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Chapter 3Chapter 3

Problem Solving and Problem Solving and Conversion FactorsConversion Factors

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Word ProblemsWord Problems The laboratory does not give you numbers The laboratory does not give you numbers

already plugged into a formulaalready plugged into a formula You have to decide how to get the answer.You have to decide how to get the answer. Like word problems in math.Like word problems in math. The chemistry book gives you word problems.The chemistry book gives you word problems.

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Problem solvingProblem solving Identify the unknown. Identify the unknown.

Both in words and what units it will be Both in words and what units it will be measured in.measured in.

May need to read the question several times.May need to read the question several times. Identify what is givenIdentify what is given

Write it down if necessary. Write it down if necessary.

Unnecessary information may also be givenUnnecessary information may also be given

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Problem solvingProblem solving Plan a solutionPlan a solution

The “heart” of problem solvingThe “heart” of problem solving

Break it down into steps.Break it down into steps.

Look up needed information.Look up needed information.

TablesTables

FormulasFormulas

ConstantsConstants

EquationsEquations

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Problem solvingProblem solving Do the calculations – math (algebra)Do the calculations – math (algebra) Finish upFinish up

Sig FigsSig Figs

UnitsUnits

Check your workCheck your work

Reread the question, did you answer itReread the question, did you answer it

Is it reasonable?Is it reasonable?

EstimateEstimate

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Dimensional AnalysisDimensional Analysis Dimension = unitDimension = unit Analyze = solveAnalyze = solve Using the units to solve the problems.Using the units to solve the problems. If the units of your answer are right, If the units of your answer are right,

chances are you did the math right.chances are you did the math right.

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Initial and Final UnitsInitial and Final Units

1. A person has a height of 2.0 meters. 1. A person has a height of 2.0 meters.

What is that height in inches?What is that height in inches?

Initial unit = mInitial unit = m Final unit = Final unit =

______________

2) Blood has a density of 0.05 g/mL. If a 2) Blood has a density of 0.05 g/mL. If a

person lost 0.30 litres of blood at 18°C, how person lost 0.30 litres of blood at 18°C, how

many grams of blood would that be?many grams of blood would that be?

Initial = litresInitial = litres Final unit = Final unit =

______________

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Conversion factorsConversion factors ““A ratio of equivalent measurements”A ratio of equivalent measurements” Start with two things that are the sameStart with two things that are the same

one meter is one hundred centimetersone meter is one hundred centimeters write it as an equationwrite it as an equation

1 m = 100 cm1 m = 100 cm can divide by each side to come up can divide by each side to come up

with two ways of writing the number 1with two ways of writing the number 1

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Conversion factorsConversion factors Called conversion factors because they Called conversion factors because they

allow us to convert units.allow us to convert units. really just multiplying by one, in a really just multiplying by one, in a

creative way.creative way.

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Conversion factorsConversion factors

100 cm1 m =100 cm 100 cm

= 1

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Conversion factorsConversion factors

11 m =100 cm

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Conversion factorsConversion factors

11 m =100 cm

100 cm=1 m1 m 1 m

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Conversion factorsConversion factors

11 m =100 cm

100 cm=1 m

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Conversion FactorsConversion FactorsThe units of measurement are not always The units of measurement are not always

convenient dimensions and it may convenient dimensions and it may become necessary to change units. In a become necessary to change units. In a lab the distance could only be lab the distance could only be measured in cm. To calculate the speed measured in cm. To calculate the speed the cm must be converted to m without the cm must be converted to m without changing the value of the measurement.changing the value of the measurement.

Distance in cm x [conversion factor] = distance in mDistance in cm x [conversion factor] = distance in m

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Conversion FactorsThe 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 = 1100cm

 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 factorsConversion factors A unique way of writing the number 1A unique way of writing the number 1 In the same system they are defined In the same system they are defined

quantities so they have unlimited quantities so they have unlimited significant figuressignificant figures

Equivalence statements always have Equivalence statements always have this relationshipthis relationship

big # big # small unit = small unit = small # small # big unitbig unit 10001000 mm = mm = 11 m m

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Write the conversion factors for Write the conversion factors for the followingthe following

kilograms to gramskilograms to grams feet to inches (1 foot = 12 inches)feet to inches (1 foot = 12 inches) 1.096 qt. = 1.00 L1.096 qt. = 1.00 L

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How many minutes are in 2.5 hours?How many minutes are in 2.5 hours?

Initial unitInitial unit 2.5 hr2.5 hr ConversionConversion Final Final factorfactor unit unit 2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min 1 hr1 hr cancelcancel Answer (2 SF) Answer (2 SF)

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Learning CheckLearning Check

A rattlesnake is 2.44 m long. A rattlesnake is 2.44 m long. How long is the snake in cm?How long is the snake in cm?

1) 1) 2440 cm2440 cm 2)2) 244 cm244 cm 3)3) 24.4 cm24.4 cm

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SolutionSolution

A rattlesnake is 2.44 m long. How A rattlesnake is 2.44 m long. How long is the snake in cm?long is the snake in cm?

2)2) 244 cm244 cm

2.44 m x 2.44 m x 100 cm 100 cm = 244 cm= 244 cm 1 m1 m

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Learning Check Learning Check

How many seconds are in 1.4 days?How many seconds are in 1.4 days? Unit plan: days hr min Unit plan: days hr min

secondsseconds

2 SF Exact2 SF Exact

1.4 day x 1.4 day x 24 hr24 hr x x 60 min60 min x x 60 sec60 sec

1 day 1 hr1 day 1 hr 1 min 1 min

= 1.2 x 10= 1.2 x 105 5 secsec

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Unit CheckUnit Check

What is What is wrongwrong with the following setup? with the following setup?

1.4 day x 1.4 day x 1 day 1 day x x 60 min 60 min x x 60 sec 60 sec 24 hr 1 hr 1 min24 hr 1 hr 1 min

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Steps to Problem SolvingSteps to Problem Solving

Read problemRead problem Identify data Identify data Write down a unit plan from the initial unitWrite down a unit plan from the initial unit

to the desired unit to the desired unit Select conversion factorsSelect conversion factors Change initial unit to desired unitChange initial unit to desired unit Cancel units and checkCancel units and check Do math on calculator Do math on calculator Give an answer using significant figuresGive an answer using significant figures

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Learning CheckLearning Check If the ski pole is 3.0 feet in length, If the ski pole is 3.0 feet in length,

how long is the ski pole in m? how long is the ski pole in m?

2.54 cm = 1.00 inch2.54 cm = 1.00 inch 12 inches = 1 foot12 inches = 1 foot

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SolutionSolutionunit plan ft in cm munit plan ft in cm m

3.0 ft x 3.0 ft x 12 in 12 in x x 2.54 cm2.54 cm x x 1m1m = 0.91m = 0.91m 1 ft 1 in. 100 cm1 ft 1 in. 100 cm

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The solutions for some problems contain multi-steps The solutions for some problems contain multi-steps (require more than one calculation to solve). (require more than one calculation to solve).

Using Dimensional Analysis can solve this type of problem.Using Dimensional Analysis can solve this type of problem.Dimensional AnalysisDimensional Analysis1.1.     Identify the given or known data (information).Identify the given or known data (information).2.2.     Identify the unknown. Identify the unknown. 3.3. Plan the solution or calculations by either:Plan the solution or calculations by either:

i.i. setting up a series of conversion factors ORsetting up a series of conversion factors ORii.ii. using a formula.using a formula.

4.4. Check your work by canceling out units. Check your work by canceling out units.     1. Calculate the number of seconds of Chemistry class 1. Calculate the number of seconds of Chemistry class

there is in a week.there is in a week.2.2. The density of gold is 19.3The density of gold is 19.3 gg. .

cmcm33

What is the density of gold expressed inWhat is the density of gold expressed in kgkg?? mm33

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PracticePracticeUse conversation factors to solve the Use conversation factors to solve the

following:following:A pain relief tablet contains 325 mg of A pain relief tablet contains 325 mg of

ASA. There are 80 tablets in the ASA. There are 80 tablets in the package of tablets. package of tablets.

(a) What is the mass of ASA in grams for (a) What is the mass of ASA in grams for each tablet?each tablet?

(b) What is the total mass, in grams, of (b) What is the total mass, in grams, of ASA in the package?ASA in the package?

(c) A person is permitted to take 1950 mg (c) A person is permitted to take 1950 mg of ASA per day. How many days will of ASA per day. How many days will this package last?this package last?

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TT HH EE

EE NN DD

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What are they good for?What are they good for? We can multiply by one creatively to We can multiply by one creatively to

change the units .change the units . 13 inches is how many yards?13 inches is how many yards? 36 inches = 1 yard.36 inches = 1 yard. 1 yard = 11 yard = 1

36 inches36 inches 13 inches x 1 yard 13 inches x 1 yard ==

36 inches36 inches

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What are they good for?What are they good for? We can multiply by one creatively to We can multiply by one creatively to

change the units .change the units . 13 inches is how many yards?13 inches is how many yards? 36 inches = 1 yard.36 inches = 1 yard. 1 yard = 11 yard = 1

36 inches36 inches 13 inches x 1 yard 13 inches x 1 yard == 0.36 0.36

inchesinches 36 inches36 inches

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Dimensional AnalysisDimensional Analysis A ruler is 12.0 inches long. How long is it A ruler is 12.0 inches long. How long is it

in cm? ( 1 inch is 2.54 cm)in cm? ( 1 inch is 2.54 cm) in meters?in meters? A race is 10.0 km long. How far is this in A race is 10.0 km long. How far is this in

miles? miles? – 1 mile = 1760 yds1 mile = 1760 yds– 1 meter = 1.094 yds)1 meter = 1.094 yds)

Pikes peak is 14,110 ft above sea level. Pikes peak is 14,110 ft above sea level. What is this in meters?What is this in meters?

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Example of Problem SolvingExample of Problem Solving How much heat is needed to raise the How much heat is needed to raise the

temperature of 56.8 g of iron by 65ºC?temperature of 56.8 g of iron by 65ºC? Identify the unknownIdentify the unknown

Heat - calories.Heat - calories. KnownsKnowns

Mass, Change in temperatureMass, Change in temperature

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Example of Problem SolvingExample of Problem Solving Plan a solutionPlan a solution

Formula Heat = SH x mass x Formula Heat = SH x mass x TT

look up SH of Iron = 0.106 cal/gºClook up SH of Iron = 0.106 cal/gºC Do the calculationsDo the calculations

heat = 0.106 cal/gºC x 56.8 g x 65ºCheat = 0.106 cal/gºC x 56.8 g x 65ºC

heat = 391.352 cal/gºC x g x ºCheat = 391.352 cal/gºC x g x ºC

heat = 390 calheat = 390 cal Check your work.Check your work.

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Dimensional AnalysisDimensional Analysis Another measuring system has different Another measuring system has different

units of measure.units of measure. 6 6 ft = 1 fathom ft = 1 fathom 100 100 fathoms = 1 cable lengthfathoms = 1 cable length 10 10 cable lengths = 1 nautical milecable lengths = 1 nautical mile 3 3 nautical miles = 1 leaguenautical miles = 1 league

Jules Verne wrote a book 20,000 leagues Jules Verne wrote a book 20,000 leagues under the sea. How far is this in feet?under the sea. How far is this in feet?