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 = ¥113 An equality statement can be written as a fraction called a CONVERSION FACTOR $1.00 _______ ¥113 ¥113 _______ $1.00 $5.00 x ¥113 ________ $1.00 = ¥565 or 1B-1 (of 24) (2 – 13-32 + 1-4) (3 – 5-24 + 1-4)

How many British pounds can you get for $5.00? £1.00 = $1.30 £1.00 _______ $1.30 $1.30 _______ £1.00 $5.00 x £1.00 ________ $1.30 = £3.85 or 1B-2

How many Japanese yen can you get for 5.00 British pounds? Equality statement between ¥ and £? No £1.00 = $1.30 $1.00 = ¥113 £5.00 x $1.30 ________ £1.00 x ¥113 ________ $1.00 = ¥735 1B-3

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 x 1 mi __________ 5,280 ft = 15.78283 mi 1B-4

How many seconds are in 1.0000 year? 1 yr = 365 dy 1 dy = 24 h 1 h = 60 min 1 min = 60 s 1.0000 yr x 365 dy ________ 1 yr x 24 h _______ 1 dy x 60 min _________ 1 h x 60 s ________ 1 min = 31,536,000 s 1B-5

How many cubic yards of air are in 18 cubic feet of air? 1 yd = 3 ft 1 yd3 ≠ 3 ft3 (1 yd)3 = (3 ft)3 1 yd3 = 27 ft3 18 ft3 x 1 yd3 ________ 27 ft3 = 0.67 yd3 1B-6

Convert 35 mi/h into ft/min 1 mi = 5,280 ft 1 h = 60 min 35 mi ________ h x 5,280 ft __________ 1 mi x 1 h _________ 60 min = 3,080 ft/min = 3,100 ft/min 1B-7

TEMPERATURE SCALES TEMPERATURE – A property of a system based upon the average energy of the particles making up the system Two common temperature scales are the Fahrenheit and Celsius scales 1B-8

y = mx + b ºF = mºC + b ← Boiling point of water m = 212 - 32 __________ 100 - 0 = 9 ___ 5 °F = 9 °C + b __ 5 ← Room Temperature ← Freezing point of water 32 = 9 (0) + b __ 5 32 = b ºF = 9 ºC + 32 __ 5 1B-9

What is the Celsius temperature when it is 95ºF? ºF = 9 ºC + 32 __ 5 ºF - 32 = 9 ºC __ 5 5 (ºF - 32) = ºC __ 9 5 (95 - 32) = __ 9 35ºC 1B-10

Scientists believe there is a lowest possible temperature ABSOLUTE SCALE – A scale with 0 as its lowest possible value The Kelvin scale is an absolute scale ← Boiling point of water : -273ºC ← Freezing point of water K = ºC + 273 ← Absolute Zero 1B-11

METRIC CONVERSIONS METRIC PREFIXES Prefix Symbol BUMF mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 1B-12

How many kilometers are 525 meters? 1 BIG km = 103 small m METRIC PREFIXES Prefix Symbol BUMF mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 1 km _______ 103 m 103 m _______ 1 km or 525 m x 1 km ________ 103 m = 0.525 km 1B-13

How many centigrams are 8.93 grams? 1 BIG g = 102 small cg METRIC PREFIXES Prefix Symbol BUMF mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 8.93 g x 102 cg ________ 1 g = 893 cg How many liters are 25.0 milliliters? 1 L = 103 mL 25.0 mL x 1 L ________ 103 mL = 0.0250 L 1B-14

How many kilograms are 150 decigrams? 1 BIG kg = 104 small dg METRIC PREFIXES Prefix Symbol BUMF mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 150 dg x 1 kg ________ 104 dg = 0.015 kg 1B-15

How many micrometers are 0.37 centimeters? 1 BIG cm = 104 small μm METRIC PREFIXES Prefix Symbol BUMF mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 0.37 cm x 104 μm _________ 1 cm = 3,700 μm 1B-16

Convert 22.5 mL/s into L/min 1 mL = 10-3 L 1 min = 60 s METRIC PREFIXES Prefix Symbol BUMF mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 22.5 mL ___________ s x 10-3 L ________ 1 mL x 60 s ________ 1 min = 1.35 L/min 1B-17

Convert 25.0 m/h into cm/min 1 h = 60 min METRIC PREFIXES Prefix Symbol BUMF mega M 106 kilo k 103 BASE UNIT 100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 25.0 m ___________ h x 102 cm ________ 1 m x 1 h _________ 60 min = 41.7 cm/min 1B-18

THE PROPERTY OF DENSITY Material Density Lead Water Cork Air Helium 11.34 g/mL 1.00 g/mL 0.24 g/mL 0.0013 g/mL 0.0001 g/mL DENSITY – Mass per unit volume D = m ___ V 1B-19

What is the density of a solid in which 2.20 g occupies 1.50 mL? D = m ___ V = 2.20 g __________ 1.50 mL = 1.47 g/mL 1B-20

What is the mass of 12. 0 mL of a solid if it has a density of 3 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 = (12.0 mL)(3.50 g/mL) = 42.0 g 1B-21

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 = 6.2 g ____________ 1.4 g/mL = 4.4 mL 1B-22

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 Density Solve for D, m, or V 1B-24