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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
  • Check your work
  • Reread the question, did you answer it
  • Is it reasonable?
  • Estimate

6
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.

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
  • 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

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.
  • 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

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
  • cancel Answer (2 SF)

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
  • 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

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
  • Check your work.

34
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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