The following lesson is one lecture in a series of Chemistry Programs developed by Professor Larry Byrd Department of Chemistry Western Kentucky University

Part 3 Using the Four Step Approach Factor – Label - Method

THE FACTOR-LABEL-METHOD in a "REVERSE DIRECTION” In many problems you will find that if you work backwards ( Work in Reverse ) from the Answer's Units, you may be able to solve very complex unit-problems.

THE FACTOR-LABEL-METHOD in a "REVERSE DIRECTION” The following are examples Will show how many steps are needed to solve a problem. Also, we will use THE FACTOR-LABEL-METHOD in a "REVERSE DIRECTION” to solve each of the following problems.

Example 4: A single aspirin table ( 1.00 tablet ) contains 5.00 grains of aspirin. Also, there are 15. grains of aspirin in 1.0 gram of aspirin. How many aspirin tablets can be made from 9.0 grams of aspirin? [ Give 2 significant figures in your final answer ] Step 1. Sought: tablets are the required units

Example 4: A single aspirin table ( 1.00 tablet ) contains 5.00 grains of aspirin. Also, there are 15. grains of aspirin in 1.0 gram of aspirin. How many aspirin tablets can be made from 9.0 grams of aspirin? [ Give 2 significant figures in your final answer ] Step 1. Sought: tablets are the required units Step 2. Given: 9.0 grams of aspirin

Example 4: Step 3. Conversion-Factor-Fractions found in problems: or as AND A single aspirin table ( 1.00 tablet ) contains 5.00 grains of aspirin. Also, there are 15. grains of aspirin in 1.0 gram of aspirin. How many aspirin tablets can be made from 9.0 grams of aspirin? [ Give 2 significant figures in your final answer ]

Example 4: Set-up (Step 3): a. First :......(tablets must be in the numerator) = tablets A single aspirin table ( 1.00 tablet ) contains 5.00 grains of aspirin. Also, there are 15. grains of aspirin in 1.0 gram of aspirin. How many aspirin tablets can be made from 9.0 grams of aspirin? [ Give 2 significant figures in your final answer ]

Example 4: Set-up (Step 3): A single aspirin table ( 1.00 tablet ) contains 5.00 grains of aspirin. Also, there are 15. grains of aspirin in 1.0 gram of aspirin. How many aspirin tablets can be made from 9.0 grams of aspirin? [ Give 2 significant figures in your final answer ] b. Next : = tablets

Example 4: Set-up (Step 3): c. We will need to cancel out the grains units, which are in the denominator of “ our fraction “ which is on the left-hand side of the equal sign! To do this we will need a fraction that contains grains as its numerator: (grains) = tablets A single aspirin table ( 1.00 tablet ) contains 5.00 grains of aspirin. Also, there are 15. grains of aspirin in 1.0 gram of aspirin. How many aspirin tablets can be made from 9.0 grams of aspirin? [ Give 2 significant figures in your final answer ]

Example 4: Set-up (Step 3): c. From our Conversion –Factors-Fractions we would then write the problem as: = tablets A single aspirin table ( 1.00 tablet ) contains 5.00 grains of aspirin. Also, there are 15. grains of aspirin in 1.0 gram of aspirin. How many aspirin tablets can be made from 9.0 grams of aspirin? [ Give 2 significant figures in your final answer ]

Example 4: Set-up (Step 3): c. After looking over our set-up we would realize that we do not need any more steps, since as it is written all the units will cancel out except the tablet units: = 27 tablets From the problem we can now say that if we have 9.0 grams of pure aspirin, we can produce twenty-seven, five-grain aspirin tablets from it. A single aspirin table ( 1.00 tablet ) contains 5.00 grains of aspirin. Also, there are 15. grains of aspirin in 1.0 gram of aspirin. How many aspirin tablets can be made from 9.0 grams of aspirin? [ Give 2 significant figures in your final answer ]

Let us first write down the Conversion Factors and the Conversion-Factor-Fractions that are given in the problem: 14 pack per week could be written as: [Simple Counting: thus, no effect on significant figures] or as Example 5: If a person smokes 14 packs a week, how many weeks of smoking would be needed to inhale 1.0 pound of tar? 1 pack = 20 cigarettes ( definition ) ; 1.0 cigarette contains 20. mg of tar ( Give 2 significant figures in your final answer )

Let us first write down the Conversion Factors and the Conversion-Factor-Fractions that are given in the problem: Example 5: If a person smokes 14 packs a week, how many weeks of smoking would be needed to inhale 1.0 pound of tar? 1 pack = 20 cigarettes ( definition ) ; 1.0 cigarette contains 20. mg of tar ( Give 2 significant figures in your final answer ) 1.0 cigarette contains 20. mg of tar as: or as [ These factors contain only 2 significant figures ]

Next, List the Starting Units and the Final Units as: Example 5: If a person smokes 14 packs a week, how many weeks of smoking would be needed to inhale 1.0 pound of tar? 1 pack = 20 cigarettes ( definition ) ; 1.0 cigarette contains 20. mg of tar ( Give 2 significant figures in your final answer ) = weeks of smoking

Then: Example 5: If a person smokes 14 packs a week, how many weeks of smoking would be needed to inhale 1.0 pound of tar? 1 pack = 20 cigarettes ( definition ) ; 1.0 cigarette contains 20. mg of tar ( Give 2 significant figures in your final answer ) (weeks) = weeks of smoking = weeks of smoking.....

Next: Example 5: If a person smokes 14 packs a week, how many weeks of smoking would be needed to inhale 1.0 pound of tar? 1 pack = 20 cigarettes ( definition ) ; 1.0 cigarette contains 20. mg of tar ( Give 2 significant figures in your final answer ) = weeks of smoking (packs).. = weeks of smoking..... Which would mean that we now need a fraction that contains packs as its Numerator:

Next: = weeks of smoking Then Use: (cig) Example 5: If a person smokes 14 packs a week, how many weeks of smoking would be needed to inhale 1.0 pound of tar? 1 pack = 20 cigarettes ( definition ) ; 1.0 cigarette contains 20. mg of tar ( Give 2 significant figures in your final answer )

Next: = weeks of smoking Then Use: (mg) Example 5: If a person smokes 14 packs a week, how many weeks of smoking would be needed to inhale 1.0 pound of tar? 1 pack = 20 cigarettes ( definition ) ; 1.0 cigarette contains 20. mg of tar ( Give 2 significant figures in your final answer )

= weeks of smoking The Final Set-Up would look like this: Before we do the arithmetic, let us look at each part to see if it does what we want… Example 5: If a person smokes 14 packs a week, how many weeks of smoking would be needed to inhale 1.0 pound of tar? 1 pack = 20 cigarettes ( definition ) ; 1.0 cigarette contains 20. mg of tar ( Give 2 significant figures in your final answer )

The grams of tar are next converted into milligrams of tar. We need mg of tar units since the amount of tar in cigarettes is always given as mg of tar. If we multiply cigarettes times 1 pack / 20 cig, this will tell us the number of packs that will need to be smoked. Finally, if we multiply packs times 1 week / 14 packs, it will tell us how many weeks of smoking are needed to inhale the one pound of tar. = weeks of smoking Example 5: Continue from last slide…