Moles Unit Dimensional Analysis

Dimensional Analysis Dimensional Analysis or the factor label method is a useful problem solving technique to convert between units.

Dimensional Analysis Solving problems using DA Always start with the GIVEN! Then set up a conversion factor with the original unit on the bottom and the new unit on the top.

Conversion factors Conversion factors for 1 ft = 12 in There are almost an infinite number of conversion factors that include meters:

Example 600 minutes = ?? Hours What’s the unit we’re looking for? Hours So…. 1 hour or 60 minutes 60 minutes 1 hour

This one cancels out minutes! 600 minutes x 1 hour = 60 minutes Example This one cancels out minutes! 600 minutes x 1 hour = 60 minutes 10 hours

Steps for using Dimensional Analysis 1 Write down your given information Write down an answer blank and the desired unit on the right side of the problem space 2 Use equivalents to cancel unwanted unit and get desired unit. 3 Calculate the answer…multiply across the top & divide across the bottom of the expression 4

Common Equivalents = = = = = = = 1 ft 12 in 1 in 2.54 cm 1 min 60 s 1 hr = 3600 s 1 quart (qt) = 0.946 L 4 pints = 1 quart = 1 pound (lb) 454 g

How many grams are equal to 1.25 pounds? Example #1 1 Write down your given information Example: How many grams are equal to 1.25 pounds? 1.25 lb

How many grams are equal to 1.25 pounds? Example #1 Write down an answer blank and the desired unit on the right side of the problem space 2 Example: How many grams are equal to 1.25 pounds? 1.25 lb = ________ g

How many grams are equal to 1.25 pounds? Example #1 Use equivalents to cancel unwanted unit and get desired unit. 3 Example: How many grams are equal to 1.25 pounds? 454 g 1.25 lb  = ________ g 1 lb Put the unit on bottom that you want to cancel out! The equivalent with these 2 units is: 1 lb = 454 g A tip is to arrange the units first and then fill in numbers later!

How many grams are equal to 1.25 pounds? Example #1 Calculate the answer…multiply across the top & divide across the bottom of the expression 4 Example: How many grams are equal to 1.25 pounds? 454 g  568 1.25 lb = ________ g 1 lb Enter into the calculator: 1.25  454  1

Multi-step problems There isn’t always an equivalent that goes directly from where you are to where you want to go! Rather than trying to determine a new equivalent, it’s faster to use more than one step in dimensional analysis! This way you have fewer equivalents to remember and you’ll make mistakes more often With multi-step problems, it’s often best to plug in units first, then go back and do numbers.

Example There are 12 inches in a foot, 0.394 inches in a centimeter, and 3 feet in a yard. How many cm are in one yard? 1 yd x 3 ft 1 yd x 12 in 1 ft x 1 cm 0.394 in = 91.37 cm

Conversion factors We have looked at conversion factors that are always true. There are conversion factors that are only true for specific questions E.g. A recipe calls for 2 eggs, 1 cup of flour and 0.5 cups of sugar We can use these conversion factors Q - the chemical equation between H2 and O2 involves 2 H2 molecules combining with 1 O2 molecule to make 2 H2O molecules. Write all possible conversion factors

2H2 + O2  2H2O 2 molecules H2 1 molecule O2 2 molecules H2 2 molecules H2O 1 molecule O2 2 molecules H2O 2 mol H2 1 mol O2 2H2 + O2  2H2O 2 mol H2 2 mol H2O 1 mol O2 2 mol H2O