196 °C + 273 = 77 K © 2014 Pearson Education, Inc. 42 The Heat Concept • Heat is the flow of energy from an object at higher temperature to an object at lower temperature – heat is a measure of total energy and temperature is a measure of average energy • Which feels hotter – quickly drinking a cup of hot tea, or a spoon of hot tea? The cup of tea has more heat than the spoon of tea, even though both are 100 °C Lesser total heat energy (lesser volume) Greater total heat energy (greater volume) © 2014 Pearson Education, Inc. 43 The Heat Concept • Heat energy is often expressed in units of calories • A calorie (symbol cal) is the amount of heat necessary to raise 1 gram of water 1 degree on the Celsius scale • A kilocalorie (kcal) is the amount of heat necessary to raise 1000 grams of water 1 degree on the Celsius scale • Nutritional Calorie (Cal) is equal to 1 kilocalorie, that is 1000 calories • The SI unit of energy is the joule (symbol J), where 1 cal = 4.184 J • The heat produced by chemical reactions is often expressed in kilocalories, as well as in kilojoules (kJ), where 1 kcal = 4.184 kJ © 2014 Pearson Education, Inc. 44 Energy Conversion • Burning one liter of natural gas produces 9.46 kcal of heat energy. Express the energy in kilojoules (given that 1 kcal = 4.184 kJ). • Burning one gram of gasoline produces 47.9 kJ of energy. Express the heat energy in kilocalories. © 2014 Pearson Education, Inc. 45 Energy Conversion • Burning one liter of natural gas produces 9.46 kcal of heat energy. Express the energy in kilojoules (given that 1 kcal = 4.184 kJ). 4.184 kJ 9.46 kcal × = 39.6 kJ 1 kcal • Burning one gram of gasoline produces 47.9 kJ of energy. Express the heat energy in kilocalories. 1 kcal 47.9 kJ × = 11.4 kcal 4.184 kJ © 2014 Pearson Education, Inc. 46 Set Up the Following Conversion Equations a) The average surface temperature of Mars is -55 °C. What is the average temperature in degrees Fahrenheit? b) A diamond displaces 3.4 mL of water. What is the mass of the diamond in grams, assuming its density is 3.52 g/mL? c) Burning one gram of gasoline produces 47.9 kJ of energy. How many kcal of energy is in 1 kg gasoline? 47 Set Up the Following Conversion Equations a) The average surface temperature of Mars is -55 °C. What is the average temperature in degrees Fahrenheit? 180 °F -55 °C × 100 °C + 32 °F = -67 °F b) A diamond displaces 3.4 mL of water. What is the mass of the diamond in grams, assuming its density is 3.52 g/mL? 3.52 g 3.4 mL × = 12.0 g 1 mL c) Burning one gram of gasoline produces 47.9 kJ of energy. How many kcal of energy is in 1 kg gasoline? 1000 g 47.9 kJ 1 kcal 1 kg × × × = 11,400 kcal 1 kg 1g 4.184 kJ 48 Specific Heat • Specific heat is the amount of heat required to raise the temperature of 1 gram of substance 1 degree Celsius – units are cal / (g × °C) • Water has a relatively high specific heat – 1 cal / (g × °C), this helps to regulate climates and maintain moderate temperatures on Earth, because oceans resist wide swings in temperature Ice Water Iron 1g 1g 1g Temperature after receiving 1 cal of heat: Specific heat of substance (in cal / (g × °C)): 1.0 °C 1.00 Silver 2.0 °C 0.492 9.3 °C 0.108 1g 17.7 °C 0.0566 © 2014 Pearson Education, Inc. 49 Specific Heat Calculations • If it takes 3.35 cal of heat energy to raise the temperature of 10.0 g of mercury by 10.0 °C, what is the specific heat of mercury? • The specific heat of ethanol is 2.46 J / (g × °C). How much heat energy (in J) is required to raise the temperature of ethanol by 5 °C? 50 Specific Heat Calculations • If it takes 3.35 cal of heat energy to raise the temperature of 10.0 g of mercury by 10.0 °C, what is the specific heat of mercury? 3.35 cal = 0.0335 cal / (g × °C) 10.0 g × 10 °C • The specific heat of ethanol is 2.46 J / (g × °C). How much heat energy (in J) is required to raise the temperature of 1 g of ethanol by 5 °C? 1 g × 5 °C × 2.46 J = 12.3 J g × °C 51 Summary • The metric system uses meters (m) for distance, grams (g) for mass, liters (L) for volume, and seconds (s) for time • The metric system base units are modified using prefixes to reduce or enlarge the base units by factors of ten • The unit analysis method is a tool to convert between units of a given value to units asked for in the answer • A percent expresses the amount of a single quantity compared to an entire sample • Volume of a solid = l × w × t; it is often reported in cm3 • Volume by displacement is used for irregular solids and gases • Density = mass/volume; specific gravity is the ratio of given density to that of water • Temperature is the average energy of molecules in motion; units are degrees Fahrenheit (°F), degrees Celsius (°C) and the Kelvin unit (K) © 2014 Pearson Education, Inc. 52 Summary • Heat is the total energy of molecules in motion, expressed in calories (cal) or joules (J), where 1 cal = 4.184 J; specific heat is the amount of heat necessary to raise 1 g of substance 1 °C, for water the value is 1.00 cal / (g × °C) Key terms: English system, metric system, meter (m), gram (g), liter (L), second (s), International System (SI), unit equation, exact equivalent, unit factor, reciprocal, unit analysis method, percent (%), cubic centimeter (cm3), volume by displacement, density, specific gravity (sp gr), temperature, Fahrenheit degree, Celsius degree, Kelvin unit, heat, calorie (cal), joule (J), specific heat © 2014 Pearson Education, Inc. 53