Chapter 1-part 2

Metric Equalities An equality states the same measurement in two different units. can be written using the relationships between two metric units. Example: 1 meter is the same as 100 cm and 1000 mm. 1 m= 100 cm 1 m= 1000 mm 2

Conversion Factors A conversion factor is obtained from an equality. E.g Metric – U.S system Equality: 1 in. = 2.54 cm written as a fraction (ratio) with a numerator and denominator. inverted to give two conversion factors for every equality. 1 in. and 2.54 cm 2.54 cm 1 in. 3

Conversion Factors in a Problem A conversion factor may be obtained from information in a word problem. is written for that problem only. Example : The cost of one gallon (1 gal) of gas is $ gallon of gasand $4.29 $4.291 gallon of gas 4

Conversion Factors for a Percentage, ppm, and ppb The term percent (%) means parts per 100 parts E.g18% body fat by mass Equality : 18 kg body fat = 100 kg body mass Conversion factors: Different mass units such as grams (g), kilograms (kg), or pounds (lb) can be used, but both units in the factors must be the same

Smaller Percents: ppm and ppb Small percents are shown as ppm and ppb. Parts per million (ppm) = mg part/kg whole Example: The EPA allows 15 ppm cadmium in food colors 15 mg cadmium = 1 kg food color Parts per billion ppb =  g part/kg whole Example: The EPA allows10 ppb arsenic in public water 10  g arsenic = 1 kg water 6

1.7 Problem Solving To solve a problem, identify the given unit. identify the needed unit. Example: A person has a height of 2.0 meters. What is that height in inches? The given unit is the initial unit of height. given unit = meters (m) The needed unit is the unit for the answer. needed unit = inches (in.)

Problem Setup Unit 1 x Unit 2 = Unit 2 Unit 1 Given x Conversion= Needed unit factor unit 8

Examples An injured person loses 0.30 pints of blood. How many milliliters of blood would that be? Identify the given and needed units given in this problem. Given unit= _______ Needed unit = _______ 9

Examples A bucket contains 4.65 L of water. Write the setup for the problem and calculate the gallons of water in the bucket. plan: Equalities: Set Up Problem: 10

Examples A rattlesnake is 2.44 m long. How many cm long is the snake? 1) 2440 cm 2)244 cm 3)24.4 cm How many in 2 in 1.5 cm 2 ? 11

Using Two or More Factors Often, two or more conversion factors are required to obtain the unit needed for the answer. Unit 1 Unit 2Unit 3 Additional conversion factors are placed in the setup problem to cancel each preceding unit. Given unit x factor 1 x factor 2 = needed unit Unit 1 x Unit 2 x Unit 3 = Unit 3 Unit 1 Unit 2 12

Examples If a ski pole is 3.0 feet in length, how long is the ski pole in mm? If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7500 feet? 13

Examples How many lb of sugar are in 120 g of candy if the candy is 25% (by mass) sugar? 14

1.8 Density Density compares the mass of an object to its volume. is the mass of a substance divided by its volume. Density Expression Density = mass = g or g = g/cm 3 volume mL cm 3 Note: 1 mL = 1 cm 3 15

Densities of Common Substances 16 (at 4 °C)

Example Osmium is a very dense metal. What is its density in g/cm 3 if 50.0 g of osmium has a volume of 2.22 cm 3 ? 1) 2.25 g/cm 3 2) 22.5 g/cm 3 3) 111 g/cm 3 17

Volume by Displacement A solid completely submerged in water displaces its own volume of water. The volume of the object is calculated from the difference in volume mL mL = 9.5 mL = 9.5 cm 3 18

Density Using Volume Displacement The density of the zinc object is then calculated from its mass and volume. Density = mass = g = 7.2 g/cm 3 volume 9.5 cm 3 19

Examples What is the density (g/cm 3 ) 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? 1) 0.17 g/cm 3 2) 6.0 g/cm 3 3) 380 g/cm 3 20 object 33.0 mL 25.0 mL

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. 21

Examples The density of octane, a component of gasoline, is g/mL. What is the mass, in kg, of 875 mL of octane? 1) kg 2) 614 kg 3) 1.25 kg 22

Examples If olive oil has a density of 0.92 g/mL, how many liters of olive oil are in 285 g of olive oil? 1) 0.26 L 2) 0.31 L 3) 310 L 23

Examples A group of students collected 125 empty aluminum cans to take to the recycling center. If 21 cans make 1.0 lb aluminum, how many liters of aluminum (D=2.70 g/cm 3 ) are obtained from the cans? 1) 1.0 L2) 2.0 L3) 4.0 L 24

Learning Check Which of the following samples of metals will displace the greatest volume of water? g of aluminum 2.70 g/mL 45 g of gold 19.3 g/mL 75 g of lead 11.3 g/mL

Specific gravity The ratio of the density of a substance compare to the density (mass of the same unit volume) of a reference substance. ◦ A Hydrometer is used as a tool to measure specific gravity