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The factor label method

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

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The factor label method

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  1. 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?

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

  3. 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

  4. 2 molecules H2 1 molecule O2 1 molecule O2 2 molecules H2 2 molecules H2 2 molecules H2O 2 molecules H2O 2 molecules H2 1 molecule O2 2 molecules H2O 2 molecules H2O 1 molecule O2 2 mol H2 1 mol O2 1 mol O2 2 mol H2 2 mol H2 2 mol H2O 2 mol H2O 2 mol H2 1 mol O2 2 mol H2O 2 mol H2O 1 mol O2 2H2+O22H2O

  5. 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

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

  7. 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

  8. 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

  9. 1 km 0.621 mi 0.621 mi 1 km Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) # km = 47 mi What conversion factors are possible?

  10. 1 km 0.621 mi 0.621 mi 1 km Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) # km = 47 mi Pick the one that will allow you to cancel out miles

  11. 1 km 0.621 mi 0.621 mi 1 km Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) # km = 47mi Pick the one that will allow you to cancel out miles

  12. 1 km 0.621 mi 0.621 mi 1 km Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) # km = 47mi Multiply given quantity by chosen conversion factor

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

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

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

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

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

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

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

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

  21. 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. x 1 Can$ 0.65 US$ x 1 mol CO2 x 22.4 L CO2 44.01 g CO2 1 mol CO2 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). 44.01 # L CO2 = 300 g CO2 = 152.7 L CO2

  23. x 3 ft x 1 cm x 12 in 1 ft 0.394 in 1 yd x 58.44 g NaCl 1 mol NaCl 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? Sodium chloride is NaCl (58.44 g/mol) #g NaCl = 3.000 mol NaCl = 175.3 g NaCl

  24. 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?

  25. 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)

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

  27. x 1 US $ x 130 Yen 25 Rubles 1 US $ 18.01 g H2O 2 mol H2O 265 g H2O x 6.02x1023 molecules x x = 1 mol H2O 1 mol O2 1 mol H2O x 1 mol H2O x 1 mol Ca3(PO4)2 18.02 g H2O 310.18 g Ca3(PO4)2 # Yen = 1 Ruble = 5.2 Yen # H2O molecules = 6. 73 g H2O 5. = 2.44 x 1024 molecules H2O # mol Ca3(PO4)2 = 7. 255 g Ca3(PO4)2 = 0.822 mol Ca3(PO4)2 8. # g H2O= 7.35 mol O2

  28. Assignment Complete the following chart:

  29. Assignment Formula Molar mass (g/mol) Mass (g) Moles (mol) Complete the following chart: FeSO4 151.9 500 3.29 (NH4)2CO3 96.1 192.2 2 SnO2 150.7 50 0.332 Sb2O5 323.6 80.9 0.25 NaClO4 122.4 100 0.817 Mg(IO3)2 374.1 1196.8 3.2 CoCl2.H2O 147.8 332 2.246

  30. 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

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