Dimensional Analysis

Dimensional Analysis Teacher’s Guide By: Rita Jones

Lesson Overview: The following lesson provides a Subject area(s): Chemistry powerpoint presentation to introduce the beginning concepts of dimensional analysis. National Science Education Standards Addressed: Topic: Dimensional Analysis 1. Dimensional Analysis 2. Conversion factors 3. SI Prefix Conversions Audience: 9th-12th grade

Resources: Suggested time: 55 minutes 1. Powerpoint inclusive 2. Lemay, H. Eugene, Jr. Chemistry. Materials: Prentice-Hall, Inc. 2002.  Powerpoint software  Calculators  SI prefix conversion table

Learning Objectives: 1. Students will be able to perform dimensional analysis. 2. Students will learn how to use SI prefix conversion tables properly. 3. Students will apply learning to actual problems.

Background: This is a fully prepared lesson plan which involves concept introduction and problems for the students to work on individually. This allows the instructor to walk around the classroom and help students who are struggling with the concept.

Assessment Strategy: The format of this lesson allows the instructor to assess whether the students are grasping the concept. If problems are seen in the students ability to work the problems individually, the instructor can work on it with them individually, or go back to the power point in order to reaffirm concepts.

Teaching tips: Students must work problems individually in order to fully grasp concepts.  Engage students by introducing concepts in the powerpoint and have students take notes on the information presented.  Have students explore their understanding by completing each problem individually.  Explain concepts by going through each problem as a group to make sure the student’s understanding is complete.

Extension(s): Additional worksheet should be given to each student as homework. CH.CH. 11--MEASUREMENTMEASUREMENT III. Unit Conversions (Sec. 1.7, pp. 38-47)

Skills Check

 Multiplication of two integers with exponents. 22 x 23 = 25  Division of two integers with exponents. 27 = 23 24 Problems

35 x 32 34

42 45 1 43

A. SI Prefix Conversions

 Use table on p. 937 to convert between prefixes.  Subtract the exponents.  Move the decimal that many places. A. SI Prefix Conversions

Prefix Symbol Factor mega- M 106 kilo- k 103 BASE --- 100 UNIT deci- d 10-1 centi- c 10-2 milli- m 10-3 micro- μ 10-6 nano- n 10-9 pico- p 10-12

A. SI Prefix Conversions page 18

 SI units for mass: grams (g)  SI units for volume: liters (L)  SI units for length: meters (m)  SI units for time seconds (s)  SI units for temperature: kelvin (K) *It is important to know that when labeling units, upper and lower case changes the meaning of the units. A. SI Prefix Conversions

 532 m = ? km

A. SI Prefix Conversions

 1) 20 cm = ______m

 2) 0.032 L = ______mL

 3) 45 μm = ______nm

 4) 805 dm = ______km B. Dimensional Analysis

 The technique of converting between units is called dimensional analysis.  The “Factor-Label” Method.  Units or “labels” are canceled, or “factored” out.

cm3 x g = g cm3

B. Dimensional Analysis

 Steps: 1) Identify starting & ending units. 2) Line up conversion factors so units cancel. (p. 38 and p. 936). 3) Multiply all top numbers & divide by each bottom number. 4) Check units & answers.

*Stop to ask yourself: “Is my answer reasonable?” B. Dimensional Analysis

 Lining up conversion factors: 1 in = 1 2.54 cm

1 = 2.54 cm 1 in

 1) Your European hairdresser wants to cut your hair 8.0 cm shorter? How many inches will he be cutting off? (See p. 38 and p. 936) B. Dimensional Analysis

2) How many milliliters are in 1.00 quart of milk?

3) Taft football needs 550 cm for a 1st down. How many yards is this? B. Dimensional Analysis

 4) You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.

 5) How many liters of water would fill a container that measures 75.0 in3? B. Dimensional Analysis

6) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?

 Dimensional analysis can also be used to convert using metric prefixes and exponents:

7) Convert 8470 s to μs. B. Dimensional Analysis

8) Convert 6.85 nL to mL.

9) If I was traveling down the interstate at 71 mph, what would this be in cm/s?