Measurement in ChemistryMeasurement in Chemistry

Factor-Label MethodFactor-Label Method

The Factor-Label MethodThe Factor-Label MethodAt the conclusion of our time At the conclusion of our time

together, you should be able to:together, you should be able to:

1. Recognize a problem that can be solved with the factor label method

2. Transform a statement of equality into a conversion factor

3. Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found

A way to solve math problems in chemistry Used to convert

km to miles, m to km, mol to g, g to mol, etc. To use this we need:

1) given quantity 2) desired quantity 3) conversion factors

Conversion factors are valid relationships or equalities expressed as a fraction and equal to one!

The Factor label MethodThe Factor label Method

Conversion FactorsConversion Factors

Fractions in which the numerator and denominator are EQUAL quantities expressed in different units but always equal to one. You can always multiply any equation by this equality and not change the quantity, just the units.

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

The Steps to FollowThe Steps to FollowNow we are ready to solve problems using the factor

label method. The steps involved are:

1. Write down the given quantity

2. Determine what conversion factors you will use to turn the given label into the needed label.

3. Set up the conversion factors 1. Given unit in the denominator

2. Desired unit in the numerator

4. Complete the math

How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles)How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles)

How many miles are in 23.4 kilometers?How many miles are in 23.4 kilometers?

Factor label ExampleFactor label Example

SummarySummary

The previous problem was not that hard

In other words, you probably could have done it faster using a different method

However, for harder problems the factor label method is easiest

Measurement in ChemistryMeasurement in Chemistry

Factor-Label MethodFactor-Label MethodPart 2Part 2

Converting Metric to MetricConverting Metric to Metric

StepsSteps1.1. Write the given quantityWrite the given quantity

2.2. Set up units in the conversion factorSet up units in the conversion factor1.1. Larger prefix gets a 1Larger prefix gets a 1

2.2. Determine what goes in front of smaller Determine what goes in front of smaller prefixprefix

3.3. Cancel unitsCancel units

4.4. Complete the mathComplete the math

Converting Metric to MetricConverting Metric to Metric

A rattlesnake is 2.44 cm long. How A rattlesnake is 2.44 cm long. How long is the snake in mm?long is the snake in mm?

Converting Metric to Metric 2Converting Metric to Metric 2

An atom has a volume of 35.67nL. An atom has a volume of 35.67nL. What is its volume in cL?What is its volume in cL?

Converting Metric to Metric 3Converting Metric to Metric 3

Max has a mass of 125kg. What is this Max has a mass of 125kg. What is this in micrograms?in micrograms?

Measurement in ChemistryMeasurement in Chemistry

Factor-Label MethodFactor-Label MethodPart 3Part 3

Convert 55.00 km/h to m/s Convert 55.00 km/h to m/s

55.00 55.00 km km x x 1000 m1000 m x x 1 h1 h___ =___ =

h 1 km h 1 km 3600 s3600 s

15.28 m/s

Dealing with Two UnitsDealing with Two Units

Dealing with Two Units, Your Dealing with Two Units, Your TurnTurn

If your pace on a treadmill is 65 meters per minute, what is your rate in km per hour

What about Square and Cubic units?What about Square and Cubic units?

Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also!

Best way: Square or cube the Entire conversion factor

Example: Convert 4.3 cm3 to mm3

4.3 cm4.3 cm33 10 mm 10 mm 33

1 cm 1 cm ( ) = 4.3 cm4.3 cm33 10 1033 mm mm33

1133 cm cm33

= 4300 mm3

Learning CheckLearning Check

A Nalgene water bottle holds 1000 cm3 of dihydrogen monoxide (DHMO). How many cubic decimeters is that?

Solution

1000 cm1000 cm33 1 dm 1 dm 33

10 cm10 cm( )

= 1 dm= 1 dm33

So, a dmSo, a dm33 is the same as a is the same as a LiterLiter!!

A cmA cm33 is the same as a is the same as a millilitermilliliter..

A person’s blood contains 185 mg of cholesterol per deciliter of blood. How many

grams of cholesterol are there in 1 liter of this blood?

A. 0.0185 g

B. 0.185 g

C. 1.85 g

D. 18.5 g

E. 1850 g

Learning CheckLearning Check