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

Excellent Assistance has been provided by: Dr. Robert Wyatt Ms. Elizabeth Romero Ms. Kathy Barnes

Also known as the Unit-Conversion Method Unit-Factor Method or the Dimensional Analysis Method Factor – Label - Method (Part 1)

Introduction If someone asks you how many inches there are in 3 feet, you would quickly tell them that there are 36 inches. Simple calculations, such as these, we are able to do with little effort. However, if we work with unfamiliar units, such as converting grams into pounds, we might multiply when we should have divided.

Chemists have developed a method that allows us to easily work problems of this type. It is called “ THE FACTOR-LABEL METHOD ” The method is also called: THE UNIT-CONVERSION METHOD or THE UNIT-FACTOR METHOD or THE DIMENSIONAL-ANALYSIS METHOD.

This method USES CONVERSION FACTORS to change one quantity into some other desired quantity having different units. In this approach, numbers with their units are written in a series so that when multiplied, all units that are not needed in the answer will cancel (factor) out. Units that accompany numbers, such as 3 feet or 5 grams, can cancel out in calculations just as the numbers will.

The fraction ( 4 x 5) / 5 can be simplified by dividing the numerator (top of fraction) and the denominator (bottom of fraction) by 5: Likewise, the units in (ft x lb) / ft reduces to pounds (lb) when the same units ( ft )are canceled: = 4 = lb

CONVERSION FACTOR A CONVERSION FACTOR is a given Ratio-Relationship between two values that can also be written as TWO DIFFERENT FRACTIONS. For example, 454 grams =1.00 pound, states that there are 454 grams in 1.00 pound or that 1.00 pound is equal to 454 grams.

Ratio-Relationship We can write this Ratio-Relationship as two different CONVERSION-FACTOR- FRACTIONS: These fractions may also be written in words as 454 grams per 1.00 pound or as 1.00 pound per 454 grams, respectively. The "per" means to divide by. or as

Example If we want to convert 2.00 pounds into grams, we would: first write down the given quantity (2.00 lbs) pick a CONVERSION-FACTOR-FRACTION that when the given quantities and fractions are multiplied, the units of pounds on each will cancel out and leave only the desired units, grams. We will write the final set-up for the problem as follows: = 908 grams

If we had used the other conversion-factor- fraction in the problem: We would know that the ABOVE problem was set-up incorrectly since WE COULD NOT CANCEL Out the units of pounds and the answer with pounds / grams makes no sense. =

Four-step approach When using the Factor-Label Method it is helpful to follow a four-step approach in solving problems:

Four-step approach When using the Factor-Label Method it is helpful to follow a four-step approach in solving problems: 1. IDENTIFY WHAT IS BEING SOUGHT: Read the problem carefully and write down the UNITS the "Final Answer" “MUST CONTAIN”.

Four-step approach When using the Factor-Label Method it is helpful to follow a four-step approach in solving problems: 2. IDENTIFY WHAT INFORMATION IS GIVEN: Read the problem and list the items given with their correct units.

Four-step approach When using the Factor-Label Method it is helpful to follow a four-step approach in solving problems: 3. OUTLINE A METHOD TO SOLVE THE PROBLEM: Plan a sequence of steps that will lead from the STARTING UNITS TO THE UNIT that MUST be on the FINAL ANSWER!! Use units to guide you in this process. You may need additional information, such as conversation factors from your textbook. Work through your sequence of steps to see if the units of all quantities will cancel out leaving ONLY the unit you want.

Four-step approach When using the Factor-Label Method it is helpful to follow a four-step approach in solving problems: 4. SOLVE THE PROBLEM: Carry out the arithmetic and check to see if the answer is reasonable.