Dimensional analysis (also known as Factor-Label Method) Steps to Problem Solving


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DIMENSIONAL ANALYSIS (also known as Factor-Label Method)


Steps to Problem Solving



Conversions

  • If you know ONE conversion for each type of measurement, you can convert anything!

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



Conversion Factors

  • Fractions in which the numerator and denominator are 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 60 min = 150 min

  • 1 hr



Sample Problem

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

  • 7.25 dollars 4 quarters

  • 1 dollar



Sample Problem – Using Metric

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

  • 200 liters 103 milliliters

  • 1 liter



Learning Check



Multi-Step Problems

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



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 Units



YOU TRY IT

  • The 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?



CONVERSION FACTORS



Practice pROBLEM

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



Multi-Step Problems

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




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