1. Moles Unit
Dimensional Analysis

2. Dimensional Analysis
Dimensional Analysis or the factor label method is a useful problem solving technique to convert between units.

3. Dimensional Analysis Solving problems using DA
Always start with the GIVEN!
Then set up a conversion factor with the original unit on the bottom and the new unit on the top.

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

5. Example
600 minutes = ?? Hours What’s the unit we’re looking for? Hours So…. 1 hour or 60 minutes 60 minutes 1 hour

6. This one cancels out minutes! 600 minutes x 1 hour = 60 minutes
Example
This one cancels out minutes! 600 minutes x 1 hour = 60 minutes
10 hours

7. Steps for using Dimensional Analysis1
Write down your given information
Write down an answer blank and the desired unit on the right side of the problem space 2
Use equivalents to cancel unwanted unit and get desired unit. 3
Calculate the answer…multiply across the top & divide across the bottom of the expression 4

8. Common Equivalents = = = = = = = 1 ft 12 in 1 in 2.54 cm 1 min 60 s
1 hr =
3600 s
1 quart (qt) =
0.946 L
4 pints =
1 quart =
1 pound (lb)
454 g

9. How many grams are equal to 1.25 pounds?
Example #1 1
Write down your given information
Example:
How many grams are equal to 1.25 pounds?
1.25 lb

10. How many grams are equal to 1.25 pounds?
Example #1
Write down an answer blank and the desired unit on the right side of the problem space 2
Example:
How many grams are equal to 1.25 pounds?
1.25 lb
= ________ g

11. How many grams are equal to 1.25 pounds?
Example #1
Use equivalents to cancel unwanted unit and get desired unit. 3
Example:
How many grams are equal to 1.25 pounds?
454 g
1.25 lb 
= ________ g 1 lb
Put the unit on bottom that you want to cancel out!
The equivalent with these 2 units is: 1 lb = 454 g
A tip is to arrange the units first and then fill in numbers later!

12. How many grams are equal to 1.25 pounds?
Example #1
Calculate the answer…multiply across the top & divide across the bottom of the expression 4
Example:
How many grams are equal to 1.25 pounds?
454 g 
568
1.25 lb
= ________ g 1 lb
Enter into the calculator: 1.25  454  1

13. Multi-step problems
There isn’t always an equivalent that goes directly from where you are to where you want to go!
Rather than trying to determine a new equivalent, it’s faster to use more than one step in dimensional analysis!
This way you have fewer equivalents to remember and you’ll make mistakes more often
With multi-step problems, it’s often best to plug in units first, then go back and do numbers.

14. Example
There are 12 inches in a foot, inches in a centimeter, and 3 feet in a yard. How many cm are in one yard?
1 yd
x 3 ft
1 yd
x 12 in
1 ft
x 1 cm
0.394 in
= 91.37 cm

15. Conversion factors
We have looked at conversion factors that are always true. There are conversion factors that are only true for specific questions
E.g. A recipe calls for 2 eggs, 1 cup of flour and 0.5 cups of sugar
We can use these conversion factors
Q - the chemical equation between H2 and O2 involves 2 H2 molecules combining with 1 O2 molecule to make 2 H2O molecules. Write all possible conversion factors

16. 2H2 + O2  2H2O 2 molecules H2 1 molecule O2 2 molecules H2
2 molecules H2O
1 molecule O2
2 molecules H2O
2 mol H2
1 mol O2
2H2 + O2  2H2O
2 mol H2
2 mol H2O
1 mol O2
2 mol H2O