2. 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?

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

4. 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

5. 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 don’t want and leave units you do want 5.Complete the math

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. Summary The previous problem was not that hard (direct conversion). In other words, you probably could have done it faster using a different method; However, for harder problems (indirect conversions) the factor label method is easiest! Let’s try a few more direct conversions, then we can move to the indirect ones!!

22. More examples(Direct Conversion) 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$

23. Conversion Factors Comparing Customary and Metric Units LengthMass/WeightCapacity 1 in = 2.5 cm1 kg = 2.2 lb1 L = 1.1 qt 1 m = 1.1 yd1 oz = 28 g1 kL = 275 gal 1 mi = 1.6 km More examples(Direct Conversion) Let’s get busy! 1.20 yd = ______________ m 2.40 g = _______________ oz 3.15 mi = _______________ km 4.10 L = _______________ qt 5.4 km = _______________ mi 6.150 gal = _____________ kL

24. 1. 20 yd = ______________ m 18.2 yd  m 1 m = 1.1 yd ( ) _____________

25. 2. 40 g = __________ oz 1.4 g  oz 1 oz = 28 g ( ) _____________

26. 3. 15 mi = __________ km 24 mi  km 1 mi = 1.6 km ( ) _____________

27. 4. 10 L = __________ qt 11 L  qt 1 L = 1.1 qt ( ) _____________

28. 5. 4 km = __________ mi 2.4 km  mi 1 km = 1.6 mi ( ) _____________

29. 6. 150 gal = __________ kL 0.5 gal  kL 1 kL = 275 gal ( ) _____________

30. More examples (Indirect Conversions ) 1. 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? yd  ft  in  cm # cm = 1 ydx 3 ft 1 yd = 91.37 cm x 12 in 1 ft x 1 cm 0.394 in

31. Assignment Answer questions using the factor label method: 1.Calculate how many feet are in 1 meter (use information from the examples above). 2.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?

32. # ft= 1 mx 100 cm 1 m = 3.28 ft x 0.394 in 1 cm x 1 ft 12 in 1.

33. 2. # Yen= 1 Rublex 1 US $ 25 Rubles = 5.2 Yen x 130 Yen 1 US $