Lesson: Dimensional Analysis and Unit Conversion FOR THE TEACHER Summary In this lesson, students will learn how to use dimensional analysis for unit conversion problems. They will then practice the skill on several chemistry-based conversion problems. Grade Level High School Objectives By the end of this lesson, students should be able to use dimensional analysis for mass, length, volume, temperature, and density unit conversion problems Chemistry Topics This lesson supports students’ understanding of unit conversion dimensional analysis Time Teacher Preparation: 5 minutes Lesson: 45 – 60 minutes Materials Dimensional Analysis PowerPoint presentation Student Handout Safety No specific safety precautions need to be noted. Teacher Notes Show your students The Temperature Guys video from the Founders of Chemistry video series on the AACT website, before starting the unit conversion lesson. This will help to begin a discussion about why units are important. Use the supplied PowerPoint presentation to guide your student through a few examples of unit conversion problems using dimensional analysis. The lesson opener asks, “When does 0.5 – 60 = 11?” The answer – it all depends on units. A half (0.5) day is 12 hours. Subtract one hour (60 minutes) and you get 11 hours. Have 100 pennies, 10 dimes, 4 quarters, and 1 dollar bill ready for the second slide. Ask students what the four have in common (same amount of money) and how they differ (each has a different monetary value and you need different amounts of each to have a dollar) Have a meter stick that also has inch markings. Talk about the metric markings and how they are related. Then compare the inch markings to the centimeters markings. You may want to follow this lesson with the Unit Conversion Online Tutorial activity.
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FOR THE STUDENT Lesson Unit Conversion with Dimensional Analysis CHEMISTRY…Math with Meaning
When does 0.5 – 60 = 11 ALL NUMBERS ARE MEASUREMENTS… ALL NUMBERS MUST HAVE UNITS!! • Mass – g, kg, lb • Volume – L, mL, cm3 • Temperature - F, C, K • Length – m, mm, cm, km, in • Amount – molecules (mole) and moles (mol)
Conversion Factors are EQUALITIES…
100 pennies =
10 dimes = 4 quarters =
100 cm = 1 m
1 dollar
1 in = 2.54 cm
These equalities can be used in UNIT CONVERTIONS
Dimensional Analysis An ORGANIZED Method to Convert Units… ONE Step: Convert 4.76 kilometers into meters…
ONE Steps: Convert 1,800 milliliters into liters…
Dimensional Analysis An ORGANIZED Method to Convert Units… TWO Steps: Convert 67,400 milligrams into pounds…
THREE Steps: Convert 5.85 feet into millimeters…
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•A 11.16 cm3 sample of copper has a mass of 100.0 g. What is the DENSITY?
•What would be the mass of a 20.0 cm3 sample?
• A 405 g sample aluminum has a volume of 150. cm3. What is the DENSITY?
• What would be the volume of a 2000. gram sample?
Temperature Conversions… Fahrenheit, Celsius, and Kelvin oF
= (1.8 x oC) + 32
K = oC + 273
Convert 22.5C to Fahrenheit…
Convert it to Kelvin…
Temperature Conversions… Fahrenheit, Celsius, and Kelvin oF
= (1.8 x oC) + 32
K = oC + 273
Convert 86F to Celsius…
Convert it to Kelvin…
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Dimensional Analysis Practice Problems
1. Convert 3.55 liters into milliliters.
2. Convert 1.64 pounds to grams and milligrams.
3. Convert 7.2 meters to centimeters and inches.
4. Convert 16,450 milligrams to grams and pounds.
5. Convert 12.0 feet into centimeters and meters.
6. Convert 1.500 days into minutes and seconds.
7. The highest temperature recorded in Washington D.C. was 106F on July 20, 1930. Convert the temperature to C and K.
8. On the 4th of July, a sparkler burns at a temperature of 1644K. Convert the temperature to both C and F.
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9. I like my steak cooked medium rare – which means it will have an internal temperature of 135F. Convert this temperature to C and K.
10. A student finds a rock on the way to school. In the laboratory he determines that the volume of the rock is 22.7 cm3, and the mass in 39.943 g. density of the rock?
What is the
11. Calculate the density of a material that has a mass of 52.457 g and a volume of 13.5 cm3.
12. The density of zinc is approximately 7.13 g/mL. 7.13 g Zinc=1 mL Zinc 7.13 g Zinc
=
1
=
1 mL Zinc
1 mL Zinc
7.13 g Zinc
a.
What is the volume, in cm3, of a 5.00 g piece of zinc?
b.
What is the mass of a 45.6 L block of zinc?
13. A sample of iron has a volume of 25.0 cm3 has a mass of 174 grams. Calculate the density of iron.
a.
What would be the mass of 15.0 of cm3 iron?
b.
What would be the volume of 1000. grams of iron?
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