Measurement in Chemistry Factor-Label Method

Measurement in Chemistry

Factor-Label Method

The Factor-Label MethodAt the conclusion of our time

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 Method

Equalities

State the same measurement in two different units

length

10.0 in.

25.4 cm

Conversion 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: 1in. and 2.54 cm 2.54 cm 1 in.

For example: 1 km = 0.6 miles

the conversion factor is

km 1miles 0.6

or miles 0.6km 1

Write conversion factors for 1 foot = 12 inches

What conversion factors can you think of that involve meters?

Conversion FactorsConversion factors for 1 ft = 12 in

foot 1inches 12

or inches 12foot 1

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

mm 1000m 1

, cm 100m 1

, km 1

m 1000

m 1yards 0.9144

, inches 39.37m 1

, feet 3.28m 1

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

label method. The steps involved are:

1. Write the desired quantity and =2. Write down the given quantity and put it over 13. Determine what conversion factors you will use to

turn the given label into the needed label.4. Multiply the given quantity by the appropriate

conversion factors to eliminate units you don’t want and leave the units you do want

5. Complete the math

Factor label ExampleHow many kilometers are in 47.0 miles?

(note: 1 km = 0.621 miles)

First write down the desired quantity

# km

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

Next, equate desired quantity to the given

quantity

# km = 47.0 mi

Factor label Example


Now we have to choose a conversion

factor

# km = 47.0 mi



What conversion factors are possible?

# km = 47.0 mi 1 km 0.621 mi

0.621 mi 1 km



Pick the one that will allow you to cancel

out miles

# km = 47.0 mi 1 km 0.621 mi

0.621 mi 1 km


Pick the one that will allow you to cancel

out miles


# km = 47.0 mi 1 km 0.621 mi

0.621 mi 1 km



Multiply given quantity by chosen conversion factor

# km = 47.0 mi 1 km 0.621 mi

0.621 mi 1 km



Multiply given quantity by chosen conversion factor

# km = 47.0 mi x 1 km 0.621 mi



Cross out common factors

# km = 47.0 mi x 1 km 0.621 mi



Cross out common factors

# km = 47.0 x 1 km 0.621



Are the units now correct?

# km = 47.0 x 1 km 0.621


Yes – km on both sides!


Now finish the math.

# km = 47.0 x 1 km 0.621

= 75.68438003 km


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

label method. The steps involved are:

1. Complete the math with no rounding2. Make certain the sig figs are correct by rounding to

the correct number of sig figs at the very end3. Don’t forget the order of operations when you

complete the math4. Conversion factors do not determine sig. figs.!


The final answer is 75.7 km

# km = 47.0 x 1 km 0.621

= 75.7 km


Summary

The previous problem was not that hardIn other words, you probably could have done it

faster using a different methodHowever, for harder problems the factor label

method is easiest

More Examples1. 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$ = 100.00 US$x 1 Can$ 0.65 US$

= 153.85 Can$

The Factor-Label MethodLet’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 mL1 Liter = 1000 mL

2. hours and minutes1 hour = 60 minutes

3. meters and kilometers1000 meters = 1 kilometer

Learning Check

How many minutes are in 2.5 hours?

Conversion factor

2.5 hr x 60 min = 150 min 1 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!

Learning Check

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

7.25 dollars 4 quarters 1 dollar

X = 29 quarters

Measurement in Chemistry

Factor-Label MethodPart 2

The Factor-Label MethodAt the conclusion of our time

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

55.00 km x 1000 m x 1 h___ = h 1 km 3600 s

15.28 m/s

Dealing 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 drug0.012 g drug mL soln

mg drug ? mL = 0.012 g of drug ( )( )g drug

mg drug1

103

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 Turn

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? 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 cm3 10 mm 3 1 cm ( ) = 4.3 cm3 103 mm3

13 cm3

= 4300 mm3

Learning Check

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

Solution

1000 cm3 1 dm 3

10 cm( )

= 1 dm3

So, a dm3 is the same as a Liter!A cm3 is the same as a milliliter.

Converting Metric to Metric

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

a) 2440 cmb) 244 cmc) 24.4 cm

Solution

A rattlesnake is 2.44 m long. How long is the snake in cm?b) 244 cm

2.44 m x 100 cm = 244 cm1 m

Converting Units of Length Made Easy 0.5 kilometer (km) = 500 meters

(m) 2.5 meter (m) = 250 centimeters

(cm) 1 centimeter (cm) = 10 millimeter

(mm) 1 nanometer (nm) = 1.0 x 10-9 meter

O—H distance =9.4 x 10-11 m9.4 x 10-9 cm0.094 nm

An Easier Way

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

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 MethodLet’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 gB. 0.185 gC. 1.85 gD. 18.5 gE. 1850 g

Learning Check

English 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

Learning Check

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

Unit plan: L qt gallon

Equalities: 1 quart = 0.946 L 1 gallon = 4 quarts

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

1 0.946 L 4 quarts

= 1.23 gallons

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 = 1 yd x 3 ft 1 yd

= 91.37 cmx 12 in1 ft

x 1 cm 0.394 in

Exit Quiz #6 on WS Change 9.4 miles to km (1 mile = 1.6 km)

# km = 9.4 mi = 15 kmx 1.6 km1 mi

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

# Yen= 1 Rublex 1 US $ 25 Rubles = 5.2 Yenx 130 Yen

1 US $

Exit Quiz

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

# ft= 1 mx 100 cm1 m = 3.28 ftx 0.394 in

1 cm x 1 ft

12 in

Exit Quiz

Measurement in Chemistry Factor-Label Method

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