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The factor label method The factor label method

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• 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 equities expressed as a fraction

E.g. for 1 km=0.6 miles the conversion factor is

The factor label method The factor label method

km

1

miles 0.6

or miles

0.6

km

1

(2)

Conversion factors Conversion factors

Conversion factors for 1 ft = 12 in

foot 1

inches 12

or inches

12

foot

1

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

mm

1000 m 1

cm , 100

m 1

km ,

1

m

1000

(3)

Conversion factors 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

sugar cups

0.5

eggs 2

flour , cup

1

sugar cups

0.5 flour ,

cup 1

eggs 2

• Q - the chemical equation between H 2 and O 2

involves 2 H molecules combining with 1 O

(4)

2 molecules H 2 1 molecule O 2

1 molecule O 2 2 molecules H 2 2 molecules H 2

2 molecules H 2 O

2 molecules H 2 O 2 molecules H 2 1 molecule O 2

2 molecules H 2 O

2 molecules H 2 O 1 molecule O 2 2 mol H 2

1 mol O 2

1 mol O 2 2 mol H 2 2 mol H 2

2 mol H O

2 mol H 2 O 2 mol H

2H 2 + O 2  2H 2 O

(5)

The steps to follow The steps to follow

Now we are ready to solve problems using the factor label method. The steps involved are:

1. Write down the desired quantity/units

2. Equate the desired quantity to given quantity 3. Determine what conversion factors you can

use (both universal and question specific) 4. Multiply given quantity by the appropriate

conversion factors to eliminate units you

(6)

Factor label example Factor label example

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

First write down the desired quantity

# km

(7)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

Next, equate

desired quantity to the given quantity

# km = 47 mi

Factor label example

Factor label example

(8)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

Now we have to choose a

conversion factor

# km = 47 mi

Factor label example

Factor label example

(9)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

What conversion factors are

possible?

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km

Factor label example

Factor label example

(10)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

Pick the one that will allow you to cancel

out miles

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km

Factor label example

Factor label example

(11)

Pick the one that will allow you to cancel

out miles

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km

Factor label example

Factor label example

(12)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

Multiply given

quantity by chosen conversion factor

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km

Factor label example

Factor label example

(13)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

Multiply given

quantity by chosen conversion factor

# km = 47 mi x 1 km

0.621 mi

Factor label example

Factor label example

(14)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

Cross out common factors

# km = 47 mi x 1 km

0.621 mi

Factor label example

Factor label example

(15)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

Cross out common factors

# km = 47 x 1 km 0.621

Factor label example

Factor label example

(16)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

Are the units now correct?

# km = 47 x 1 km 0.621

Factor label example

Factor label example

(17)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

Yes. Both sides have km as units.

# km = 47 x 1 km 0.621

Factor label example

Factor label example

(18)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

Yes. Both sides have km as units.

# km

= 47 x 1 km 0.621

# km

Factor label example

Factor label example

(19)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

Now finish the math.

# km = 47 x 1 km 0.621

= 75.7 km

Factor label example

Factor label example

(20)

Q - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

The final answer is 75.7 km

# km = 47 x 1 km 0.621

= 75.7 km

Factor label example

Factor label example

(21)

Summary Summary

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

(22)

More examples More examples

1. You want to buy 100 U.S. dollars. If the exchange rate is 1 Can$ = 0.65 US$, how much will it cost?

# Can$ = 100 US$ x 1 Can$

0.65 US$

= 153.85 Can$

2. One mole of a gas has a volume of 22.4 L.

How many L will 300 grams of CO 2 occupy?

(hint: the molar mass of CO 2 is ____ g/mol).

# L CO 2 =

44.01

(23)

More examples More examples

3. 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?

# cm = 1 yd x 3 ft

1 yd x 12 in = 91.37 cm 1 ft

x 1 cm 0.394 in

4. A chemical reaction requires 3.000 moles of sodium chloride. How many grams is this?

#g NaCl =

Sodium chloride is NaCl (58.44 g/mol)

(24)

Assignment Assignment

Answer questions using the factor label method:

1. How many moles of H 2 are in 100 g of H 2 ?

2. 300 g of CuSO 4 is needed in an experiment.

How many moles does this represent?

3. A chemical reaction requires 23.78 moles of silver chloride. How many grams is this?

4. Calculate how many feet are in 1 meter (use information from the examples above).

5. With a U.S. dollar you can buy 1.1 Euros,

(25)

6. How many molecules are in 73 grams H 2 O?

(hint: form a conversion factor using Avogadro’s #)

7. 255 g of calcium phosphate are produced in a chemical reaction. How many moles of

calcium phosphate does this represent?

8. According to the equation 2H 2 + O 2  2H 2 O, how many grams of H 2 O would be produced if 7.35 mol of O 2 is used up? (hint: you will need two conversion factors – 1 from the

Assignment

Assignment

(26)

1.

2.

# mol H = 100 g H 2 2 x 1 mol H 2

2.02 g H 2 = 49.5 mol H 2

# mol CuSO 4 =

300 g CuSO 4 x 1 mol CuSO 4

159.61 g CuSO = 1.88 mol CuSO 4 4

# g AgCl =

23.78 mol AgCl x 143.32 g AgCl

1 mol AgCl = 3408 g AgCl 3.

4.

(27)

5.

6.

# Yen = 1 Ruble x 1 US $

25 Rubles = 5.2 Yen

# H 2 O molecules = 73 g H 2 O x 1 mol H 2 O

18.02 g H 2 O

= 2.44 x 10 24 molecules H 2 O

# mol Ca 3 (PO 4 ) 2 =

255 g Ca 3 (PO 4 ) 2 x 1 mol Ca 3 (PO 4 ) 2

310.18 g Ca 3 (PO 4 ) 2 = 0.822 mol Ca 3 (PO 4 ) 2 7.

x 130 Yen 1 US $

x 6.02x10 23 molecules 1 mol H 2 O

# g H O=

8.

(28)

Assignment

Formula Molar mass (g/mol)

Mass (g)

Moles (mol)

FeSO 4 500

(NH 4 ) 2 CO 3 2

SnO 2 50

Sb 2 O 5 0.25

NaClO 4 100

Complete the following chart:

(29)

Assignment

0.817 100

122.4 NaClO 4

0.25 80.9

323.6 Sb 2 O 5

0.332 50

150.7 SnO 2

2 192.2

(NH 4 ) 2 CO 3 96.1

3.29 500

151.9 FeSO 4

Moles (mol) Mass

(g) Molar mass

(g/mol) Formula

Complete the following chart:

(30)

Assignment Assignment

1. AgCl = 143.35 g/mol

#g = 2 mol x 143.35 g/mol = 286.7 g (2) 2. H 2 = 2.016 g/mol

#mol = 100 g x mol/2.016 g = 49.6 mol (2) 3. CuSO 4 = 159.62 g/mol

#mol= 300 g x mol/159.62 g=1.879 mol (2)

4. KClO = 90.55 g/mol

References

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