2. The factor label method u A way to solve math problems in chemistry u Used to convert km to miles, m to km, mol to g, g to mol, etc. u To use this we need: 1) desired unit, 2) given unit, 3) conversion factors u Conversion factors are relationships expressed as a fraction E.g. for 1 km=0.6 miles the conversion factor is

3. The steps to follow Now we are ready to solve problems using the factor label method. The steps are: 1. Write down the starting unit 2. Write down the desired units 3. Determine what conversion factors you can use 4. Make sure the conversion factor has the starting unit on the bottom and the next unit on top 5. Multiply and divide to eliminate units you don’t want and leave units you do want

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

5. 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

6. 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

7. 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 1 km 0.621 mi 1 km

8. 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 1 km 0.621 mi 1 km

9. 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 1 km

10. 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 x 1 km 0.621 mi

11. Factor label example 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

12. Factor label example 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

13. 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# km = 47 x 1 km 0.621 # km

14. Factor label example 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

15. 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 x 1 km 0.621 = 75.7 km

16. Moles in chemical equations u The coefficients tell us how many moles of each substance 2 Al 2 O 3  Al + 3 O 2 2 Na + 2 H 2 O  2 NaOH + H 2 u A balanced equation is a Molar Ratio

17. Mole to Mole conversions 2 Al 2 O 3  Al + 3 O 2 each time we use 2 moles of Al 2 O 3 we make 3 moles of O 2 2 moles Al 2 O 3 3 mole O 2 or 2 moles Al 2 O 3 3 mole O 2

18. Mole to Mole conversions u How many moles of O 2 are produced when 3.34 moles of Al 2 O 3 decompose? 2Al 2 O 3  Al + 3O 2 3.34 mol Al 2 O 3 2 mol Al 2 O 3 3 mol O 2 = 5.01 mol O 2 If you know the amount of ANY chemical in the reaction, you can find the amount of ALL the other chemicals!

19. Practice: 2C 2 H 2 + 5 O 2  4CO 2 + 2 H 2 O If 3.84 moles of C 2 H 2 are burned, how many moles of O 2 are needed? (9.6 mol) How many moles of C 2 H 2 are needed to produce 8.95 mole of H 2 O? (8.95 mol) If 2.47 moles of C 2 H 2 are burned, how many moles of CO 2 are formed? (4.94 mol)

20. End Day 1

21. Calculations with Molar Mass molar mass Grams Moles Molar mass is a conversion factor for grams to moles

22. Converting Moles and Grams Aluminum is often used for the structure of light-weight bicycle frames. How many grams of Al are in 3.00 moles of Al? 3.00 moles Al ? g Al

23. 1. Molar mass of Al= 27 g/mol 1 mole Al = 27.0 g Al 2. Conversion factors for Al 27.0g Al or 1 mol Al 1 mol Al 27.0 g Al 3. Setup3.00 moles Al x 27.0 g Al 1 mole Al Answer = 81.0 g Al

24. Practice u How many grams are there in 2 moles of H 2 0? 2 mol H 2 0 (18.0 g H 2 0 /1 mol H 2 0) = 36.0 g H 2 0 u How many moles of NaOH are in 160 grams? 160 g NaOH (1 mol NaOH / 40.0 g NaOH)= 4.0 mol NaOH u How many grams are there in 3.5 moles of NaCl? 3.5 mol NaCl (48.5 g NaCl/1 mol NaCl)= 169.75 g NaCl u How many moles of AgNO 3 are in 87 grams? 87 g AgNO 3 (1 mol AgNO 3 / 169.9 g AgNO 3 )=.51 mol AgNO 3

25. End Day 2

26. Mass to mass conversions u Must go through moles!!!! u Use factor label method and make sure of your units. u Remember that the top of one conversion must cancel with the bottom of the next.

27. Mass-Mass Problem: 6.50 grams of aluminum reacts with an excess of oxygen. How many grams of aluminum oxide are formed? 4Al + 3O 2  2Al 2 O 3 = 6.50 g Al ? g Al 2 O 3 1 mol Al 26.98 g Al 4 mol Al 2 mol Al 2 O 3 1 mol Al 2 O 3 101.96 g Al 2 O 3 (6.50 x 1 x 2 x 101.96) ÷ (26.98 x 4 x 1) = 12.3 g Al 2 O 3 are formed

28. Another example: 4 Al + 3 O 2  2 Al 2 O 3 u How many grams of Al is needed to react with 100 grams O 2 ? 100 g O 2 X 1 mol O 2 X 4 mol Al X 27.0 g Al = 32.0 g O 2 3 mol O 2 1 mol Al (100 X 1 X 4 X 27.0) / (32.0 X 3 X 1) = 112.5 g Al

29. Another example: u If 10.1 g of Fe are added to a solution of CuSO 4, how many grams of Cu would form? 2Fe + 3CuSO 4  Fe 2 (SO 4 ) 3 + 3Cu Answer = 17.2 g Cu