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 The factor label method Q. write conversion factors for 1 foot =12 inches
Q. what conversion factors can you think of that involve meters?
Conversion factors : Conversion factors Conversion factors for 1 ft = 12 in There are almost an infinite number of conversion factors that include meters:
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 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
Slide 4 : 2H2 + O2 2H2O
The steps to follow : 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
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
Factor label example : 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 : 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 : Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) What conversion factors are possible? # km = 47 mi Factor label example
Factor label example : 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 Factor label example
Factor label example : 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 Factor label example
Factor label example : Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Multiply given quantity by chosen conversion factor # km = 47 mi Factor label example
Factor label example : Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Multiply given quantity by chosen conversion factor # km = 47 mi Factor label example
Factor label example : Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Cross out common factors # km = 47 mi Factor label example
Factor label example : Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Cross out common factors # km = 47 Factor label example
Factor label example : Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Are the units now correct? # km = 47 Factor label example
Factor label example : Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Yes. Both sides have km as units. # km = 47 Factor label example
Factor label example : Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Yes. Both sides have km as units. = 47 # km Factor label example
Factor label example : Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Now finish the math. # km = 47 = 75.7 km Factor label example
Factor label example : Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) The final answer is 75.7 km # km = 47 = 75.7 km Factor label example
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
More examples : 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$ = 153.85 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). # L CO2 = 300 g CO2 = 152.7 L CO2 44.01
More examples : 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? # cm = 1 yd = 91.37 cm A chemical reaction requires 3.000 moles of sodium chloride. How many grams is this? #g NaCl = 3.000 mol NaCl = 175.3 g NaCl Sodium chloride is NaCl (58.44 g/mol)
Assignment : 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 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) Assignment
Slide 26 : 1. 2. # mol H2 = 100 g H2 = 49.5 mol H2 # mol CuSO4 = 300 g CuSO4 = 1.88 mol CuSO4 # g AgCl = 23.78 mol AgCl = 3408 g AgCl 3. # ft = 1 m = 3.28 ft 4.
Slide 27 : 5. 6. # Yen = 1 Ruble = 5.2 Yen # H2O molecules = 73 g H2O = 2.44 x 1024 molecules H2O # mol Ca3(PO4)2 = 255 g Ca3(PO4)2 = 0.822 mol Ca3(PO4)2 7. # g H2O= 7.35 mol O2 8.
Assignment : Assignment Complete the following chart:
Assignment : Assignment 2.246 332 147.8 CoCl2.H2O 3.2 1196.8 374.1 Mg(IO3)2 0.817 100 122.4 NaClO4 0.25 80.9 323.6 Sb2O5 0.332 50 150.7 SnO2 2 192.2 96.1 (NH4)2CO3 3.29 500 151.9 FeSO4 Moles
(mol) Mass
(g) Molar mass
(g/mol) Formula Complete the following chart:
Assignment : Assignment AgCl = 143.35 g/mol
#g = 2 mol x 143.35 g/mol = 286.7 g (2)
H2 = 2.016 g/mol
#mol = 100 g x mol/2.016 g = 49.6 mol (2)
CuSO4 = 159.62 g/mol
#mol= 300 g x mol/159.62 g=1.879 mol (2)
KClO = 90.55 g/mol
#mol = 250 g x mol/90.55 g = 2.76 mol (2) For more lessons, visit www.chalkbored.com