Ch. 1: Measurements Chem 20-1204 El Camino College 1 Units Units of Length meter (m), centimeter (cm), inch (in.) 1 m = 100 cm 1 m = 39.4 in. 2.54 cm = 1 in. Ex. Which is larger, a meter or a cm? a meter Ex. Which is larger, an in. or a meter? a meter. 2 Units Units of Volume liter (L), milliliter (mL), quart (qt) 1 L = 1000 mL 1 L = 1.06 qt 946 mL = 1 qt Ex. Which is larger, a milliliter or a liter? a liter Ex. Which is larger, a quart or a liter? a liter. 3 4 Units Units of Mass gram (g), kilogram (kg), pound (lb) 1 kg = 1000 g 1 kg = 2.20 lb 454 g = 1 lb Ex. Which is larger, a g or a kg? Ex. Do you weigh a higher number of pounds or kilograms? a kg lbs 5 6 Units Units of Temperature Fahrenheit (oF), Celsius (oC), Kelvin (K) freezing pt of H2O is 32 oF, 0 oC, 273 K boiling pt of H2O is 212 oF, 100 oC, 373 K Ex. What is being measured: length, volume, mass, or temp? temp 292 K 23 mL volume 0.004 cm. length 7 8 9 10 For Very Large or Small Numbers Scientific notation has a specific form a.bcd x 10e a.bc (the number must be 1 to <10) 10e (the e is the exponent) x 101 = x 10 x 10-1 = x .1 x 102 = x 100 x 10-2 = x .01 x 103 = x1000 x 10-3 = x .001 11 Solved Examples Write 53 in scientific notation Convert to a.bc form (between 1 and 10) 5.3 To go from the a.bc form to 53, the decimal moves 1 place to the right 5.3 x 101 12 Solved Examples Write 8769 in scientific notation Convert to a.bc form (between 1 and 10) 8.769 To go from the a.bc form to 8769, the decimal moves 3 places to the right 8.769 x 103 13 Solved Examples Write 100.30 in scientific notation Convert to a.bc form (between 1 and 10) 1.0030 To go from the a.bc form to 100.30, the decimal moves 2 places to the right 1.0030 x 102 14 Solved Examples Write 0.00367 in scientific notation Convert to a.bc form (between 1 and 10) 3.67 To go from the a.bc form to 0.00367, the decimal moves 3 places to the left 3.67 x 10-3 15 Examples Write these in scientific notation 501 = 5.01 x 102 3,256,000 = 3.256 x 106 0.042 = 4.2 x 10-2 0.0005395 = 5.395 x 10-4 16 Solved Examples Write 1.0389 x 102 in decimal form 1.0389 x 102 means that the decimal moves 2 places to the right 103.89 Write 8.0 x 10-3 in decimal form 8.0 x 10-3 means that the decimal moves 3 places to the left .0080 17 Examples Write these in decimal notation 3 x 100 = 3 6.022 x 104 = 60220 5.33 x 10-3 = 0.00533 9.99 x 101 = 99.9 18 On Your Calculator Don’t use the 10x key Don’t press “x 10” You must use the EE or EXP key 5.62 x 10-3 is 5.62 exp 3 +/ Try this calculation. If you get a different result, see me after class 5.62 x 10-3 -8 = 6.36 x 10 8.84 x 104 19 20 21 22 Place Names ___ ___ ___ . tenths ___ hundreds tens ones ___ ___ thousandths hundredths 23 Dimensional Analysis How many minutes are in 2.0 hrs? The 2.0 hrs is your given information The conversion (60 min/1 hr) is called a conversion factor Always start with the given information Write the conversion factor so the units to be cancelled are on the bottom. 2.0 hrs 60 min 1 hr = 120 min 24 Dimensional Analysis How many minutes in 936.2 sec? 936.2 sec 1 min = 15.60 min 60 sec How many hrs in 53 min? 53 min 1 hr 60 min = 0.88 hr 25 Dimensional Analysis If you need two conversions, don’t stop in the middle. Write one conversion after the other. Hit the times (X) key between numerators Hit the divide (/) key between denominators How many hours in 9365 sec? 9365 sec 1 min 60 sec 1 hour 60 min = 2.601 hr 26 Dimensional Analysis How many hrs in 5,877 sec? 5,877 sec 1 min 60 sec 1 hour 60 min = 1.633 hr How many minutes in 0.052 days? 0.052 days 24 hrs 1 day 60 min 1 hr = 75 min 27 Metric Prefixes to Memorize prefix kilo symbol k multiple 1000 g / 1 kg centi milli micro nano c m m n 1 m / 100 cm 1 L / 1000 mL 1 g / 1 x 106 mg 1 m / 1 x 109 nm also useful is 1 cm = 10 mm 28 Metric Conversion Factors There are many ways to write conversion factors Make sure you know which unit is bigger Many small units = one big unit A fraction of a big unit = one small unit 1m 100 cm 100 cm 1m 1 x 102 cm 1m 1 cm .01 m 29 Examples: Use Dimensional Analysis Always put the number by itself before the conversion factor How many cm in 4.6 m? 4.6 m 100 cm 1m = 460 cm How many kg in 54.8 g? 54.8 g 1 kg = 0.0548 kg 1000 g 30 Examples How many kL in 4,329,647 L? 1 kL = 4329.647 kL 4,329,647 L 1000 L How many mm in 0.33 m? 0.33 m 1 x 106 mm = 3.3 x 105 mm 1m How many kg in 828 mg? 828 mg 1g 1 kg = 8.28 x 10-4 kg 1000 mg 1000 g 31 English Units These are the most common US units mass: ounce, pound length: inch, foot, yard volume: cubic inch, fl. oz., gallon 32 Metric-US Conversions: Don’t Memorize 1 lb = 454 g 1 oz = 28.3 g 2.20 lb = 1 kg 1.06 qt = 1 L 1 qt = 946 mL 1 in. 2.54 cm 39.4 in. = 1 m 0.621 mi = 1 km 33 Examples How many liters are in 2.98 quarts? 2.98 qt 1L = 2.81 L 1.06 qt How many ounces are in 500.0 g? 500.0 g 1 oz = 17.7 oz 28.3 g How many cm in 8.994 in.? 8.994 in. 2.54 cm = 22.84 cm 1 in. 34 Place Names ___ ___ ___ . tenths ___ hundreds tens ones ___ ___ thousandths hundredths 35 Significant Figures Sig figs apply to measured amounts Sig figs don’t apply to counted things 36 Significant Figures For any apparatus, read 1 place past the smallest mark The last significant digit is estimated (the doubtful digit). 37 Significant Figures 28 oC 50o 40o 30o 20o 10o 0 oC The smallest mark is in the tens place One place past the smallest mark is the ones. 38 Ex. Read These 3.6 oC 110 oC 4.7 oC 5.5 oC meas-4 39 Right on the Line? Always read to one place past the smallest mark Always read a piece of equipment to the same place. Note: Read the meniscus (the bottom of the belly for water) 40 Right on the Line? 3.0 mL 41 Conversion Factors in Problems Read the problem carefully, then write a conversion factor When solving, write a number by itself first, then write the conversion factor 42 Example A car is traveling 65.9 miles per hour. How many miles will it go in 13.3 hrs? 65.9 miles 1 hour The conversion factor is 1 hour or 65.9 miles 13.3 hrs 65.9 miles 1 hour = 876 miles 43 A car is traveling 38.8 miles per hour. How many hrs will it take to go 51.0 miles? 51.0 mi 1 hr 38.8 mi = 1.31 hr A pool empties at 4.2 gal per sec. How many min will it take to empty 3200 gal? 3200 gal 1 sec 1 min = 13 min 4.2 gal 60 sec 44 Density Density is mass/volume D = m v Find the density of 3.8 mL of liquid that has a mass of 5.8 g. 5.8 g = 1.5 g/mL 3.8 mL Note: 1 mL 1 cm3 1 cc 45 46 47 The density of gold is 19.3 g/cm3. Find the mass of 87.3 cm3 of gold. 87.3 cm3 19.3 g cm3 = 1685 g Find the volume of 0.53 g of gold using the density of 19.3 g/cm3. 0.53 g 1 cm3 19.3 g = 0.027 cm3 48 49 Density and Solids The mass of a solid is measured on a balance or scale The volume of a solid may be measured by volume displacement Measure the vol of water in a cylinder Add the solid Measure the vol of water again Vfinal - Vinitial = Vsolid 50 A cylinder contains 11.3 mL water. A piece of aluminum is added, and the water level rises to 16.0 mL. What is the volume of the aluminum? 16.0 mL - 11.3 mL = 4.7 mL If the Al has a mass of 12.7 g, what is the density of the Al? 12.7 g = 2.7 g/mL 4.7 mL 51 Example A cylinder contains 35.5 mL water. A piece of zinc is added, and the water level rises to 45.0 mL. If the mass of the zinc is 68.60 g, what is the density of the zinc? Volume 45.0 mL - 35.5 mL = 9.5 mL Density 68.60 g = 7.2 g/mL 9.5 mL 52