Chapter 4Chapter 4Problem Solving in Problem Solving in

ChemistryChemistryMilbank High SchoolMilbank High School

Section 4.1Section 4.1What Do I Do Now?What Do I Do Now?

• OBJECTIVES:– List several useful problem-solving

skills.

Section 4.1Section 4.1What Do I Do Now?What Do I Do Now?

• OBJECTIVES:– Describe the three-step problem-solving

approach.

Word ProblemsWord 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 (just like real life!)

Problem solvingProblem solving1. ANALYZE

a) Identify the unknown

Both in words and what units it will be measured in. Write it down!

May need to read the question several times.

b) Identify what is given (the “known”)

Write it down!

Unnecessary information may also be given

Problem solvingProblem solving

c) Plan a solution The “heart” of problem solving Break it down into steps. Look up needed information: Tables Formulas Constants, or conversion factors *Choose an equation

Problem solvingProblem solving2. CALCULATE

doing the arithmetic; use of calculator?3. EVALUATE Round off to proper # of sig. figs. Proper units? Need Scientific Notation? Check your work! Reread the question, did you answer it? Is it reasonable? Estimate an approximate answer

Example of Problem Example of Problem SolvingSolving

• Remember to:

–Analyze

–Calculate

–Evaluate• Sample problem 4-1, page 86

• Sample problem 4-2, page 87

Section 4.2Section 4.2Simple Conversion ProblemsSimple Conversion Problems

• OBJECTIVES:– Construct conversion factors from

equivalent measurements.

Section 4.2Section 4.2Simple Conversion ProblemsSimple Conversion Problems

• OBJECTIVES:– Apply the techniques of dimensional

analysis to a variety of conversion problems.

Conversion factorsConversion 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 factorsConversion factors

100 cm1 m =100 cm 100 cm

Conversion factorsConversion factors

11 m =100 cm

Conversion factorsConversion factors

11 m =100 cm

100 cm=1 m1 m 1 m

Conversion factorsConversion factors

11 m =100 cm

100 cm=1 m

1

Conversion factorsConversion 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

Write the possible conversion Write the possible conversion factors for the following:factors for the following:

• Between kilograms and grams

• between feet and inches

• using 1.096 qt. = 1.00 L

What are they good What are they good for?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

What are they good for?What are they good for?

We can multiply by a conversion factor to We can multiply by a conversion factor to change the units .change the units .

Problem: 13 inches is how many yards?Problem: 13 inches is how many yards? Known: 36 inches = 1 yard.Known: 36 inches = 1 yard. 1 yard = 11 yard = 1 36 36

inchesinches 13 inches x 1 yard 13 inches x 1 yard == 0.36 yards0.36 yards

36 inches 36 inches

Conversion factorsConversion factors

• Called conversion factors because they allow us to convert units.

• really just multiplying by one, in a creative way.

Dimensional AnalysisDimensional Analysis

• A way to analyze and solve problems, by using units (or dimensions) of the measurement

• Dimension = unit (such as g, L, mL)

• Analyze = solve

• Using the units to solve the problems.

• If the units of your answer are right, chances are you did the math right!

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

cm? ( 1 inch = 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?

Dimensional AnalysisDimensional 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

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

• Sample 4-5, page 93

Converting Between Converting Between UnitsUnits

• We often need to express a measurement in different units from the one given or measured.

• Use dimensional analysis!• Remember to:

– Analyze

– Calculate

– Evaluate

Converting Between Converting Between UnitsUnits

• Sample 4-6, page 94

• Sample 4-7, page 94

Section 4.3Section 4.3More Complex ProblemsMore Complex Problems

• OBJECTIVES:– Solve problems by breaking the solution

into steps.

Section 4.3Section 4.3More Complex ProblemsMore Complex Problems

• OBJECTIVES:– Convert complex units, using

dimensional analysis.

Multistep ProblemsMultistep Problems

• Many complex tasks in daily life are handled by breaking them down into manageable parts

• Consider cleaning a car:– vacuum the inside– wash the exterior– dry the exterior– apply a coat of wax

Multistep ProblemsMultistep Problems

• When converting between units, it is often necessary to use more than one conversion factor.

• Sample 4-8, page 97

• Sample 4-9, page 98

Converting Complex Converting Complex UnitsUnits

• By complex, we mean units that may be expressed as a ratio:– speed is: miles/hour

– gas mileage is: miles/gallon

– density is: g/cm3

• Sample 4-10, page 99

• Sample of ft2 to yd2 and mm3 to cm3