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Measurement in Chemistry Factor-Label Method

Measurement in Chemistry Factor-Label Method. Standard. SCSh5. Students will demonstrate the computation and Estimation skills necessary for analyzing data and developing reasonable scientific explanations.

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Measurement in Chemistry Factor-Label Method

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  1. Measurement in ChemistryFactor-Label Method

  2. Standard SCSh5. Students will demonstrate the computation and Estimation skills necessary for analyzing data and developing reasonable scientific explanations. • Express appropriate numbers of significant figures for calculated data, using scientific notation where appropriate. • Solve scientific problems by substituting quantitative values, using dimensional analysis and/or simple algebraic formulas as appropriate.

  3. Are Units important? "The 'root cause' of the loss of the spacecraft was the failed translation of English units into metric units in a segment of ground-based, navigation-related mission software, as NASA has previously announced," said Arthur Stephenson, chairman of the Mars Climate Orbiter Mission Failure Investigation Board. "The failure review board has identified other significant factors that allowed this error to be born, and then let it linger and propagate to the point where it resulted in a major error in our understanding of the spacecraft's path as it approached Mars." http://mars.jpl.nasa.gov/msp98/orbiter/ 4

  4. 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

  5. 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!

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

  7. 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.

  8. 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?

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

  10. 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

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

  12. 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

  13. 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

  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 = 47.0 mi What conversion factors are possible?

  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 = 47.0 mi Pick the one that will allow you to cancel out miles

  16. 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

  17. 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

  18. 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

  19. 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

  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 Cross out common factors

  21. 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!

  22. 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.

  23. 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.!

  24. 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

  25. 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

  26. 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$

  27. 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

  28. 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

  29. 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!

  30. 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

  31. Measurement in ChemistryFactor-Label MethodPart 2

  32. 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.

  33. 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

  34. 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

  35. 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

  36. 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

  37. 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

  38. 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.

  39. 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

  40. 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

  41. 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

  42. 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

  43. 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

  44. x 1 US $ x 130 Yen 25 Rubles 1 US $ Exit Quiz 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? = 1 Ruble # Yen = 5.2 Yen

  45. x 1 ft 12 in x 100 cm x 0.394 in 1 m 1 cm Exit Quiz Calculate how many feet are in 1 meter. (use 1 cm = 0.394 in) # ft = 1 m = 3.28 ft

  46. Conversion Factors…. • In grade school we learned that 1 gallon contained 4 quarts or stating that relationship as an equality: • 1 gallon = 4 quarts • Since 1 gallon and 4 quarts represent the same amount, we have a Conversion Factor

  47. Conversion Factors • Start with 1 gallon = 4 quarts • Now divide each side by 1 gallon • we get this equation • 1 gallon = 4 quarts 1 gallon 1 gallon Since 1 gallon divided by 1 gallon equals 1 • Our equality becomes: 1 = 4 quarts 1 gallon

  48. Conversion Factors…. • Again start with 1 gallon = 4 quarts • But this time we’ll divide each side of the equality by 4quarts • The resulting equation is • 1 gallon = 4 quarts 4 quarts 4 quarts Which becomes

  49. Conversion Factors…. • The right side of our equation becomes one because 4 quarts divided by 4 quarts is 1 • 1 gallon = 14 quarts • Rearranging this becomes 1 = 1 gallon 4 quarts

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