DIMENSIONALANALYSIS

(also known as Factor-Label Method)

Steps to Problem SolvingSteps to Problem Solving

Read problemRead problem

Identify data Identify data Make a unit plan from the initial unit to the Make a unit plan from the initial unit to the

desired unitdesired 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

ConversionsConversionsIf you know ONE conversion If you know ONE conversion

for each type of measurement, for each type of measurement, you can convert anything!you can convert anything!

You must memorize and be You must memorize and be able to use the metric able to use the metric conversions:conversions:

Conversion FactorsConversion Factors

Fractions in which the numerator and denominator Fractions in which the numerator and denominator are EQUAL quantities expressed in different unitsare EQUAL quantities expressed in different units

Example: 1 ft = 12 in.

Factors: 1 ft. and 12 in

12 in 1 ft.

Example: 1 g = 102 cg.

Factors: 1 g. and 102 cg

102 cg 1 g

How many minutes are in 2.5 hours?

Conversion factor

2.5 hr x 2.5 hr x 60 min 60 min = 150 min= 150 min

1 hr1 hr

By using dimensional analysis / factor-label method, By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the side up, and the UNITS are calculated as well as the

numbers!numbers!

Sample Problem

You have $7.25 in your pocket You have $7.25 in your pocket in quarters. How many quarters in quarters. How many quarters do you have?do you have?

7.25 dollars7.25 dollars 4 quarters4 quarters

1 dollar1 dollar

X = 29 quarters= 29 quarters

Sample Problem – Using Metric

You have 200 L of gasoline in You have 200 L of gasoline in your car. How many milliliters your car. How many milliliters do you have?do you have?

200 liters200 liters 101033 milliliters milliliters

1 liter1 liter = 2 x 10= 2 x 1033 mL mL

Learning CheckLearning Check

SET UP THESE PROBLEMS USING SET UP THESE PROBLEMS USING DA - DA -

2.22 cg = _______g

1.7 x 106 ng = ___________ g

.288 g = __________mg

1.5 KL = ___________L

Multi-Step Problems

You are in Paris and want some peaches for You are in Paris and want some peaches for lunch. The sign in the fruit stand indicates lunch. The sign in the fruit stand indicates that peaches are 11.5 francs per kilogram. that peaches are 11.5 francs per kilogram. Given that there are approximately 5 Given that there are approximately 5 francs to the dollar, calculate what a francs to the dollar, calculate what a pound of peaches will cost in dollars.pound of peaches will cost in dollars.

1 lb.

1 lb. 455 g

1000 g

1Kg 11.5 f

1Kg 5 f

1 $ NOW WHAT?

?

Practice Problems

Mrs. Borden has 3 classes of Chemistry. Each class has 25 students in it and they are each required to pay $15.00 for their lab fee. How much money will she have at the end of the semester if everyone pays their fee?

Students in chemistry are required to write 10 lab reports per year. Each lab report has 6 sections each. Mrs. Borden requires that each section consists of a paragraph with no less than 7 sentences. How many paragraphs will each student write in 1 year time?

Complex UnitsMany times a problem will ask for you to convert 2 different units in one problem.

Example: Change miles per hour to feet per minute.

Given 20 miles per hour, how many feet is that per minute? ( 5280 ft = 1 mile)

20 miles

1 hour

1 hour

60 min. 1 mile

5280 ft.

= 1760 ft./min.

YOU TRY ITThe density of gold is 19.3

g/mL. What is gold’s density in decigrams per

liter?

NEW UNITS These are units you have never used but

you must know for the rest of the year.

1 mole of any element or compound = its mass

1 mole of any element or compound = 6.02 x 1023 representative particles

CONVERSION FACTORS

1 mole of NaCl = mass of NaCl

How to calculate mass, using the periodic table: Na = 23.0 g and Cl = 35.5 g

23.0+ 35.5 therefore 1 mole of NaCl = 58.5 g 58.5 g or 1 mole of NaCl

58.5 g

Practice pROBLEM

You are given 3.5 moles of NaCl, how many grams of NaCl do you have?

3.5 moles NaCl

1 mole NaCl

58.5 g NaCl= 204.75 g of NaCl

CONVERSION FACTORS

1 mole of NaCl = 6.02 x 1023 particles of NaCl

Nothing to calculate, the number of particles is the same for every element

therefore 1 mole of NaCl = 6.02 x 1023 Particles or 1 mole of NaCl

6.20 x 1023 particles

Practice pROBLEM

You are given 3.5 moles of NaCl, how many particles of NaCl do you have?

3.5 moles NaCl

1 mole NaCl

6.20 x 1023

particles of NaCl= 21.07 x 1023

particles of NaCl or

2.107 x 1024 particles

Multi-Step Problems

You are given 4.55 x 1025 particles of oxygen, how many grams of oxygen do you have?

4.55 x 1025 rp of O

6.02 x 1023 rp 1 mole of O

1 mole of O 16.0 g of O= 12.09 x 102

grams

of O or

1.209 x 103 grams of O