PWISTA
Math of Chemistry
Problem Solving
Dimensional analysis
Factor Label Method
Word Problems
• The laboratory does not give you numbers
already plugged into a formula.
• You have to decide how to get the answer.
• Like word problems in math.
• The chemistry book gives you word
problems.
Problem solving
1) Identify the unknown.
Both in words and what units it will be
measured in.
May need to read the question several times.
2) Identify what is given
Write it down if necessary.
Unnecessary information may also be given.
Problem solving
3) Plan a solution
The “heart” of problem solving
Break it down into steps.
Look up needed information.
Tables
Formulas
Constants
Equations
Problem solving
4) Do the calculations - algebra
5) Finish up
Sig Figs
Units
Check your work
Reread the question, did you answer it?
Is it reasonable?
Estimate
FLM
• GIVEN - List all pertinent information with
dimension symbol, number and unit.
• FIND - List the dimension of the quantity
requested in problem.
• FORMULA - With the dimensions in
GIVEN and FIND, list the formula of
formulas that fit.
FLM
• SOLVE - Solve the formula for what you
are looking for (FIND), substitute the
number values in GIVEN, and perform the
math on both the units and the numbers.
• ANSWER - Check the answer for
likeliness, make sure the units are
appropriate, express the answer in
scientific notation and to the accuracy
required, and draw a box around it so it is
obvious which number your answer is.
Example of Problem Solving
• How much heat is needed to raise the
temperature of 56.8 g of iron by 65ºC?
1) Identify the unknown
Heat - calories.
2) Knowns
Mass, Change in temperature
Example of Problem Solving
3) Plan a solution
Formula Heat = SH x mass x DT
look up SH of Iron = 0.106 cal/gºC
4) Do the calculations
heat = 0.106 cal/gºC x 56.8 g x 65ºC
heat = 391.352 cal/gºC x g x ºC
heat = 390 cal
5) Check your work.
Conversion factors
• “A ratio of equivalent measurements.”
• Start with two things that are the same.
One meter is one hundred centimeters.
• Write it as an equation.
1 m = 100 cm
• Can divide by each side to come up with
two ways of writing the number 1.
Conversion factors
1m
100 cm
=
100 cm
100 cm
Conversion factors
1m
100 cm
=
1
Conversion factors
1m
100 cm
1m
1m
=
=
1
100 cm
1m
Conversion factors
1m
100 cm
1
=
=
1
100 cm
1m
Conversion factors
• A unique way of writing the number 1.
• In the same system they are defined
quantities so they have unlimited
significant figures.
• Equivalence statements always have this
relationship.
• big # small unit = small # big unit
ex: 1000 mm = 1 m
Prefix Abbreviation Meaning Example
mega-
M
106
1 megameter (Mm) = 1 x 106 m
kilo-
k
103
1 kilogram (kg) = 1 x 103 g
centi-
c
10-2
1 centimeter (cm) = 1 x 10-2 m
milli-
m
10-3
1 milligram (mg) = 1 x 10-3 g
micro-
mc
10-6
1 micrometer (mcg) = 1 x 10-6 g
nano-
n
10-9
1 nanogram (ng) = 1 x 10-9 g
Write the conversion factors
for the following
• kilograms to grams
• feet to inches
• 1.096 qt. = 1.00 L
What are they good for?
We can multiply by one creatively to
change the units .
 13 inches is how many yards?
 36 inches = 1 yard.
 1 yard
=1
36 inches
 13 inches x
1 yard
=
36 inches

Conversion factors
• Called conversion factors because they
allow us to convert units.
• Really just multiplying by one, in a creative
way.
Dimensional Analysis
•
•
•
•
Dimension = unit
Analyze = solve
Using the units to solve the problems.
If the units of your answer are right,
chances are you did the math right.
How many centimeters are in 6.00
inches?
How many seconds are in 2.0
years?
Dimensional Analysis
• A ruler is 12.0 inches long. How long is it
in cm? ( 1 inch is 2.54 cm)
• in meters?
• A race is 10.0 km long. How far is this in
miles?
– 1 mile = 1760 yds
– 1 meter = 1.094 yds
• Pikes peak is 14,110 ft above sea level.
What is this in meters?
Multiple units
• The speed limit is 65 mi/hr. What is this in
m/s?
– 1 mile = 1760 yds
– 1 meter = 1.094 yds
65 mi
hr
1760 yd
1m
1 hr 1 min
1 mi
1.094 yd 60 min 60 s
What is the density of mercury
(13.6 g/cm3) in units of kg/m3?
Units to a Power
• How many m3 is 1500 cm3?
1500 cm3
1500
1m
1m
1m
100 cm 100 cm 100 cm
cm3
1m
100 cm
3
Dimensional Analysis
• Another measuring system has different
units of measure.
6 ft = 1 fathom
100 fathoms = 1 cable length
10 cable lengths = 1 nautical mile
3 nautical miles = 1 league
• Jules Verne wrote a book 20,000 leagues
under the sea. How far is this in feet?
FLM in Chemistry
• How many atoms of hydrogen can be
found in 45 g of ammonia, NH3?
We know
•
1 mole of NH3 has a mass of 17 grams.
•
1 mole of NH3 contains 6.02 x 1023
molecules of NH3.
•
1 molecule of NH3 has 3 atoms of
hydrogen in it.
FLM example
Lead is 11.3 g/cc. What is the volume of
24.5 kg of lead?
• ALWAYS put the unit you want to find ON
TOP!
• 1cc
x 24.5 kg x 1000g x 1 liter
11.3 g
1
1 kg
1000 cc
2.168 L
Quiz
• How many millimeters are present in 20.0
inches?
• The volume of a wooden block is 6.30 in3.
This is equivalent to how many cubic
centimeters?
• A sample of calcium nitrate, Ca(NO3)2,
with a formula weight of 164 g/mol, has
5.00 x 1027 atoms of oxygen. How many
kilograms of Ca(NO3)2 are present?
• Answers:
• (1) 508 mm
• (2) 103 cm3
• (3) 227 kg
More Fun
• The US Quarter has a mass of 5.67g and
is approximately 1.55mm thick.
– How many quarters would have to be stacked
to reach 575 feet, the height of the
Washington Monument?
– How much would this stack weigh?
– How much money would this stack contain?
– How many of these stacks would be needed
to pay off the national debt of 9.0 trillion
dollars?