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# Measurement in Chemistry Factor-Label Method

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1. Measurement in ChemistryFactor-Label Method

2. The Factor-Label MethodAt the conclusion of our time together, you should be able to: Recognize a problem that can be solved with the factor label method Transform a statement of equality into a conversion factor Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found

3. 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 equalities expressed as a fraction and equal to one!

4. Equalities State the same measurement in two different units length 10.0 in. 25.4 cm

5. Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units but always equal to one. You can always multiply any equation by this equality and not change the quantity, just the units. Example: 1 in. = 2.54 cm Factors: 1in. and 2.54 cm 2.54 cm 1 in.

6. For example: 1 km = 0.6 miles the conversion factor is Write conversion factors for 1 foot = 12 inches What conversion factors can you think of that involve meters?

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

8. The Steps to Follow Now we are ready to solve problems using the factor label method. The steps involved are: • Write the desired quantity and = • Write down the given quantity and put it over 1 • Determine what conversion factors you will use to turn the given label into the needed label. • Multiply the given quantity by the appropriate conversion factors to eliminate units you don’t want and leave the units you do want • Complete the math

9. Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km First write down the desired quantity

10. Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 mi Next, equate desired quantity to the given quantity

11. Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 mi Now we have to choose a conversion factor

12. 1 km 0.621 mi 0.621 mi 1 km Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 mi What conversion factors are possible?

13. 1 km 0.621 mi 0.621 mi 1 km Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 mi Pick the one that will allow you to cancel out miles

14. 1 km 0.621 mi 0.621 mi 1 km Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0mi Pick the one that will allow you to cancel out miles

15. 1 km 0.621 mi 0.621 mi 1 km Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0mi Multiply given quantity by chosen conversion factor

16. x 1 km 0.621mi Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0mi Multiply given quantity by chosen conversion factor

17. x 1 km 0.621mi Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0mi Cross out common factors

18. x 1 km 0.621 Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 Cross out common factors

19. x 1 km 0.621 Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 Are the units now correct? Yes – km on both sides!

20. x 1 km 0.621 Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 = 75.68438003 km Now finish the math.

21. The Steps to Follow Now we are ready to solve problems using the factor label method. The steps involved are: • Complete the math with no rounding • Make certain the sig figs are correct by rounding to the correct number of sig figs at the very end • Don’t forget the order of operations when you complete the math • Conversion factors do not determine sig. figs.!

22. x 1 km 0.621 Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) = 75.7 km # km = 47.0 The final answer is 75.7 km

23. 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

24. x 1 Can\$ 0.65 US\$ More Examples 1. You want to convert 100.00 U.S. dollars to Canadian dollars. If the exchange rate is 1 Can\$ = 0.65 US\$, how much will it cost? # Can\$ = 100.00 US\$ = 153.85 Can\$

25. The Factor-Label MethodLet’s see if you can: Recognize a problem that can be solved with the factor label method Transform a statement of equality into a conversion factor Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found

26. Learning Check Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 1 Liter = 1000 mL 2. hours and minutes 1 hour = 60 minutes 3. meters and kilometers 1000 meters = 1 kilometer

27. How many minutes are in 2.5 hours? Conversion factor 2.5 hr x 60 min = 150 min 1 hr By using dimensional analysis/factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

28. Learning Check • You have \$7.25 in your pocket in quarters. How many quarters do you have? 7.25 dollars 4 quarters 1 dollar = 29 quarters X

29. Measurement in ChemistryFactor-Label MethodPart 2

30. The Factor-Label MethodAt the conclusion of our time together, you should be able to: Recognize a problem that can be solved by moving the decimal point. Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found with two changes of labels or labels that are squared or cubed.

31. Dealing with Two Units Convert 55.00 km/h to m/s 55.00 km x 1000 mx 1 h___ = h 1 km 3600 s 15.28 m/s

32. A patient requires injection of 0.012 g of a pain killer available in a 15 mg/mL solution. How many milliliters should be administered? When you see a number with two units like 15 mg/mL, it can be used as a conversion factor. What it really says is that 1 ml of the solution contains 15 mg of the drug. ? mL = 0.012 g of drug 0.012 g drug  mL soln mg drug  103 mg drug 1 mL soln ? mL = 0.012 g of drug 1 g drug 15 mg drug = 0.80 mL soln

33. x 60 s 1 min x 1 m x 1 min 3.28 ft 65 m Dealing with Two Units, Your Turn If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet? 1 meter = 3.28 feet 2380 seconds # s = 8450 ft

34. What about Square and Cubic units? • Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also! • Best way: Square or cube the Entire conversion factor • Example: Convert 4.3 cm3 to mm3 ( ) 4.3 cm3 10 mm 3 1 cm 4.3 cm3 103 mm3 13 cm3 = = 4300 mm3

35. Learning Check • A Nalgene water bottle holds 1000 cm3 of dihydrogen monoxide (DHMO). How many cubic decimeters is that?

36. Solution 1000 cm3 1 dm 3 10 cm ( ) = 1 dm3 So, a dm3 is the same as a Liter! A cm3 is the same as a milliliter.

37. Converting Metric to Metric A rattlesnake is 2.44 m long. How long is the snake in cm? a) 2440 cm b) 244 cm c) 24.4 cm

38. Solution A rattlesnake is 2.44 m long. How long is the snake in cm? b) 244 cm 2.44 m x 100 cm = 244 cm 1 m

39. Converting Units of Length Made Easy O—H distance = 9.4 x 10-11 m 9.4 x 10-9 cm 0.094 nm 0.5 kilometer (km) = 500 meters (m) 2.5 meter (m) = 250 centimeters (cm) 1 centimeter (cm) = 10 millimeter (mm) 1 nanometer (nm) = 1.0 x 10-9 meter

40. An Easier Way A rattlesnake is 2.44 m long. How long is the snake in cm? G _ _ M _ _ k h da _ d c m _ _ μ _ _ n A move from 1 meter to centimeters is two places right Move the decimal place of the number two places right 244 cm

41. Another Example: How many millimeters are there in 4.5 cm? G _ _ M _ _ k h da _ d c m _ _ μ _ _ n A move from cm to mm is one place right Move the decimal place of the number one place right 45 mm

42. Another Example: How many kilometers are there in 4.5 cm? G _ _ M _ _ k h da _ d c m _ _ μ _ _ n A move from cm to km is five places left Move the decimal place of the number five places left 0.000 045 km

43. The Factor-Label MethodLet’s see if you can: Recognize a problem that can be solved by moving the decimal point. Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found with two changes of labels or labels that are squared or cubed.

44. Learning Check: 2 kilometers is the same as how many millimeters G _ _ M _ _ k h da _ d c m _ _ μ _ _ n A move from km to mm is six places right Move the decimal place of the number six places right 2 000 000 mm, 2 x 106 mm

45. Metric Conversions #1: Write 550 mm as meters. G _ _ M _ _ k h da _ d c m _ _ μ _ _ n A move from mm to m is 3 places left Move the decimal place of the number 3 places left 0.55 m

46. Learning Check A person’s blood contains 185 mg of cholesterol per deciliter of blood. How many grams of cholesterol are there in 1 liter of this blood? • 0.0185 g • 0.185 g • 1.85 g • 18.5 g • 1850 g

47. English and Metric Conversions • If you know ONE conversion for each type of measurement, you can convert anything! • You must use these conversions: • Mass: 454 grams = 1 pound • Length: 2.54 cm = 1 inch • Volume: 0.946 L = 1 quart

48. Learning Check An adult human has 4.65 L of blood. How many gallons of blood is that? Unit plan: L qt gallon Equalities: 1 quart = 0.946 L 1 gallon = 4 quarts Your Setup: gal = 4.65 L x 1 quart x 1 gallon 1 0.946 L 4 quarts = 1.23 gallons

49. x 3 ft x 12 in x 1 cm 1 yd 1 ft 0.394 in Exit Quiz There are 12 inches in a foot, 0.394 inches in a centimeter, and 3 feet in a yard. How many centimeters are in 1.000 yard? # cm = 1 yd = 91.37 cm

50. x 1.6 km 1 mi Exit Quiz #6 on WS Change 9.4 miles to km (1 mile = 1.6 km) # km = 9.4 mi = 15 km