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

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

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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 H 2 and O 2 involves 2 H 2 molecules combining with 1 O 2 molecule to make 2 H 2 O molecules. Write all possible conversion factors

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

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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 dont want and leave units you do want 5.Complete the math

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

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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

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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

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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 1 km Factor label example

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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 1 km Factor label example

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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 1 km Factor label example

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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 1 km Factor label example

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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

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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

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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

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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

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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

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

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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

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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

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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

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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 = 300 g CO 2 x 1 mol CO 2 44.01 g CO 2 = 152.7 L CO 2 x 22.4 L CO 2 1 mol CO 2 44.01

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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 ydx 3 ft 1 yd = 91.37 cm x 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 NaClx 58.44 g NaCl 1 mol NaCl = 175.3 g NaCl Sodium chloride is NaCl (58.44 g/mol)

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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, 130 Yen, or 25 Rubles. How many Yen can you buy with one Ruble?

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6.How many molecules are in 73 grams H 2 O? (hint: form a conversion factor using Avogadros #) 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 balanced equation and 1 from a molar mass) Assignment

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1. 2. # mol H 2 = 100 g H 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 4 = 1.88 mol CuSO 4 # g AgCl = 23.78 mol AgClx 143.32 g AgCl 1 mol AgCl = 3408 g AgCl 3. # ft= 1 mx 100 cm 1 m = 3.28 ft x 0.394 in 1 cm x 1 ft 12 in 4.

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5. 6. # Yen= 1 Rublex 1 US $ 25 Rubles = 5.2 Yen # H 2 O molecules = 73 g H 2 Ox 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 2 mol H 2 O 1 mol O 2 x # g H 2 O= 7.35 mol O 2 265 g H 2 O = 18.01 g H 2 O 1 mol H 2 O x 8.

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Assignment FormulaMolar 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 Mg(IO 3 ) 2 3.2 CoCl 2.H 2 O332 Complete the following chart:

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Assignment 2.246332147.8CoCl 2.H 2 O 3.21196.8374.1Mg(IO 3 ) 2 0.817100122.4NaClO 4 0.2580.9323.6Sb 2 O 5 0.33250150.7SnO 2 2192.296.1(NH 4 ) 2 CO 3 3.29500151.9FeSO 4 Moles (mol) Mass (g) Molar mass (g/mol) Formula Complete the following chart:

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

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