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## Problem Solving and Conversion Factors

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### Problem Solving and Conversion Factors Dimensional Analysis Another measuring system has different units of measure. 6 ft = 1 fathom 100 fathoms = 1 cable ... – PowerPoint PPT presentation

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Title: Problem Solving and Conversion Factors

1
Chapter 3
• Problem Solving and Conversion Factors

2
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.

3
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

4
Problem solving
• Plan a solution
• The heart of problem solving
• Break it down into steps.
• Look up needed information.
• Tables
• Formulas
• Constants
• Equations

5
Problem solving
• Do the calculations math (algebra)
• Finish up
• Sig Figs
• Units
• Is it reasonable?
• Estimate

6
Dimensional Analysis
• Dimension unit
• Analyze solve
• Using the units to solve the problems.
are you did the math right.

7
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 18C, how many grams of blood would that
be? Initial litres Final unit _______
8
Conversion factors
• A ratio of equivalent measurements
• 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

9
Conversion factors
• Called conversion factors because they allow us
to convert units.
• really just multiplying by one, in a creative way.

10
Conversion factors

1
11
Conversion factors
1
1 m

100 cm
12
Conversion factors
1
1 m

100 cm
13
Conversion factors
1
1 m

100 cm
100 cm

1
1 m
14
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

15
Conversion Factors
• The only number that can multiply any other
number without changing the numbers 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.
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

16
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

17
Write the conversion factors for the following
• kilograms to grams
• feet to inches (1 foot 12 inches)
• 1.096 qt. 1.00 L

18
How many minutes are in 2.5 hours?
• Initial unit
• 2.5 hr
• Conversion Final
• factor unit
• 2.5 hr x 60 min 150 min
• 1 hr

19
Learning Check
• A rattlesnake is 2.44 m long. How long is the
snake in cm?
• 1) 2440 cm
• 2) 244 cm
• 3) 24.4 cm

20
Solution
• A rattlesnake is 2.44 m long. How long is the
snake in cm?
• 2) 244 cm
• 2.44 m x 100 cm 244 cm
• 1 m

21
Learning Check
• How many seconds are in 1.4 days?
• Unit plan days hr min
seconds
• 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

22
Unit Check
• What is wrong with the following setup?
• 1.4 day x 1 day x 60 min x 60
sec
• 24 hr 1 hr
1 min

23
Steps to Problem Solving
• 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

24
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

25
Solution unit plan ft in cm m
• 3.0 ft x 12 in x 2.54 cm x 1m
0.91m
• 1 ft 1 in.
100 cm

26
• 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
•   Identify the given or known data (information).
•   Identify the unknown.
• Plan the solution or calculations by either
• setting up a series of conversion factors OR
• using a formula.
• Check your work by canceling out units.
•
•  1. Calculate the number of seconds of
Chemistry class there is in a week.
• The density of gold is 19.3 g.
• cm3
• What is the density of gold expressed in kg?
• m3

27
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?

28
• T
• H
• E
• E
• N
• D

29
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

30
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

31
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?

32
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

33
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