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DIMENSIONAL ANALYSIS Problem solving using equalities How many Japanese yen can you get for $5.00? An EQUALITY STATEMENT between yen and dollars is needed $1.00 = ¥131 An equality statement can be written as a fraction called a CONVERSION FACTOR $1.00 _______ ¥131 or ¥131 1B-1 (of 24) _______ $1.00 $5.00 x ¥131 ________ $1.00 = ¥655 How many British pounds can you get for $5.00? £1.00 = $1.80 £1.00 _______ $1.80 1B-2 $1.80 or _______ £1.00 $5.00 x £1.00 ________ $1.80 = £2.78 How many Japanese yen can you get for 5.00 British pounds? Equality statement between ¥ and £? No £1.00 = $1.80 $1.00 = ¥131 £5.00 x $1.80 ________ £1.00 1B-3 x ¥131 ________ $1.00 = ¥1,179 How many miles are in 1,000,000. inches? 1 ft = 12 in 1 mi = 5,280 ft 1,000,000. in x 1 ft _______ 12 in 1B-4 x 1 mi __________ 5,280 ft = 15.78283 mi How many seconds are in 1.0000 year? 1B-5 How many cubic yards of air are in 18 cubic feet of air? 1 yd = 3 ft (1 yd)3 = (3 ft)3 18 ft3 x (1 yd)3 ________ (3 ft)3 18 ft3 x 1 yd3 ________ 27 ft3 1B-6 = 0.67 yd3 Convert 35 mi/h into ft/min 1 mi = 5,280 ft 1 h = 60 min 35 mi ________ h 1B-7 x 5,280 ft x 1h __________ _________ 1 mi 60 min = 3,080 ft/min = 3,100 ft/min TEMPERATURE SCALES TEMPERATURE – A property of a system based upon the average energy of the particles making up the system Solid – vibrational energy of the atoms or molecules Liquid or Gas – vibrational, rotational, and translational energy of the atoms or molecules 1B-8 Two common temperature scales are the Fahrenheit and Celsius scales ← Boiling point of water ← Room Temperature ← Freezing point of water 1B-9 y = mx + b ºF = mºC + b m = 212 - 32 = 9 100 - 0 5 __________ 32 = __ 9 (0) + b 5 32 = b ºF = __ 9 ºC + 32 5 1B-10 ___ What is the Celsius temperature when it is 90ºF? ºF = __ 9 ºC + 32 5 ºF - 32 = __ 9 ºC 5 5 __ (ºF - 32) = ºC 9 5 __ (90 - 32) = 32ºC 9 1B-11 Scientists believe there is a lowest possible temperature : -273ºC ABSOLUTE SCALE – A scale with 0 as its lowest possible value The Kelvin scale is an absolute scale K = ºC + 273 ← Boiling point of water ← Freezing point of water ← Absolute Zero 1B-12 METRIC CONVERSIONS METRIC PREFIXES Prefix mega kilo BASE UNIT deci centi milli micro nano 1B-13 Symbol M k d c m μ n Base Unit Multiplying Factor 106 103 100 10-1 10-2 10-3 10-6 10-9 How many kilometers are 525 meters? 1 km = 103 m 103 m 1 km _______ 103 m 1B-14 or _______ 1 km 525 m x 1 km ________ 103 m = 0.525 m How many centigrams are 8.93 grams? 1 cg = 10-2 g 8.93 g x 1 cg ________ = 893 g 10-2 g How many liters are 25.0 milliliters? 1B-15 How many kilograms are 150 decigrams? Equality statement between kg and dg? No 1 dg = 10-1 g 1 kg = 103 g 150 dg x 10-1 g ________ 1 dg 1B-16 x 1 kg ________ 103 g = 0.015 kg How many micrometers are 0.37 centimeters? 1B-17 Convert 22.5 mL/s into L/min 1 mL = 10-3 L 1 min = 60 s 22.5 mL x 10-3 L ___________ ________ s 1 mL 1B-18 x 60 s ________ 1 min = 1.35 L/min THE PROPERTY OF DENSITY DENSITY – Mass per unit volume D = m ___ V Material Lead Water Cork Air Helium 1B-19 Density 11.34 1.00 0.24 0.0013 g/mL g/mL g/mL g/mL 0.0001 g/mL What is the density of a solid in which 2.20 g occupies 1.50 mL? D = m ___ V 1B-20 = 2.20 g __________ 1.50 mL = 1.47 g/mL What is the mass of 12.0 mL of a solid if it has a density of 3.50 g/mL? D = m ____ V VD = m 1B-21 = (12.0 mL)(3.50 g/mL) = 42.0 g What volume does 6.2 g of a liquid occupy if its density is 1.4 g/mL? D = m ____ V VD = m V = m ____ D 1B-22 = 6.2 g ____________ 1.4 g/mL = 4.4 mL REVIEW FOR TEST Identify laboratory equipment Location of safety equipment Accuracy of graduated glassware Safety procedures Scientific notation Reading graduated equipment Significant figures Operations with significant figures 1B-23 REVIEW FOR TEST Metric prefixes Dimensional analysis Know metric and time equalities Temperature scales Know equalities between them Denisty Solve for D, m, or V 1B-24