1. Measurement in Chemistry Factor-Label Method

2. The Factor-Label Method At the conclusion of our time together, you should be able to:
Recognize a problem that can be solved with the factor label method
Transform a statement of equality into a conversion factor
Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found

3. The Factor label Method
A way to solve math problems in chemistry
Used to convert
km to miles, m to km, mol to g, g to mol, etc.
To use this we need:
1) desired quantity
2) given quantity
3) conversion factors
Conversion factors are valid relationships or equalities expressed as a fraction and equal to one!

4. Equalities length 10.0 in. 25.4 cm
State the same measurement in two different units
length
10.0 in.
25.4 cm

5. Conversion Factors Example: 1 in. = 2.54 cm
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units but always equal to one. You can always multiply any equation by this equality and not change the quantity, just the units.
Example: in. = 2.54 cm
Factors: 1in and cm
2.54 cm in.

6. For example: 1 km = 0.6 miles the conversion factor is
Write conversion factors for 1 foot = 12 inches
What conversion factors can you think of that involve meters?

7. Conversion Factors Conversion factors for 1 ft = 12 in
There are almost an infinite number of conversion factors that include meters:

8. The Steps to Follow
Now we are ready to solve problems using the factor label method. The steps involved are:
Write the desired quantity and =
Write down the given quantity and put it over 1
Determine what conversion factors you will use to turn the given label into the needed label.
Multiply the given quantity by the appropriate conversion factors to eliminate units you don’t want and leave the units you do want
Complete the math

9. First write down the desired quantity
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
First write down the desired quantity

10. Next, equate desired quantity to the given quantity
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
Next, equate desired quantity to the given quantity

11. Now we have to choose a conversion factor
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
Now we have to choose a conversion factor

12. What conversion factors are possible?
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
1 km
0.621 mi
0.621 mi
1 km
What conversion factors are possible?

13. Pick the one that will allow you to cancel out miles
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
1 km
0.621 mi
0.621 mi
1 km
Pick the one that will allow you to cancel out miles

14. Pick the one that will allow you to cancel out miles
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
1 km
0.621 mi
0.621 mi
1 km
Pick the one that will allow you to cancel out miles

15. Multiply given quantity by chosen conversion factor
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
1 km
0.621 mi
0.621 mi
1 km
Multiply given quantity by chosen conversion factor

16. Multiply given quantity by chosen conversion factor
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
x 1 km
0.621 mi
Multiply given quantity by chosen conversion factor

17. Cross out common factors
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= mi
x 1 km
0.621 mi
Cross out common factors

18. Cross out common factors
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
x 1 km
0.621
# km
= 47.0
Cross out common factors

19. Are the units now correct?
Factor label Example
How many kilometers are in 47.0 miles? (note: 1 km = miles)
x 1 km
0.621
# km
= 47.0
Are the units now correct?
Yes – km on both sides!

20. Factor label Example Now finish the math.
How many kilometers are in 47.0 miles? (note: 1 km = miles)
# km
= 47.0
x 1 km
0.621
= km
Now finish the math.

21. The Steps to Follow
Now we are ready to solve problems using the factor label method. The steps involved are:
Complete the math with no rounding
Make certain the sig figs are correct by rounding to the correct number of sig figs at the very end
Don’t forget the order of operations when you complete the math
Conversion factors do not determine sig. figs.!

22. Factor label Example The final answer is 75.7 km
How many kilometers are in 47.0 miles? (note: 1 km = miles)
x 1 km
0.621
= 75.7 km
# km
= 47.0
The final answer is 75.7 km

23. Summary The previous problem was not that hard
In other words, you probably could have done it faster using a different method
However, for harder problems the factor label method is easiest

24. More Examples
1. You want to convert U.S. dollars to Canadian dollars. If the exchange rate is Can$ = 0.65 US$, how much will it cost?
# Can$
= US$
x 1 Can$
0.65 US$
= Can$

25. The Factor-Label Method Let’s see if you can:
Recognize a problem that can be solved with the factor label method
Transform a statement of equality into a conversion factor
Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found

26. Learning Check
Write conversion factors that relate each of the following pairs of units:
1. Liters and mL
1 Liter = 1000 mL
2. hours and minutes
1 hour = 60 minutes
3. meters and kilometers
1000 meters = 1 kilometer

27. How many minutes are in 2.5 hours?
Conversion factor
2.5 hr x min = min
1 hr
By using dimensional analysis/factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

28. Learning Check 7.25 dollars 4 quarters 1 dollar = 29 quarters
You have $7.25 in your pocket in quarters. How many quarters do you have?
7.25 dollars quarters
1 dollar
= 29 quarters X

29. Measurement in Chemistry Factor-Label Method Part 2

30. The Factor-Label Method At the conclusion of our time together, you should be able to:
Recognize a problem that can be solved by moving the decimal point.
Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found with two changes of labels or labels that are squared or cubed.

31. Dealing with Two Units Convert 55.00 km/h to m/s
km x m x 1 h___ =
h km s
15.28 m/s

32. A patient requires injection of 0
A patient requires injection of g of a pain killer available in a 15 mg/mL solution. How many milliliters should be administered?
When you see a number with two units like 15 mg/mL, it can be used as a conversion factor. What it really says is that 1 ml of the solution contains 15 mg of the drug.
? mL = g of drug
0.012 g drug  mL soln
mg drug 
103
mg drug 1
mL soln
? mL = g of drug 1
g drug 15
mg drug
= 0.80 mL soln

33. Dealing with Two Units, Your Turn
If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet?
1 meter = 3.28 feet
2380 seconds
# s
= 8450 ft
x 1 m
3.28 ft
x 1 min
65 m
x 60 s
1 min

34. What about Square and Cubic units?
Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also!
Best way: Square or cube the Entire conversion factor
Example: Convert 4.3 cm3 to mm3
( )
4.3 cm mm 3
1 cm
4.3 cm mm3
13 cm3 =
= 4300 mm3

35. Learning Check
A Nalgene water bottle holds 1000 cm3 of dihydrogen monoxide (DHMO). How many cubic decimeters is that?

36. Solution
( )
1000 cm dm 3
10 cm
= 1 dm3
So, a dm3 is the same as a Liter!
A cm3 is the same as a milliliter.

37. Converting Metric to Metric
A rattlesnake is 2.44 m long. How long is the snake in cm?
a) cm
b) 244 cm
c) 24.4 cm

38. Solution
A rattlesnake is 2.44 m long. How long is the snake in cm?
b) 244 cm
2.44 m x cm = 244 cm
1 m

39. Converting Units of Length Made Easy
0.5 kilometer (km) = 500 meters (m)
2.5 meter (m) = 250 centimeters (cm)
1 centimeter (cm) = 10 millimeter (mm)
1 nanometer (nm) = 1.0 x 10-9 meter
O—H distance =
9.4 x m
9.4 x 10-9 cm
0.094 nm

40. A rattlesnake is 2.44 m long. How long is the snake in cm?
An Easier Way
A rattlesnake is 2.44 m long. How long is the snake in cm?
G _ _ M _ _ k h da _ d c m _ _ μ _ _ n
A move from 1 meter to centimeters is two places right
Move the decimal place of the number two places right
244 cm

41. Another Example: How many millimeters are there in 4.5 cm?
G _ _ M _ _ k h da _ d c m _ _ μ _ _ n
A move from cm to mm is one place right
Move the decimal place of the number one place right
45 mm

42. Another Example: How many kilometers are there in 4.5 cm?
G _ _ M _ _ k h da _ d c m _ _ μ _ _ n
A move from cm to km is five places left
Move the decimal place of the number five places left km

43. The Factor-Label Method Let’s see if you can:
Recognize a problem that can be solved by moving the decimal point.
Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found with two changes of labels or labels that are squared or cubed.

44. Learning Check: 2 kilometers is the same as how many millimeters
G _ _ M _ _ k h da _ d c m _ _ μ _ _ n
A move from km to mm is six places right
Move the decimal place of the number six places right
mm, 2 x 106 mm

45. Metric Conversions #1: Write 550 mm as meters.
G _ _ M _ _ k h da _ d c m _ _ μ _ _ n
A move from mm to m is 3 places left
Move the decimal place of the number 3 places left
0.55 m

46. Learning Check
A person’s blood contains 185 mg of cholesterol per deciliter of blood. How many grams of cholesterol are there in 1 liter of this blood? g
0.185 g
1.85 g
18.5 g
1850 g

47. English and Metric Conversions
If you know ONE conversion for each type of measurement, you can convert anything!
You must use these conversions:
Mass: grams = 1 pound
Length: cm = 1 inch
Volume: L = 1 quart

48. An adult human has 4.65 L of blood. How many gallons of blood is that?
Learning Check
An adult human has 4.65 L of blood. How many gallons of blood is that?
Unit plan: L qt gallon
Equalities: 1 quart = L
1 gallon = 4 quarts
Your Setup: gal = 4.65 L x 1 quart x 1 gallon
L 4 quarts
= 1.23 gallons

49. Exit Quiz # cm = 1 yd x 3 ft 1 yd x 12 in 1 ft x 1 cm 0.394 in
There are 12 inches in a foot, inches in a centimeter, and 3 feet in a yard. How many centimeters are in yard?
# cm
= 1 yd
x 3 ft
1 yd
x 12 in
1 ft
x 1 cm
0.394 in
= cm

50. Change 9.4 miles to km (1 mile = 1.6 km)
Exit Quiz #6 on WS
Change 9.4 miles to km (1 mile = 1.6 km)
# km
= 9.4 mi
x 1.6 km
1 mi
= 15 km

51. Exit Quiz
With a U.S. dollar you can buy 1.1 Euros, 130 Yen, or 25 Rubles. How many Yen can you buy with one Ruble?
# Yen
= 1 Ruble
x 1 US $
25 Rubles
x 130 Yen
1 US $
= 5.2 Yen

52. Exit Quiz
Calculate how many feet are in 1 meter. (use 1 cm = in)
# ft
= 1 m
x 100 cm
1 m
x in
1 cm
x 1 ft
12 in
= 3.28 ft