measurement in chemistry factor-label method

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) desired quantity 2) given 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

EqualitiesEqualities

State the same measurement in two different units

lengthlength

10.0 in.10.0 in.

25.4 25.4 cmcm

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: 10 in. = 25.4 cm

Factors: 10 in. and 25.4 cm 25.4 cm 10 in.

For example: 1 km = 0.6 miles For example: 1 km = 0.6 miles the conversion factor is the conversion factor is

km 1

miles 0.6 or

miles 0.6

km 1

Write conversion factors for 1 foot = 12 inchesWrite conversion factors for 1 foot = 12 inches

What conversion factors can you think of that involve What conversion factors can you think of that involve meters?meters?

Conversion FactorsConversion Factors

Conversion factors for 1 ft = 12 inConversion factors for 1 ft = 12 in

foot 1

inches 12 or

inches 12

foot 1

There are almost an infinite number of There are almost an infinite number of conversion factors that include meters:conversion factors that include meters:

mm 1000

m 1 ,

cm 100

m 1 ,

km 1

m 1000

m 1

yards 0.9144 ,

inches 39.37

m 1 ,

feet 3.28

m 1

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 and put it over 1

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

3. Multiply the given quantity by the appropriate conversion factors to eliminate units you don’t want and leave the units you do want

4. Complete the math

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

Factor label ExampleFactor label Example

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

label method. The steps involved are:

1. Complete the math with no rounding

2. Make certain the sig figs are correct by rounding to the correct number of sig figs at the very end

3. Don’t forget the order of operations when you complete the math:

“Please Excuse My Dear Aunt Sally”!

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

The final answer is 75.7 km

## km km = 47.0= 47.0 x 1 km x 1 km 0.6210.621

= 75.7 km= 75.7 km

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

More ExamplesMore Examples

1. You want to convert 100.00 U.S. dollars to Canadian dollars. If the exchange rate is

1 Can$ = 0.65 US$, how much will it cost?

## Can$ Can$ = 100 US$= 100 US$ x 1 Can$ x 1 Can$ 0.65 US$0.65 US$

= 1= 1553.85 Can$3.85 Can$

The Factor-Label MethodThe Factor-Label MethodLetLet’’s see if you can:s see if you can:

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

Write conversion factors that relate each of the following pairs of units:

1. Liters and mL

1 Liter = 1000 mL

2. hours and minutes

1 hour = 60 minutes

3. meters and kilometers

1000 meters = 1 kilometer

Learning CheckLearning Check

How many minutes are in 2.5 hours?How many minutes are in 2.5 hours?

Conversion factorConversion factor

2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min

1 hr1 hr

By using dimensional analysis/factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are

calculated as well as the numbers!


You have $7.25 in your pocket in quarters. How many quarters do you have?

7.25 dollars 4 quarters 1 dollar

X = 29 = 29 quartersquarters

Measurement in ChemistryMeasurement in Chemistry

Factor-Label MethodFactor-Label MethodPart 2Part 2

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 by moving the decimal point.

2. Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found with two changes of labels or labels that are squared or cubed.

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

A patient requires injection of 0.012 g of a pain killer available in a 15 mg/mL solution.

How many milliliters should be administered?

? mL = 0.012 g of drug

0.012 g drug mL soln

mg drug

? mL = 0.012 g of drug

( )( )g drugmg drug

1103

mg drug

mL soln15

1

= 0.80 mL soln

When you see a number with two units like 15 mg/mL, it can be used as a conversion factor. What it really says is that 1 ml of the solution

contains 15 mg of the drug.

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

If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet?

1 meter = 3.28 feet

2380 seconds

# s = 8450 ft x 1 m3.28 ft

x 1 min65 m

x 60 s 1

min

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


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..

Converting Metric to MetricConverting Metric to Metric

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

a) a) 2440 cm2440 cm

b)b) 244 cm244 cm

c)c) 24.4 cm24.4 cm

SolutionSolution


b)b) 244 cm244 cm

2.44 m x 2.44 m x 100 cm 100 cm = 244 cm= 244 cm

1 m1 m

Converting Units of Length Made EasyConverting Units of Length Made Easy

0.50.5 kilometer (km) = 500 meters (m) kilometer (km) = 500 meters (m)

2.5 meter (m) = 2.5 meter (m) = 250250 centimeters (cm) centimeters (cm)

1 centimeter (cm) = 1 centimeter (cm) = 1010 millimeter (mm) millimeter (mm)

11 nanometer (nm) = 1.0 x 10 nanometer (nm) = 1.0 x 10-9-9 meter meter

O—H distance =O—H distance =9.4 x 109.4 x 10-11 -11 mm9.4 x 109.4 x 10-9 -9 cmcm0.094 0.094 nmnm

O—H distance =O—H distance =9.4 x 109.4 x 10-11 -11 mm9.4 x 109.4 x 10-9 -9 cmcm0.094 0.094 nmnm

An Easier WayAn Easier Way


G _ _ M _ _ k h da _ d c m _ _ μ _ _ n

1. A move from 1 meter to centimeters is two places right

2. Move the decimal place of the number two places right

3. 244 cm

Another Example: How many millimeters are there in 4.5 cm?

G _ _ M _ _ k h da _ d c m _ _ μ _ _ n

1. A move from cm to mm is one place right

2. Move the decimal place of the number one place right

3. 45 mm

Another Example: How many kilometers are there in 4.5 cm?

G _ _ M _ _ k h da _ d c m _ _ μ _ _ n

1. A move from cm to km is five places left

2. Move the decimal place of the number five places left

3. 0.000 045 km

The Factor-Label MethodThe Factor-Label MethodLetLet’’s see if you can:s see if you can:

1. Recognize a problem that can be solved by moving the decimal point.

2. Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found with two changes of labels or labels that are squared or cubed.

Learning Check: 2 kilometers is the same as how many millimeters

G _ _ M _ _ k h da _ d c m _ _ μ _ _ n

1. A move from km to mm is six places right

2. Move the decimal place of the number six places right

3. 2 000 000 mm, 2 x 106 mm

Metric Conversions #1: Write 550 mm as meters.

G _ _ M _ _ k h da _ d c m _ _ μ _ _ n

1. A move from mm to m is 3 places left

2. Move the decimal place of the number 3 places left

3. 0.55 m

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


English and Metric ConversionsEnglish and Metric Conversions

If you know ONE conversion for each type of measurement, you can convert anything!

You must use these conversions: Mass: 454 grams = 1 pound Length: 2.54 cm = 1 inch Volume: 0.946 L = 1 quart


An adult human has 4.65 L of blood. How many gallons of blood is that?

Unit plan: L qt Unit plan: L qt gallon gallon

Equalities:Equalities: 1 quart = 0.946 L 1 quart = 0.946 L

1 gallon = 4 quarts 1 gallon = 4 quarts

Your Setup: gal = 4.65 L x 1 quart x 1 gallonYour Setup: gal = 4.65 L x 1 quart x 1 gallon

1 0.946 L 4 quarts1 0.946 L 4 quarts

= 1.23 gallons= 1.23 gallons

Exit Quiz Exit Quiz

There are 12 inches in a foot, 0.394 inches in a centimeter, and 3 feet in a yard. How many centimeters are in 1.000 yard?

## cm cm = 1 yd= 1 yd x 3 ft x 3 ft 1 yd1 yd

= 91.= 91.337 cm7 cmx 12 inx 12 in1 ft1 ft

x 1 cm x 1 cm 0.394 in0.394 in

Exit Quiz #6 on WS Exit Quiz #6 on WS

Change 9.4 miles to km (1 mile = 1.6 km)

## km km = 9.4 mi= 9.4 mi = 15 km= 15 kmx 1.6 kmx 1.6 km1 mi1 mi

With a U.S. dollar you can buy 1.1 Euros, With a U.S. dollar you can buy 1.1 Euros, 130 Yen, or 25 Rubles. How many 130 Yen, or 25 Rubles. How many Yen can you buy with one Ruble?Yen can you buy with one Ruble?

# Yen= 1 Rublex 1 US $ 25 Rubles = 5.2 Yen

x 130 Yen 1 US $

Exit QuizExit Quiz

Calculate how many feet are in 1 meter. Calculate how many feet are in 1 meter. (use 1 cm = 0.394 in)(use 1 cm = 0.394 in)

# ft= 1 mx 100 cm1 m

= 3.28 ftx 0.394 in1 cm

x 1 ft 12 in

Exit QuizExit Quiz

measurement in chemistry factor-label method

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