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PROBLEM-SOLVING

PROBLEM-SOLVING. The SMART way FACTOR-LABEL (aka DIMENSIONAL ANALYSIS). Solve in 5 minutes. An ancient measurement of volume mentioned in the Bible is the EPHAH. CHALLENGE: You have 5 minutes to figure out how many liters are equal to an ephah , using the following information:

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PROBLEM-SOLVING

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  1. PROBLEM-SOLVING The SMART way FACTOR-LABEL (aka DIMENSIONAL ANALYSIS)

  2. Solve in 5 minutes • An ancient measurement of volume mentioned in the Bible is the EPHAH. • CHALLENGE: • You have 5 minutes to figure out how many liters are equal to an ephah, using the following information: • 1 EPHAH = 2.429 MODIUM (ancient Roman measurement) • 1 MODIUM =0.7076 VEDRO (old Russian measurement) • 1 VEDRO = 0.349 BUSHELS (customary unit of measurement) • 1 BUSHEL = 2150 CUBIC INCHES • 61.01 CUBIC INCHES = 1 LITER

  3. We convert all the time. When the values are familiar, it is easy. When the problem is short it is simple. But in chem, you will need to solve problems that are neither familiar nor short!

  4. Factor-Label • Use CONVERSION FACTORS • LABEL all units The labels on the factors guide you through the problem as they cancel out

  5. Factor-label to the rescue! FACTOR-LABEL Here I come to save the day!

  6. Factor-Label Method • Use for conversion problems • Changing from one unit to another • Only use for multiplication and division problems

  7. Equalities • Equalities • Two ways to express the same thing • The quantities are equal, but they are expressed in different units EX: 1” = 2.54 cm 7 days = 1 week

  8. Equalities • If the 2 equal quantities are divided, the answer is 1…you get unity. • If you divide a value by itself, you get 1 • So we get CONVERSION FACTORS from 1” = 2.54 cm 7 days = 1 week 1” = 2.54 cm = 1 2.54 cm 1” 7 days = 1 week = 1 1 week 7 days

  9. HOW TO DO FACTOR-LABEL CONVERSION PROBLEMS Write down the starting factor and units. EX: How many cm in 1.98 m? Give yourself room on the paper to work and go to the end and write the desired unit or final factor EX: 1.98 m = cm

  10. Use the appropriate conversion factor(s) (from equalities) to cancel unwanted units and leave desired units. Any label on both top and bottom of the fractions cancels. EX: Equality 1 m = 100 cm This yields two conversion factors 1 m or 100 cm = 1 100 cm 1 m

  11. EX: Equality 1 m = 100 cm this yields two conversion factors 1 m or 100 cm = 1 100 cm 1 m Which one to use? Set up the problems with the one that results in the cancellation of the starting unit. 1.98 m | 100 cm = cm 1 m Cancel the UNITS ONLY that are on the top and bottom of the fractions. 1.98 m| 100 cm = cm 1 m

  12. Do the math to solve. Multiply by all values on the top Divide by all values on the bottom Write the answer with units and the correct number of sigdigs Note: Counted values and defined conversion factors do not limit sigdigs…only measured values. Why? Sigdigs convey the precision of a measurement. We can count exactly and we define certain values exactly. EX: 1.98 m| 100 cm = 198 cm | 1 m

  13. Note: with this “picket fence” set up, the vertical bars separate fractions 1.98 m| 100 cm = 198 cm | 1 m Is the same as 1.98 mX100 cm = 198 cm 1 m You may set yours up either way, but many students find it easier to keep long problems organized with the picket fence style.

  14. How many SCHNIZZLES in 12 TWIZZLES? What do you know? Starting factor What do you want to know? Final factor Start: 12 Twizzles Desired/Final: ______ Schnizzles How do you get from the START to FINAL? You need to find or know some EQUALITIES to use as CONVERSION FACTORS 10 Sizzles = 5 Fizzles 1 Frizzle = 3 Sizzles 18 Fizzles = 1 Twizzle 2 Frizzles = 5 Schnizzles These are defined and counted conversion factors. Report all digits as significant. Start TwizzlesConversion Factors   Final Schnizzles

  15. Congratulations! Factor-Label has guided you through a problem that you knew nothing about! It will guide you through lots chemistry problems, too!

  16. A familiar example

  17. WARNING Avoid Factor-Label (Dimensional Analysis) if … You enjoy making mistakes You have a phobia of correct answers You enjoy solving problems in a convoluted manner You take pleasure in re-inventing the wheel

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