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Chapter 3
Problem Solving and
Conversion Factors
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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.
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Problem solving
 Identify the unknown.
Both in words and what units it will be
measured in.
May need to read the question several times.
 Identify what is given
Write it down if necessary.
Unnecessary information may also be given
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Problem solving
 Plan a solution
The “heart” of problem solving
Break it down into steps.
Look up needed information.
Tables
Formulas
Constants
Equations
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Problem solving
 Do the calculations – math (algebra)
 Finish up
Sig Figs
Units
Check your work
Reread the question, did you answer it
Is it reasonable?
Estimate
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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.
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Initial and Final Units
1. A person has a height of 2.0 meters.
What is that height in inches?
Initial unit = m
Final unit = _______
2) Blood has a density of 0.05 g/mL. If a
person lost 0.30 litres of blood at 18°C, how
many grams of blood would that be?
Initial = litres
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Final unit = _______
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
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Conversion factors
Called conversion factors because they
allow us to convert units.
 really just multiplying by one, in a
creative way.
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Conversion factors
1m
100 cm
10
=
100 cm
100 cm
= 1
Conversion factors
1m
100 cm
11
=
1
Conversion factors
1m
100 cm
1m
1m
12
=
=
1
100 cm
1m
Conversion factors
1m
100 cm
1
13
=
=
1
100 cm
1m
Conversion Factors
The units of measurement are not always
convenient dimensions and it may
become necessary to change units. In a
lab the distance could only be
measured in cm. To calculate the speed
the cm must be converted to m without
changing the value of the measurement.
Distance in cm x [conversion factor] = distance in m
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Conversion Factors
The only number that can multiply any other number without
changing the number’s value is 1. The conversion factor is
a ratio. The value of the ratio is 1. For the ratio to have a
value of one the top term has to equal the bottom term.
Start with 1255cm, want to find the number of m, then:
By definition 1m = 100 cm
1 m
=1
100cm
1255 cm x
1 m = 12.55m
100cm
The conversion factor must cancel the present unit and
introduce the desired unit
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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
 1000 mm = 1 m
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Write the conversion factors for
the following
kilograms to grams
 feet to inches (1 foot = 12 inches)
 1.096 qt. = 1.00 L
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How many minutes are in 2.5 hours?
Initial unit
 2.5 hr
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Conversion

factor
 2.5 hr x 60 min
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1 hr
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cancel
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Final
unit
= 150 min
Answer (2 SF)
Learning Check
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A rattlesnake is 2.44 m long. How
long is the snake in cm?
1)
2)
3)
2440 cm
244 cm
24.4 cm
Solution
A rattlesnake is 2.44 m long. How long
is the snake in cm?
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2) 244 cm
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2.44 m x 100 cm
1m
= 244 cm
Learning Check
How many seconds are in 1.4 days?
 Unit plan: days
hr
min
seconds
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2 SF
Exact
1.4 day x 24 hr x 60 min x 60 sec
1 day
1 hr
1 min
= 1.2 x 105 sec
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Unit Check
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What is wrong with the following setup?
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1.4 day
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x 1 day
24 hr
x
60 min
1 hr
x 60 sec
1 min
Steps to Problem Solving
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Read problem
Identify data
Write down a unit plan from the initial unit
to the desired unit
Select conversion factors
Change initial unit to desired unit
Cancel units and check
Do math on calculator
Give an answer using significant figures
Learning Check
If the ski pole is 3.0 feet in length,
how long is the ski pole in m?
2.54 cm = 1.00 inch 12 inches = 1 foot
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unit plan
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3.0 ft x 12 in
1 ft
Solution
ft in
cm
m
x 2.54 cm x 1m = 0.91m
1 in.
100 cm
The solutions for some problems contain multi-steps
(require more than one calculation to solve).
Using Dimensional Analysis can solve this type of problem.
Dimensional Analysis
1.
Identify the given or known data (information).
2.
Identify the unknown.
3.
Plan the solution or calculations by either:
i.
setting up a series of conversion factors OR
ii. using a formula.
4.
Check your work by canceling out units.
1. Calculate the number of seconds of Chemistry class
there is in a week.
2.
The density of gold is 19.3 g.
cm3
What is the density of gold expressed in kg?
m3
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Practice
Use conversation factors to solve the
following:
A pain relief tablet contains 325 mg of
ASA. There are 80 tablets in the
package of tablets.
(a) What is the mass of ASA in grams for
each tablet?
(b) What is the total mass, in grams, of
ASA in the package?
(c) A person is permitted to take 1950 mg
of ASA per day. How many days will
this package last?
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T
H
E
E
N
D
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
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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
=
0.36 inches
36 inches
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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?
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Example of Problem Solving
How much heat is needed to raise the
temperature of 56.8 g of iron by 65ºC?
 Identify the unknown
Heat - calories.
 Knowns
Mass, Change in temperature
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Example of Problem Solving
 Plan a solution
Formula Heat = SH x mass x DT
look up SH of Iron = 0.106 cal/gºC
 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
 Check your work.
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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?
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