pwista math of chemistry problem solving dimensional analysis factor label method

PWISTAMath of Chemistry

Problem SolvingDimensional analysisFactor 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 - algebra5) 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 Solving3) Plan a solution Formula Heat = SH x mass x T 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 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 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?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 inches 36 inches 13 inches x 1 yard 13 inches x 1 yard ==

36 inches 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 mihr

1760 yd1 mi 1.094 yd

1 m 1 hr60 min

1 min60 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 cm33 1 m100 cm

1 m100 cm

1 m100 cm

1500 cm33 1 m

100 cm

33

Dimensional Analysis

• Another measuring system has different units of measure.

6 ft = 1 fathom 100 fathoms = 1 cable length10 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 exampleLead 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?