DIMENSIONAL ANALYSISDIMENSIONAL ANALYSIS

MHS MHS ChemistrChemistr

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Chapter 4

Conversion FactorsConversion Factors

Fractions in which the numerator and denominator Fractions in which the numerator and denominator are EQUAL quantities expressed in different unitsare EQUAL quantities expressed in different units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm

2.54 cm 1 in.

How many minutes are in 2.5 How many minutes are in 2.5 hourshours??

Conversion factor

2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min

1 hr1 hr

cancelBy using dimensional analysis / factor-label method, By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the side up, and the UNITS are calculated as well as the

numbers!numbers!

Sample ProblemSample Problem

You have $7.25 in your pocket in You have $7.25 in your pocket in quarters. How many quarters do quarters. How many quarters do you have?you have?

7.25 dollars 4 quarters7.25 dollars 4 quarters

1 dollar1 dollar X = 29 quarters= 29 quarters

Learning CheckLearning Check

Write conversion factors that relate Write conversion factors that relate each of the following pairs of units:each of the following pairs of units:

1. Liters and mL1. Liters and mL

2. Hours and minutes2. Hours and minutes

3. Meters and kilometers3. Meters and kilometers

Learning CheckLearning Check

A rattlesnake is 2.44 m long. How A rattlesnake is 2.44 m long. How long is the snake in cm?long is the snake in cm?

a) a) 2440 cm2440 cm

b)b) 244 cm244 cm

c)c) 24.4 cm24.4 cm

Learning CheckLearning Check

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

1.4 days x 24 hr x ?? 1 day

Wait a minute!Wait a minute!

What is What is wrongwrong with the following with the following setup?setup?

1.4 day x 1.4 day x 1 day 1 day x x 60 min 60 min x x 60 sec 60 sec

24 hr 1 hr 1 min24 hr 1 hr 1 min

English and Metric English and Metric ConversionsConversions

If you know ONE conversion for each type If you know ONE conversion for each type of measurement, you can convert anything!of measurement, you can convert anything!

You must You must memorizememorize and use these and use these conversions:conversions:– Mass: 454 grams = 1 poundMass: 454 grams = 1 pound– Length: 2.54 cm = 1 inchLength: 2.54 cm = 1 inch– Volume: 0.946 L = 1 quartVolume: 0.946 L = 1 quart

Learning CheckLearning Check

An adult human has 4.65 L of blood. An adult human has 4.65 L of blood. How many gallons of blood is that?How many gallons of blood is that?

Unit plan: L qt gallon

Equalities: 1 quart = 0.946 L

1 gallon = 4 quarts

Your Setup:

SolutionSolution

Unit planUnit plan:: L qt gallon L qt gallon

Setup: Setup: 4.65 L x 4.65 L x 1 qt 1 qt x x 1 gal 1 gal = 1.23 gal = 1.23 gal

0.946 L 4 qt 0.946 L 4 qt

Dealing with Two Units – Pre-Dealing with Two Units – Pre-AP OnlyAP Only

If your pace on a treadmill is 65 If your pace on a treadmill is 65 meters per minute, how many seconds meters per minute, how many seconds will it take for you to walk a distance will it take for you to walk a distance of 8450 feet?of 8450 feet?

8450 ft 1m 1 min 60 sec1 3.28 ft 65m 1 min