PROBLEM-SOLVING
The SMART way
FACTOR-LABEL
(aka DIMENSIONAL ANALYSIS)
Solve in 5 minutes
• An ancient measurement of volume mentioned in the Bible
is the EPHAH.
• CHALLENGE:
• You have 5 minutes to figure out how many liters are equal
to an ephah, using the following information:
• 1 EPHAH = 2.429 MODIUM (ancient Roman measurement)
• 1 MODIUM =0.7076 VEDRO (old Russian measurement)
• 1 VEDRO = 0.349 BUSHELS (customary unit of
measurement)
• 1 BUSHEL = 2150 CUBIC INCHES
• 61.01 CUBIC INCHES = 1 LITER
We convert all the time.
When the values are familiar, it is easy.
When the problem is short it is simple.
But in chem, you will need to solve problems that are
neither familiar nor short!
Factor-Label
• Use CONVERSION
FACTORS
• LABEL all units
The labels on the factors
guide you through the
problem as they cancel out
Factor-label to the rescue!
Here I come to save the day!
Factor-Label Method
• Use for conversion problems
– Changing from one unit to another
• Only use for multiplication and division
problems
Equalities
• Equalities
– Two ways to express the same thing
– The quantities are equal, but they are expressed
in different units
EX: 1”
7 days
=
=
2.54 cm
1 week
Equalities
• If the 2 equal quantities are divided, the answer is
1…you get unity.
• If you divide a value by itself, you get 1
• So we get CONVERSION FACTORS from
1” = 2.54 cm
1”
=
2.54 cm
7 days = 1 week
2.54 cm = 1
1”
7 days = 1 week = 1
1 week 7 days
HOW TO DO FACTOR-LABEL CONVERSION PROBLEMS
1. Write down the starting factor and units.
EX: How many cm in 1.98 m?
2. Give yourself room on the paper to work and go
to the end and write the desired unit or final
factor
EX: 1.98 m
=
cm
3. Use the appropriate conversion factor(s) (from
equalities) to cancel unwanted units and leave
desired units. Any label on both top and bottom
of the fractions cancels.
EX: Equality 1 m = 100 cm
This yields two conversion factors
1m
or
100 cm
100 cm
1m
=
1
EX: Equality 1 m = 100 cm
this yields two conversion factors
1m
or
100 cm
100 cm
1m
=
1
Which one to use?
Set up the problems with the one that results in the
cancellation of the starting unit.
1.98 m |
100 cm
1m
=
cm
4. Cancel the UNITS ONLY that are on the top and bottom
of the fractions.
1.98 m |
100 cm
1m
=
cm
5. Do the math to solve.
Multiply by all values on the top
Divide by all values on the bottom
Write the answer with units and the correct number of
sigdigs
Note: Counted values and defined conversion factors do not
limit sigdigs…only measured values.
Why? Sigdigs convey the precision of a measurement. We
can count exactly and we define certain values exactly.
EX: 1.98 m |
|
100 cm
1m
= 198
cm
Note: with this “picket fence” set up, the vertical
bars separate fractions
1.98 m |
|
100 cm
1m
= 198
cm
Is the same as
1.98 m X 100 cm
1m
= 198
cm
You may set yours up either way, but many
students find it easier to keep long problems
organized with the picket fence style.
How many SCHNIZZLES in 12 TWIZZLES?
What do you know? Starting factor
What do you want to know? Final factor
Start:
Desired/Final:
12
Twizzles
______ Schnizzles
How do you get from the START to FINAL?
You need to find or know some EQUALITIES to use as CONVERSION FACTORS
10 Sizzles = 5 Fizzles
1 Frizzle = 3 Sizzles
18 Fizzles = 1 Twizzle
2 Frizzles = 5 Schnizzles
These are defined and counted conversion factors. Report all digits as significant.
Start TwizzlesConversion Factors   Final Schnizzles
Congratulations!
Factor-Label has guided you through a
problem that you knew nothing about!
It will guide you through lots chemistry
problems, too!
A familiar example
WARNING
Avoid
Factor-Label
(Dimensional Analysis)
if …
You enjoy making mistakes
You have a phobia of correct answers
You enjoy solving problems in a convoluted manner
You take pleasure in re-inventing the wheel