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 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. 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$

23. More examples 2. 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

24. The Chemist's Dozen: Avogadro’s Number Chemists count atoms, molecules and ions in groups called moles. (abbreviated mol). The number 6.02 x 10 23 is called Avogadro’s number (N A ) 1 mol = 6.02 x 10 23

25. What 2 factors can you make from that relationship? 1mol and 6.02 x 10 23 6.02 x 10 23 1 mol The unit with Avogadro’s number could be atoms, ions or molecules.

26. Let’s do a calculation A sample contains 1.25 mol of nitrogen dioxide molecules. a.How many molecules are in the sample? b.How many atoms are in the sample?

27. a. How many molecules? x molecules NO 2 = 1.25 mol x conversion factor Which factor is appropriate? 1mol or 6.02 x 10 23 molecules 6.02 x 10 23 molecules 1 mol

28. How many molecules in 1.25 moles? x molecules = 1.25 mol x 6.02 x 10 23 molecules 1 mol = 7.525 x 10 23 molecules The unit mol cancels out and we have the unit molecules in our answer.

29. How many atoms in 1.25 moles of NO 2 ? There are 2 relationships we need. 1 mol = 6.02 x 10 23 molecules 1 molecule of NO 2 contains 3 atoms of 1 molecule = 3 atoms. Note this last factor is specific to NO 2. It would not be the same for CH 4 or other molecules.

30. How many atoms in 1.25 moles NO 2 ? x atoms in NO 2 = 1.25 mol NO 2 x 6.02 x 10 23 molecules NO 2 x 3 atoms in NO 2 1 mol NO 2 1 molecule NO 2 Use the units to guide the calculation. NO 2 is a compound so its particles are molecules. We used that in part a. In part b we want to know how many atoms are in the 1.25 mol sample so we add a conversion factor that shows that there are 3 atoms (1 N and 2 O) atoms in each molecule of NO 2. After doing the math x atoms in NO 2 = 1.25 x 6.02 x 10 23 x 3 atoms = 2.58 x 10 23 atoms This could also be done as a 2 step problem using your answer from part a followed by the 3 atom/1 molecules conversion factor.