Problem Solving using Conversion Factors Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Given and Needed Units To solve a conversion problem you need to: 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.)

Learning Check pints milliliters An injured person loses 0.30 pints of blood. How many milliliters of blood would that be? 1. Identify the given and needed units given in this problem. Given unit = _______ Needed unit = _______ pints milliliters

contd 2. Write the given and needed units. 3. Write a unit plan to convert the given unit to the needed unit. 4. Write equalities and conversion factors that connect the units. 5. Use conversion factors to cancel the given unit and provide the needed unit. Unit 1 x Unit 2 = Unit 2 Unit 1 Given x Conversion = Needed unit factor unit pints  milliliters # pints = # milliliters

Conversion An injured person loses 0.30 pints of blood. How many milliliters of blood would that be? 0.30 pints x 463 ml = 139 ml 1 pint

Setting up a Problem How many minutes are 2.5 hours? Given unit = 2.5 hr Needed unit = min Unit Plan = hr min Setup problem to cancel hours (hr). Given Conversion Needed unit factor unit 2.5 hr x 60 min = 150 min (2 SF) 1 hr Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Example Problem A rattlesnake is 2.44 m long. How many centimeters long is the snake? 1) 2440 cm 2) 244 cm 3) 24.4 cm

Solution A rattlesnake is 2.44 m long. How many centimeters long is the snake? Given Conversion Needed unit factor unit 2.44 m x 100 cm = 244 cm 1 m

Using Two or More Factors Often, two or more conversion factors are required to obtain the unit needed for the answer. Unit 1 Unit 2 Unit 3 Additional conversion factors are placed in the setup 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

Example: Problem Solving How many minutes are in 1.4 days? Given unit: 1.4 days Factor 1 Factor 2 Plan: days hr min Set up problem: 1.4 days x 24 hr x 60 min = 2016 min 1 day 1 hr 2 SF Exact Exact = 2 SF = 2.0 x 103 min

Check the Unit Cancellation Be sure to check your unit cancellation in the setup. The units in the conversion factors must cancel to give the correct unit for the answer. What is wrong with the following setup? 1.4 day x 1 day x 1 hr 24 hr 60 min Units = day2/min is not the unit needed Units don’t cancel properly.

Example Problems What is 165 lb in kg? STEP 1 Given 165 lb Need kg STEP 2 Plan STEP 3 Equalities/Factors 1 kg = 2.20 lb 2.20 lb and 1 kg 1 kg 2.20 lb STEP 4 Set Up Problem 165 lb x 1 kg = 75.0 kg 2.20 lb

More examples A bucket contains 4.65 L of water. How many gallons of water is that? Unit plan: L qt gallon Equalities: 1.06 qt = 1 L 1 gal = 4 qt Set up Problem:

Solution Given: 4.65 L Needed: gallons Plan: L qt gallon Equalities: 1.06 qt = 1 L; 1 gal = 4 qt Set Up Problem: 4.65 L x x 1.06 qt x 1 gal = 1.23 gal 1 L 4 qt 3 SF 3 SF exact 3 SF

Density Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

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/cm3 volume mL cm3 Note: 1 mL = 1 cm3

Densities of Common Substances

Example Osmium is a very dense metal. What is its density in g/cm3 if 50.0 g of osmium has a volume of 2.22 cm3? 1) 2.25 g/cm3 2) 22.5 g/cm3 3) 111 g/cm3

Solution Given: mass = 50.0 g volume = 22.2 cm3 Plan: Place the mass and volume of the osmium metal in the density expression. D = mass = 50.0 g volume 2.22 cm3 calculator = 22.522522 g/cm3 final answer (2) = 22.5 g/cm3 (3 SF)

Density How many mL of mercury are in a thermometer that contains 20.4 g of mercury? Have: mass Need: volume Use: density of mercury (d=13.6 g/mL) found in Table 1.11 d = m/vol vol = m/d

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. Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Think about it! Which diagram correctly represents the liquid layers in the cylinder? Karo (K) syrup (1.4 g/mL), vegetable (V) oil (0.91 g/mL,) water (W) (1.0 g/mL) 1 2 3 K W V V W K V W K

Volume by Displacement A solid completely submerged in water displaces its own volume of water. The volume of the solid is calculated from the volume difference. 45.0 mL - 35.5 mL = 9.5 mL = 9.5 cm3 Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Density Using Volume Displacement The density of the zinc object is then calculated from its mass and volume. mass = 68.60 g = 7.2 g/cm3 volume 9.5 cm3 Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Specific Gravity Ratio between the density of a substance and the density of water (= 1.00 g/ml) Example: Coconut oil has a density of 0.925 g/ml. What is the specific gravity?

Solution Specific gravity of coconut oil: no units!! Sp gr = density of oil 0.925 g/ml Sp gr = = = 0.925 density of water 1.00 g/ml no units!!

More examples: Specific Gravity What is the specific gravity of ice if 35.0 g of ice has a volume of 38.2 ml? Specific gravity = density of ice/density of water Density of ice = mass/volume

Chapter 2.3 Temperature Conversion Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Temperature Scales Temperature Scales are Fahrenheit, Celsius, and Kelvin. have reference points for the boiling and freezing points of water. Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Think about it A. What is the temperature of freezing water? 1) 0°F 2) 0°C 3) 0 K B. What is the temperature of boiling water? 1) 100°F 2) 32°F 3) 373 K C. How many Celsius units are between the boiling and freezing points of water? 1) 100 2) 180 3) 273

Temperature Conversion Fahrenheit TF - 32 Tc = TF = 1.8(TC) + 32 1.8 Celsius

Celsius - Fahrenheit A person with hypothermia has a body temperature of 34.8°C. What is that temperature in °F? TF = 1.8 TC + 32 TF = 1.8 (34.8°C) + 32° exact tenth's exact = 62.6 + 32° = 94.6°F tenth’s Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Temperature Conversion The normal temperature of a chickadee is 105.8°F. What is that temperature on the Celsius scale? 1) 73.8°C 2) 58.8°C 3) 41.0°C TC= (TF – 32°)/1.8 = (105.8°F - 32°)/1.8 = 41°C

One more time A pepperoni pizza is baked at 455°F. What temperature is needed on the Celsius scale? 1) 423°C 2) 235°C 3) 221°C TC= (TF – 32°)/1.8 = (455°F - 32°)/1.8 = 235°C

Learning Check TF = 1.8(TC) + 32° = 1.8(-15°) + 32° = 5°F On a cold winter day, the temperature is –15°C. What is that temperature in °F? 1) 19°F 2) 59°F 3) 5°F TF = 1.8(TC) + 32° = 1.8(-15°) + 32° = 5°F

Kelvin Temperature Scale The Kelvin temperature scale has 100 units between the freezing and boiling points of water. is obtained by adding 273 to the Celsius temperature. TK = TC + 273 contains the lowest possible temperature, absolute zero (0 K). 0 K = –273°C

Temperature Conversion Fahrenheit TF = 1.8(TC) + 32 TF - 32 Tc = 1.8 TK = TC +273 Celsius Kelvin TC = TK - 273

Temperatures TABLE 2.5

Calculate What is normal body temperature of 37.0°C in Kelvins? TK = TC + 273 = 37.0°C + 273 = 310. K

Temperature Conversion On the planet Mercury, the average night temperature is 13 K, and the average day temperature is 683 K. What are these temperatures in Celsius degrees? In Fahrenheit? TC = TK -273 TF = 1.8(TC) +32