1. Chapter 1-part 2 Measurements

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 10 -2 m= 1cm 1 m= 1000 mm 10 -3 m = 1 mm 2

3. 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. = 1 = 2.54 cm 2.54 cm 1 in. 3

4. 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 $4.29. 1 gallon of gasand $4.29 $4.29 1 gallon of gas 4

5. 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

6. 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

7. 1.7 Problem Solving To solve a problem, identify the given unit. identify the needed unit. Unit 1 x Unit 2 = Unit 2 Unit 1 Given x Conversion= Needed unit factor 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.)

8. 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 8

9. Examples If 189.0 mL of orange juice is prepared from orange juice concentrate, how many liters of orange juice is that ? 9

10. 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 10

11. Examples If a ski pole is 3.0 feet in length, how long is the ski pole in mm? 11

12. 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 12

13. Densities of Common Substances 13 (at 4 °C)

14. 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 14

15. 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. 45.0 mL - 35.5 mL = 9.5 mL = 9.5 cm 3 15

16. Density Using Volume Displacement The density of the zinc object is then calculated from its mass and volume. Density = mass = 68.60 g = 7.2 g/cm 3 volume 9.5 cm 3 16

17. 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 17 object 33.0 mL 25.0 mL

18. Using Density as a Conversion Factor The units of density is an derived unit where they are written as a ratio. Knowing the density we can calculate the mass or volume of an object Write the two possible conversion factors for density If the mass is known, what is the set up for calculating the volume ?

19. Examle A thermometer containing 8.3 g of mercury has broken. If mercury has a density of 13.6 g/ml, what volume (ml) spilled?

20. Learning Check Which of the following samples of metals will displace the greatest volume of water? 12 3 20 25 g of aluminum 2.70 g/mL 45 g of gold 19.3 g/mL 75 g of lead 11.3 g/mL

21. 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

22. 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 Reference solution is water Density of water is 1.00 g/ml

23. Example What is the specific gravity of ice if 35.0 g of ice has a volume of 38.2 mL?