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Chapter 3

Chapter 3. The Metric System by Christopher Hamaker. The Metric System. The English system was used primarily in the British Empire and wasn ’ t very standardized. The French organized a committee to devise a universal measuring system.

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Chapter 3

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  1. Chapter 3 The Metric System by Christopher Hamaker Chapter 3

  2. The Metric System • The English system was used primarily in the British Empire and wasn’t very standardized. • The French organized a committee to devise a universal measuring system. • After about 10 years, the committee designed and agreed on the metric system. • The metric system offers simplicity with a single base unit for each measurement. Chapter 3

  3. Metric System Basic Units Chapter 3

  4. Original Metric Unit Definitions • A meter was defined as 1/10,000,000 of the distance from the North Pole to the equator. • A kilogram (1000 grams) was equal to the mass of a cube of water measuring 0.1 m on each side. • A liter was set equal to the volume of one kilogram of water at 4 C. Chapter 3

  5. Metric System Advantage • Another advantage of the metric system is that it is a decimal system. • It uses prefixes to enlarge or reduce the basic units. • For example: • A kilometer is 1000 meters. • A millimeter is 1/1000 of a meter. Chapter 3

  6. Metric System Prefixes • The following table lists the common prefixes used in the metric system: Chapter 3

  7. Metric Prefixes, Continued • For example, the prefix kilo- increases a base unit by 1000: • 1 kilogram is 1000 grams. • The prefix milli- decreases a base unit by a factor of 1000: • There are 1000 millimeters in 1 meter. Chapter 3

  8. Metric Symbols • The names of metric units are abbreviated using symbols. Use the prefix symbol followed by the symbol for the base unit, so: • Nanometer is abbreviated nm. • Microgram is abbreviated mg. • Deciliter is abbreviated dL. • Gigasecond is abbreviated Gs. Chapter 3

  9. Nanotechnology • Nanotechnology refers to devices and processes on the 1–100 nm scale. • For reference, a human hair is about 100,000 nm thick! • A DNA helix is a nanoscale substance, with a diameter of about 1 nm. • Nanoscale hollow tubes, called carbon nanotubes, have slippery inner surfaces that allow for the easy flow of fluids. Chapter 3

  10. Metric Equivalents • We can write unit equations for the conversion between different metric units. • The prefix kilo- means 1000 basic units, so 1 kilometer is 1000 meters. • The unit equation is 1 km = 1000 m. • Similarly, a millimeter is 1/1000 of a meter, so the unit equation is 1000 mm = 1 m. Chapter 3

  11. Metric Unit Factors • Since 1000 m = 1 km, we can write the following unit factors for converting between meters and kilometers: 1 km or 1000 m 1000 m 1 km • Since 1000 mm = 1 m, we can write the following unit factors: 1000 mm or 1 m . 1 m 1000 mm Chapter 3

  12. Metric–Metric Conversions • We will use the unit analysis method we learned in Chapter 2 to do metric–metric conversion problems. • Remember, there are three steps: • Write down the unit asked for in the answer. • Write down the given value related to the answer. • Apply unit factor(s) to convert the given unit to the units desired in the answer. Chapter 3

  13. Metric–Metric Conversion Problem 1 g 325 mg x = 0.325 g 1000 mg What is the mass in grams of a 325 mg aspirin tablet? • Step 1: We want grams. • Step 2: We write down the given: 325 mg. • Step 3: We apply a unit factor (1000 mg = 1 g) and round to three significant figures. Chapter 3

  14. Two Metric–Metric Conversions A hospital has 125 deciliters of blood plasma. What is the volume in milliliters? • Step 1: We want the answer in mL. • Step 2: We have 125 dL. • Step 3: We need to first convert dL to L and then convert L to mL: 1 L and1000 mL 10 dL 1 L Chapter 3

  15. Two Metric–Metric Conversions, Continued 1 L 1000 mL 125 dLx x = 12,500 mL 10 dL 1 L • Apply both unit factors, and round the answer to three significant digits. • Notice that both dL and L units cancel, leaving us with units of mL. Chapter 3

  16. Another Example 1 Mg 1000 g 7.35 x 1022 kg × x = 5.98 x 1019 Mg 1000000 g 1 kg The mass of the Earth’s moon is 7.35 × 1022 kg. What is the mass expressed in megagrams, Mg? • We want Mg; we have 7.35 x 1022 kg. • Convert kilograms to grams, and then grams to megagrams. Chapter 3

  17. Metric and English Units • The English system is still very common in the United States. • We often have to convert between English and metric units. Chapter 3

  18. Metric–English Conversion 0.914 m 120 yd x = 110 m 1 yd The length of an American football field, including the end zones, is 120 yards. What is the length in meters? • Convert 120 yd to meters (given that 1 yd = 0.914 m). Chapter 3

  19. English–Metric Conversion 1 qt 946 mL 64.0 fl oz x x = 1,890 mL 32 fl oz 1 qt A half-gallon carton contains 64.0 fl oz of milk. How many milliliters of milk are in a carton? • We want mL; we have 64.0 fl oz. • Use 1 qt = 32 fl oz, and 1 qt = 946 mL. Chapter 3

  20. Compound Units • Some measurements have a ratio of units. • For example, the speed limit on many highways is 55 miles per hour. How would you convert this to meters per second? • Convert one unit at a time using unit factors. • First, miles → meters • Next, hours → seconds Chapter 3

  21. Compound Unit Problem 75 km 1 hr 1000 m x x = 21 m/s 1 km hr 3600 s A motorcycle is traveling at 75 km/hour. What is the speed in meters per second? • We have km/h; we want m/s. • Use 1 km = 1000 m and 1 h = 3600 s. Chapter 3

  22. Volume by Calculation • The volume of an object is calculated by multiplying the length (l) by the width (w) by the thickness (t). volume = lxwxt • All three measurements must be in the same units. • If an object measures 3 cm by 2 cm by 1 cm, the volume is 6 cm3 (cm3 is cubic centimeters). Chapter 3

  23. Cubic Volume and Liquid Volume • The liter (L) is the basic unit of volume in the metric system. • One liter is defined as the volume occupied by a cube that is 10 cm on each side. Chapter 3

  24. Cubic and Liquid Volume Units • 1 liter is equal to 1000 cubic centimeters. • 10 cm x 10 cm x 10 cm = 1000 cm3 • 1000 cm3 = 1 L = 1000 mL. • Therefore, 1 cm3 = 1 mL. Chapter 3

  25. Cubic–Liquid Volume Conversion 1 in 1 in 1 in 498 cm3x x x = 30.4 in3 2.54 cm 2.54 cm 2.54 cm An automobile engine displaces a volume of 498 cm3 in each cylinder. What is the displacement of a cylinder in cubic inches, in3? • We want in3; we have 498 cm3. • Use 1 in = 2.54 cm three times. Chapter 3

  26. Volume by Displacement • If a solid has an irregular shape, its volume cannot be determined by measuring its dimensions. • You can determine its volume indirectly by measuring the amount of water it displaces. • This technique is called volume by displacement. • Volume by displacement can also be used to determine the volume of a gas. Chapter 3

  27. Solid Volume by Displacement You want to measure the volume of an irregularly shaped piece of jade. • Partially fill a volumetric flask with water and measure the volume of the water. • Add the jade, and measure the difference in volume. • The volume of the jade is 10.5 mL. Chapter 3

  28. Gas Volume by Displacement You want to measure the volume of gas given off in a chemical reaction. • The gas produced displaces the water in the flask into the beaker. The volume of water displaced is equal to the volume of gas. Chapter 3

  29. The Density Concept mass = density volume • The density of an object is a measure of its concentration of mass. • Density is defined as the mass of an object divided by the volume of the object. Chapter 3

  30. Density • Density is expressed in different units. It is usually grams per milliliter (g/mL) for liquids, grams per cubic centimeter (g/cm3) for solids, and grams per liter (g/L) for gases. Chapter 3

  31. Densities of Common Substances Chapter 3

  32. Estimating Density • We can estimate the density of a substance by comparing it to another object. • A solid object will float on top of a liquid with a higher density. • Object S1 has a density less than that of water, but larger than that of L1. • Object S2 has a density less than that of L2, but larger than that of water. Chapter 3

  33. Calculating Density 224.50 g = 22.5 g/cm3 10.0 cm3 What is the density of a platinum nugget that has a mass of 224.50 g and a volume of 10.0 cm3 ?Recall, density is mass/volume. Chapter 3

  34. Density as a Unit Factor 1.84 g mL 1275 mL x = 2350 g • We can use density as a unit factor for conversions between mass and volume. • An automobile battery contains 1275 mL of acid. If the density of battery acid is 1.84 g/mL, how many grams of acid are in an automobile battery? – We have 1275 mL; we want grams: Chapter 3

  35. Critical Thinking: Gasoline 730 g 3.784 L At 0 ºC: 1.00 gal x x = 2760 g L 1 gal 713 g 3.784 L At 25 ºC: 1.00 gal x x = 2700 g L 1 gal The density of gasoline is 730 g/L at 0 ºC (32 ºF) and 713 g/L at 25 ºC (77 ºF). What is the mass difference of 1.00 gallon of gasoline at these two temperatures (1 gal = 3.784L)? • The difference is about 60 grams (about 2 %). Chapter 3

  36. Temperature • Temperature is a measure of the average kinetic energy of the individual particles in a sample. • There are three temperature scales: • Celsius • Fahrenheit • Kelvin • Kelvin is the absolute temperature scale. Chapter 3

  37. Temperature Scales • On the Fahrenheit scale, water freezes at 32 °F and boils at 212 °F. • On the Celsius scale, water freezes at 0 °C and boils at 100 °C. These are the reference points for the Celsius scale. • Water freezes at 273 K and boils at 373 K on the Kelvin scale. Chapter 3

  38. Temperature Conversions ( ) ( ) 100°C 180°F °C x = °F = °C (°F - 32°F) x 180°F 100°C • This is the equation for converting °C to °F. • This is the equation for converting °F to °C. • To convert from °C to K, add 273. °C + 273 = K Chapter 3

  39. Fahrenheit–Celsius Conversions ( ) = 37.0°C (98.6°F - 32°F) x 100°C 180°F • Body temperature is 98.6 °F. What is body temperature in degrees Celsius? In Kelvin? K = °C + 273 = 37.0 °C + 273 = 310 K Chapter 3

  40. Heat • Heat is the flow of energy from an object of higher temperature to an object of lower temperature. • Heat measures the total energy of a system. • Temperature measures the average energy of particles in a system. • Heat is often expressed in terms of joules (J) or calories (cal). Chapter 3

  41. Heat Versus Temperature • Although both beakers below have the same temperature (100 ºC), the beaker on the right has twice the amount of heat because it has twice the amount of water. Chapter 3

  42. Specific Heat • The specific heat of a substance is the amount of heat required to bring about a change in temperature. • It is expressed with units of calories per gram per degree Celsius. • The larger the specific heat, the more heat is required to raise the temperature of the substance. Chapter 3

  43. Chapter Summary • The basic units in the metric system are grams for mass, liters for volume, and meters for distance. • The base units are modified using prefixes to reduce or enlarge the base units by factors of ten. • We can use unit factors to convert between metric units. • We can convert between metric and English units using unit factors. Chapter 3

  44. Chapter Summary, Continued • Volume is defined as length x width x thickness. • Volume can also be determined by displacement of water. • Density is mass divided by volume. Chapter 3

  45. Chapter Summary, Continued • Temperature is a measure of the average energy of the particles in a sample. • Heat is a measure of the total energy of a substance. • Specific heat is a measure of how much heat is required to raise the temperature of a substance. Chapter 3

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