The factor label method 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 Q. write conversion factors for 1 foot =12 inches Q. what conversion factors can you think of that involve meters?

Conversion factors Conversion factors for 1 ft = 12 in There are almost an infinite number of conversion factors that include meters:

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 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

2H2 + O2  2H2O 2 molecules H2 1 molecule O2 2 molecules H2 2 molecules H2O 1 molecule O2 2 molecules H2O 2 mol H2 1 mol O2 2H2 + O2  2H2O 2 mol H2 2 mol H2O 1 mol O2 2 mol H2O

The steps to follow Now we are ready to solve problems using the factor label method. The steps involved are: Write down the desired quantity/units Equate the desired quantity to given quantity Determine what conversion factors you can use (both universal and question specific) Multiply given quantity by the appropriate conversion factors to eliminate units you don’t want and leave units you do want Complete the math

First write down the desired quantity Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) # km First write down the desired quantity

Next, equate desired quantity to the given quantity Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) # km = 47 mi Next, equate desired quantity to the given quantity

Now we have to choose a conversion factor Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) # km = 47 mi Now we have to choose a conversion factor

What conversion factors are possible? Factor label example 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 What conversion factors are possible?

Pick the one that will allow you to cancel out miles Factor label example 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 Pick the one that will allow you to cancel out miles

Pick the one that will allow you to cancel out miles Factor label example 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 Pick the one that will allow you to cancel out miles

Multiply given quantity by chosen conversion factor Factor label example 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 Multiply given quantity by chosen conversion factor

Multiply given quantity by chosen conversion factor Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) x 1 km 0.621 mi # km = 47 mi Multiply given quantity by chosen conversion factor

Cross out common factors Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) x 1 km 0.621 mi # km = 47 mi Cross out common factors

Cross out common factors Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) x 1 km 0.621 # km = 47 Cross out common factors

Are the units now correct? Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) x 1 km 0.621 # km = 47 Are the units now correct?

Yes. Both sides have km as units. Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) x 1 km 0.621 # km = 47 Yes. Both sides have km as units.

Yes. Both sides have km as units. Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) x 1 km 0.621 # km = 47 Yes. Both sides have km as units.

Factor label example Now finish the math. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) x 1 km 0.621 = 75.7 km # km = 47 Now finish the math.

Factor label example The final answer is 76 km Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) x 1 km 0.621 = 75.7 km = 76 km # km = 47 The final answer is 76 km

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

More examples 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$ = 150 Can $ 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). 44.01 # L CO2 = 300. g CO2 x 1 mol CO2 44.01 g CO2 x 22.4 L CO2 1 mol CO2 = 152.7 L = 153 L

More examples 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 (1.00 yards) ? # cm =1.00 yd x 3 ft 1 yd x 12 in 1 ft x 1 cm 0.394 in = 91.37 cm = 91.4 cm A chemical reaction requires 3.000 moles of sodium chloride. How many grams is this? Sodium chloride is NaCl (58.44 g/mol) #g NaCl = 3.000 mol NaCl x 58.44 g NaCl 1 mol NaCl = 175.3 g NaCl

Assignment Answer questions using the factor label method: How many moles of H2 are in 100. g of H2? 300. g of CuSO4 is needed in an experiment. How many moles does this represent? A chemical reaction requires 23.78 moles of silver chloride. How many grams is this? Calculate how many feet are in 1.00 meter (use information from the examples above). 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?

Assignment How many molecules are in 73 grams H2O? (hint: form a conversion factor using Avogadro’s #) 255 g of calcium phosphate are produced in a chemical reaction. How many moles of calcium phosphate does this represent? 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)

1. # mol H2 = 100. g H2 x 1 mol H2 2.02 g H2 = 49.5 mol H2 2. # mol CuSO4 = 300. g CuSO4 x 1 mol CuSO4 159.61 g CuSO4 = 1.88 mol CuSO4 3. # g AgCl = 23.78 mol AgCl x 143.32 g AgCl 1 mol AgCl = 3408 g AgCl 4. # ft = 1.00 m x 100 cm 1 m x 0.394 in 1 cm x 1 ft 12 in = 3.28 ft

5. # Yen = 1 Ruble x 1 US $ 25 Rubles x 130 Yen 1 US $ = 5.2 Yen # H2O molecules = 6. 73 g H2O x 1 mol H2O 18.02 g H2O x 6.02x1023 molecules 1 mol H2O = 2.44 x 1024 molecules H2O 7. # 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 8. # g H2O= 2 mol H2O 1 mol O2 x 18.01 g H2O 1 mol H2O x 265 g H2O = 7.35 mol O2

Assignment Complete the following chart: Formula Molar mass (g/mol) Moles (mol) FeSO4 500. (NH4)2CO3 2.00 SnO2 50. Sb2O5 0.250 NaClO4 100. Mg(IO3)2 3.200 CoCl2.H2O 332

Assignment Complete the following chart: Formula Molar mass (g/mol) Moles (mol) FeSO4 151.9 500. 3.29 (NH4)2CO3 96.1 192.2 2.00 SnO2 150.7 50. 0.33 Sb2O5 323.6 80.9 0.250 NaClO4 122.4 100. 0.817 Mg(IO3)2 374.1 1196.8 3.200 CoCl2.H2O 147.8 332 2.25

Assignment 1. How many grams are there in 2.000 moles of silver chloride? 2. How many moles does 100. g of hydrogen gas represent? 3. How many moles are there in 300. g of copper (II) carbonate? 4. How many moles are in 250. g of potassium hypochlorite?

Assignment AgCl = 143.35 g/mol #g = 2.000 mol x 143.35 g/mol = 286.7 g H2 = 2.016 g/mol #mol = 100. g x mol/2.016 g = 49.6 mol CuSO4 = 159.62 g/mol #mol= 300. g x mol/159.62 g=1.879 mol KClO = 90.55 g/mol #mol = 250. g x mol/90.55 g = 2.76 mol