1. Problem Solving using Conversion Factors
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2. 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.)

3. 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

4. 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 x Unit = Unit 2
Unit 1
Given x Conversion = Needed
unit factor unit
pints  milliliters
# pints = # milliliters

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

6. Setting up a Problem How many minutes are 2.5 hours?
Given unit = 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
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7. Example Problem
A rattlesnake is 2.44 m long. How many centimeters long is the snake?
1) cm
2) 244 cm
3) 24.4 cm

8. 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 cm = 244 cm
1 m

9. 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 x Unit x Unit = Unit 3
Unit Unit 2

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

11. 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 hr
24 hr min
Units = day2/min is not the unit needed
Units don’t cancel properly.

12. 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 kg
1 kg lb
STEP 4 Set Up Problem
165 lb x kg = kg
2.20 lb

13. 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:

14. 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 qt x 1 gal = gal
1 L qt
3 SF SF exact SF

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

16. 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

17. Densities of Common Substances

18. 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) g/cm3
2) g/cm3
3) g/cm3

19. 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 = g
volume cm3
calculator = g/cm3
final answer (2) = g/cm3 (3 SF)

20. 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

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.
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22. 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) K W V V W K V W K

23. 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 mL
= 9.5 mL = 9.5 cm3
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24. Density Using Volume Displacement
The density of the zinc object is
then calculated from its mass
and volume.
mass = g = 7.2 g/cm3 volume cm3
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25. 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 g/ml.
What is the specific gravity?

26. 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!!

27. 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

28. Chapter 2.3 Temperature Conversion
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29. Temperature Scales Temperature Scales
are Fahrenheit, Celsius, and Kelvin.
have reference points for the boiling and freezing points of water.
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30. Think about it A. What is the temperature of freezing water?
1) 0°F ) 0°C ) 0 K
B. What is the temperature of boiling water?
1) 100°F ) 32°F ) 373 K
C. How many Celsius units are between the boiling and freezing points of water?
1) ) ) 273

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

32. Celsius - Fahrenheit A person with hypothermia has a
body temperature of 34.8°C. What is that temperature in °F?
TF = 1.8 TC 
TF = 1.8 (34.8°C) °
exact tenth's exact
= °
= 94.6°F
tenth’s
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33. 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

34. 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

35. 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

36. 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
contains the lowest possible temperature, absolute zero (0 K).
0 K = –273°C

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

38. Temperatures
TABLE 2.5

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

40. 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