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

Part 2 Using the Four Step Approach Factor – Label - Method

Problem Solving The four-step approach may seem to be a long procedure, but it will be especially helpful when at first-look a problem seems impossible to solve. Let us now look at several examples that use the four-step approach:

Example 1 Convert 15 grams into milligrams. Give 2 significant figures in your answer.

Example 1 Convert 15 grams into milligrams. Give 2 significant figures in your answer. Step 1. An answer in milligrams (mg) is sought.

Example 1 Convert 15 grams into milligrams. Give 2 significant figures in your answer. Step 1. An answer in milligrams (mg) is sought. Step 2. The known value is 15 grams (g). The 15 grams has 2 significant figures.

Example 1 Convert 15 grams into milligrams. Give 2 significant figures in your answer. Step 1. An answer in milligrams (mg) is sought. Step 2. The known value is 15 grams (g). The 15 grams has 2 significant figures. Step 3. We need to convert a value in grams to one in milligrams.

We will use the Ratio-Relationship that 1000 mg is equal to 1 gram. Example 1 In order to convert a value in grams to one in milligrams. This Ratio-Relationship is also called a Conversion Factor, and it can be rewritten as TWO Conversion-Factor- Fractions:

Convert 15 grams into milligrams. Give 2 significant figures in your answer. Example 1: To convert grams into milligrams, we will need to multiply grams times the Conversion-Factor-Fraction that has mg in the numerator and grams in the denominator This method will cancel out the gram units and leave us with the units we want, milligrams: (Still Step 3 ) = mg

Example 1: Convert 15 grams into milligrams. Give 2 significant figures in your answer. Step 4. In our SET-UPS WE WILL ALWAYS treat each part as a FRACTION. Remember that in multiplying fractions, we must multiply numerators times numerators and denominators times denominators. We can make 15 grams a fraction by simply placing a one as its denominator. When we have completed this problem, we will have a number that contains the correct units and all the other units have canceled out. = 15,000 mg = In correct scientific notation form: 1.5 x 10 4 mg

Example 2 A male patient weighs 138 pounds. What is his weight in kilograms? Step 1. Sought: kilogram units ( kilograms units are found in the Metric System ) Step 2. Given: 138 pounds (pounds are an English unit) [3 significant figures] Step 3. Conversion Factor: 1.00 kilogram = 2.20 pounds.

Still Step 3, Conversion Factor: 1.00 kilogram = 2.20 pounds. The only two possible Conversion-Factor-Fractions are: * Our SET-UP* MUST Cancel OUT pound units and leave only kilogram units: *YOUR – SET-UPS MUST ALWAYS have FRACTIONS in each part: or as = kg

Example 2 A male patient weighs 138 pounds. What is his weight in kilograms? Step 4. Solve: (The answer has 3 significant figures) = 62.7 kg

Example 3 How many liters of gasoline are equal to 10.0 gallons of gasoline? (Give 3 significant figures in your answer) Step 1. Sought: Liter units (Liters are from the Metric System) Step 2. Given: 10.0 gallons (Gallons are from the English System) Step 3. Get the Conversion Factors …

Still Example 3: How many liters of gasoline are equal to 10.0 gallons of gasoline? ( Give 3 significant figures in your answer ) Step 3. Conversion Factors and their specific Conversion-Factor-Fractions: 1 gallon = 4 quarts 1.00 liter = 1.06 quarts [exact value = unlimited significant figures] (a value only good to 3 significant figures) or Set-up: = Liter

Step 4. The ANSWER is = 37.7 liters (The answer has 3 significant figures) Still Example 3: How many liters of gasoline are equal to 10.0 gallons of gasoline? ( Give 3 significant figures in your answer ) Set-up: = Liter

Reverse Method USING THE FACTOR-LABEL- METHOD IN REVERSE TO SET-UP PROBLEMS: In the last problem, it was observed that often we will use more than one conversion factor (thus, more than one step) when doing problems.

Reverse Method A method that is often helpful to students is to first write down the starting value with its units on the far-left-hand-side of the equal sign and the final answer's units on the right-hand side of the equal sign.

Cont… Also, convert the starting value into a fraction by placing it over the number one, 1. Remember that the number one( 1 ), when used to form a fraction is a "defined value" with unlimited numbers of significant figures!! = liters Starting Value With Units Final Answer's Units

Next, if there is not a conversion factor that directly relates the starting units and the final answer's units, then we will need more than one step to solve the problem. –We will then rewrite the problem so there is a ( ) just next to the left-hand-side of the equal sign. –In the Numerator (top) of that fraction we must have the Units of the Final Answer. –Remember that we want to cancel out all the units except the Final Answer's Units (liters) = liters

Cont… We must next decide what units will be in the denominator (bottom) of our fraction that will be next to the equal sign. We know that 1.06 quarts are equal to 1.00 liter; thus, the last fraction, just left of the equal sign, will have liters over quarts as the required units = liters

Cont… Once we have written this much of the problem, we can easily see that if we use a fraction between the other two fractions that contains quarts as its Numerator and gallons as its Denominator, that all the units will cancel out except the liter units: = 37.7 liters

This is the end of Part 2

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