A way to solve math problems in chemistry Used to convert km to miles, m to km, mol to g, g to mol,...

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

The factor label methodThe factor label method

km 1

miles 0.6 or

miles 0.6

km 1

Q. write conversion factors for 1 foot =12 inchesQ. what conversion factors can you think of that

involve meters?

Conversion factorsConversion factorsConversion 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

m 1

yards 0.9144 ,

inches 39.37

m 1 ,

feet 3.28

m 1

Conversion factorsConversion 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 H2 and O2 involves 2 H2 molecules combining with 1 O2 molecule to make 2 H2O molecules. Write all possible conversion factors

2 molecules H2

1 molecule O2

1 molecule O2

2 molecules H2

2 molecules H2

2 molecules H2O2 molecules H2O2 molecules H2

1 molecule O2

2 molecules H2O2 molecules H2O

1 molecule O2

2 mol H2

1 mol O2

1 mol O2

2 mol H2

2 mol H2

2 mol H2O2 mol H2O2 mol H2

1 mol O2

2 mol H2O2 mol H2O1 mol O2

2H2 + O2 2H2O

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 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 don’t want and leave units you do want

5. Complete the math

Factor label exampleFactor label exampleQ - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

First write down the desired quantity

# km

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 exampleFactor label example


Now we have to choose a

conversion factor

# km = 47 mi



What conversion factors are possible?

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km



Pick the one that will allow you to cancel

out miles

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km


Pick the one that will allow you to cancel

out miles


# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km



Multiply given quantity by chosen conversion factor

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km



Multiply given quantity by chosen conversion factor

# km = 47 mi x 1 km 0.621 mi



Cross out common factors

# km = 47 mi x 1 km 0.621 mi



Cross out common factors

# km = 47 x 1 km 0.621



Are the units now correct?

# km = 47 x 1 km 0.621



Yes. Both sides have km as units.

# km = 47 x 1 km 0.621



Yes. Both sides have km as units.

# km

= 47 x 1 km 0.621

# km



Now finish the math.

# km = 47 x 1 km 0.621

= 75.7 km



The final answer is 75.7 km

# km = 47 x 1 km 0.621

= 75.7 km


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 examples1. 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 CO2 occupy? (hint: the molar mass of CO2 is ____ g/mol).

# L CO2 =300 g CO2 x 1 mol CO2

44.01 g CO2

= 152.7 L CO2x 22.4 L CO2

1 mol CO2

44.01

More examplesMore examples3. 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

= 91.37 cmx 12 in

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 =3.000 mol NaCl x 58.44 g NaCl

1 mol NaCl= 175.3 g NaCl

Sodium chloride is NaCl (58.44 g/mol)

AssignmentAssignmentAnswer questions using the factor label method:1. How many moles of H2 are in 100 g of H2?

2. 300 g of CuSO4 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, 130 Yen, or 25 Rubles. How many Yen can you buy with one Ruble?

6. How many molecules are in 73 grams H2O? (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 2H2 + O2 2H2O, how many grams of H2O would be produced if 7.35 mol of O2 is used up? (hint: you will need two conversion factors – 1 from the balanced equation and 1 from a molar mass)

AssignmentAssignment

1.

2.

# mol H2= 100 g H2 x 1 mol H2 2.02 g H2

= 49.5 mol H2

# mol CuSO4 =

300 g CuSO4 x 1 mol CuSO4 159.61 g CuSO4

= 1.88 mol CuSO4

# g AgCl =23.78 mol AgCl x 143.32 g AgCl

1 mol AgCl= 3408 g AgCl

3.

# ft = 1 mx 100 cm1 m

= 3.28 ftx 0.394 in

1 cm x 1 ft

12 in

4.

5.

6.

# Yen= 1 Ruble x 1 US $ 25 Rubles

= 5.2 Yen

# H2O molecules =

73 g H2O x 1 mol H2O 18.02 g H2O

= 2.44 x 1024 molecules H2O# mol Ca3(PO4)2 =

255 g Ca3(PO4)2 x 1 mol Ca3(PO4)2 310.18 g Ca3(PO4)2

= 0.822 mol Ca3(PO4)2

7.

x 130 Yen 1 US $

x 6.02x1023 molecules 1 mol H2O

2 mol H2O1 mol O2

x

# g H2O=7.35 mol O2

265 g H2O

= 18.01 g H2O1 mol H2O

x

8.

Assignment

Formula Molar mass

(g/mol)

Mass

(g)

Moles

(mol)

FeSO4 500

(NH4)2CO3 2

SnO2 50

Sb2O5 0.25

NaClO4 100

Mg(IO3)2 3.2

CoCl2.H2O 332

Complete the following chart:

Assignment

2.246332147.8CoCl2.H2O

3.21196.8374.1Mg(IO3)2

0.817100122.4NaClO4

0.2580.9323.6Sb2O5

0.33250150.7SnO2

2192.296.1(NH4)2CO3

3.29500151.9FeSO4

Moles

(mol)

Mass

(g)

Molar mass

(g/mol)

Formula

Complete the following chart:

AssignmentAssignment

1. AgCl = 143.35 g/mol

#g = 2 mol x 143.35 g/mol = 286.7 g (2)

2. H2 = 2.016 g/mol

#mol = 100 g x mol/2.016 g = 49.6 mol (2)

3. CuSO4 = 159.62 g/mol

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

4. KClO = 90.55 g/mol

#mol = 250 g x mol/90.55 g = 2.76 mol (2)For more lessons, visit www.chalkbored.com

http://www.chalkbored.com/

A way to solve math problems in chemistry Used to convert km to miles, m to km, mol to g, g to mol,...

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