Problem solving Intro FLM plain

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Problem solving Intro FLM plain Powered By Docstoc
					    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       1
1m       =   100 cm
1m            1m
Conversion factors

 1m      =
100 cm       1
         =   100 cm
    1         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   1760 yd   1m      1 hr 1 min
   hr    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      1m     1m     1m
             100 cm 100 cm 100 cm
                            3
                     1m
      1500   cm3
                   100 cm
       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?

				
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