POGIL: No Problem I Can t Handle

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1 ! Page 1 of 5 Name: Group Members: Why: Dimensional analysis is a procedure that produces the units associated with answers to mathematical calculations. It facilitates problem solving, validates the solutions, and sometimes involves unit conversions. Scientists often rely on dimensional analysis during their work. Dimensional analysis is also referred to as unit analysis, factor-label method, and unit-factor method. Learning Objectives: Rationalize/justify the set-up a problem s solution using unit analysis. Convert from one set of unit to another. Identify, set-up, compute, and validate the solutions (units and the magnitude) of computational problems. Text Reference: Chang and Goldsby (Chemistry: The Essential Concepts, McGraw-Hill, 2014) pp Model I: Dimensional Analysis Applied to Unit Conversions Question: Your favorite song plays for 4.53 minutes. How many seconds does your song take? 4.53 minutes number of seconds 1 minute = 60 seconds So the fractions may be... 1minute 60s or 60s 1minute Set up the solu%on using the unit factor connectors so that the unit you don t want cancels and the unit you want remains. Be sure to include all units everywhere. Compute the mathema%cal results and record answers with the correct units. 4.53min 60sec 1min 272 seconds Give complete answers to the key questions, exercises and problems. You MIUST use DIMENSIONAL ANALYSIS. Key Questions 1. How many conversion factors result from a single equality statement? Explain. 2. Which is the correct conversion factor used to convert minutes to seconds in the model? Why?

2 " Exercises 3. Complete the following table by filling in the 3 rd and 4 th columns with correct information. Page 2 of 5 Equality Statement Conversion needed Set-up Result (w/unit) 1.0 mi = 1.6 km 45 mi km 45mi 1.6km 72 km 1.0mi 2.54 cm = 1.00 in 165 cm in 1.0 kg = 2.2 lb 8.3 lb kg 36.0 pasos = paras 95.0 paras pasos Problems 4. The top surface of your lab bench is 36.0 inches wide by 120. inches long. NOTE: 1.00cm = in (a) What is the width of your lab bench in centimeters? What is the length of your lab bench in centimeters? Show both. (b) How many square centimeters is the surface of your lab bench? (c) You need to purchase acid resistance film to cover your bench. How many square meters of this film do you need to purchase? 5. The distance from your chemistry classroom to the nearest bus stop is miles. One day you calibrated your step size on the 200.-m running track. It took you 328 steps to cover that distance. How many steps is it from your chemistry classroom to the bus stop? (Remember, you must use unit analysis.) (Note: 1.00 mi = 1609 m) 6. Convert mm 3 into its volume in km 3. (The correct answer is 7.38x10-4 km 3. Are you correct?)

3 Page 3 of 5 Model II: Problem Solving with Dimensional Analysis Question: The density of silicon is 2.33 g/cm 3. What is the volume of a 62.9g sample of silicon? Set up the solu%on using the unit factor connectors. Start with what you have an use the appropriately posi2oned conversion frac2ons to cancel out the unit you have and get the unit you want. Compute the mathema%cal results and record answers with the correct units. mass = 62.9 g density = 2.33 g/cm 3 volume 2.33 g = 1 cm g 1cm3 2.33g m = 27.0 cm 3 7. If the unit you are looking to cancel is in the numerator of a complex unit fraction, where does it have to go in your conversion fraction to cancel? Where does it go if it is in the denominator? Why? 8. What meaning is lost when units are omitted, and what are the general implications for not using units? Sometimes you have to convert a complex unit into another complex unit. When you do this, treat each part separately and use the conversion fractions to cancel the units appropriately. Question: The density of metal X is lb/ft 3. What is the density of metal X in g/cm 3? Note: 1 inch = 2.54 cm and 1 ounce = g. density = lb/ft 3 lb/ft 3 g/cm 3 1 inch = 2.54 cm 1 lb = 16 oz (I already know this exact number) 1 ounce = g

4 Page 4 of 5 Set up the solu%on using the unit factor connectors. Start with what you have an use the appropriately posi2oned conversion frac2ons to cancel out the unit you have and get the unit you want lb 16oz ft 3 1lb 28.35g 1oz (1ft)3 (12in) 3 (1in) 3 (2.54cm) 3 Compute the mathema%cal results and record answers with the correct units. d = g/cm 3 Notice how each half of the complex unit is dealt with independently. The lb is converted to ounces then grams. Then the cubic foot is converted to cubic inches and then cm 3. Notice how the units get canceled when the quantity you are working with is the numerator versus the denominator. Exercises 9. A small piece of gold has a volume of 1.35 cm 3. (a) What is the mass of the gold piece, given the density of gold is 19.3 g/cm 3? (b) What is the value of the gold piece if the market value of gold is $ per troy ounce? (1.000 troy ounce is equal to g.) 10. Convert 65.0 miles per hour to an equivalent speed in meters per second (m/s)? (Note: 1.00 foot = m; 1mi = 5280 ft) 11. Convert a quantity of mole per liter into its equivalent quantity in grams per cubic centimeter. Note: for this problem, 1 mole is equal to g. Problems

5 Page 5 of M is a concentration unit equal to moles/volume (in liters). You need to make a sodium chloride with a concentration of 0.500M for use in a lab. If the mass of 1.00 mole of sodium chloride is 58.5 grams, what mass of sodium chloride is required to make 2.50L of this solution for your lab? (Hint: Re-write 0.500M with its other units.) 13. Earth is approximately 1.5x10 8 km from the sun. How many minutes does it take light to travel from the sun to Earth? The speed of light is 3.00x10 8 m/s. One More Thing Let x = number of meters and y = number of kilometers. An equation using the symbols x and y and the number 1000 which expresses the relationship between the number of meters and the number of kilometers is: (A) 1000 x = y (B) 1000 y = x (C) x + y = 1000 (D) xy = 1000 Tips for working with Dimensional Analysis You must show ALL units EVERYWHERE! Record all measurements with their correct significant figures. Write 40.00cm not 40cm just because it saves effort. The zero doesn t change the calculation but it changes the meaning of the significant figures. It will also cost you points. Clearly use UNIT ANALYSIS showing all steps, conversion fractions with units, etc. Show what you start with; this is the thing you are trying to convert into something else. Place that quantity (number and measurement) to the left and use conversion fractions to get rid of the units you don t want and get the units you do want. You CANNOT use ratios/proportions. Unit analysis is what we need to use in this class. Ratios get you NO CREDIT! If you are asked to explain or justify, a calculation may support your explanation but it is not usually the only thing you will need to explain. Add in a few words or phrases to complete the explanation. Modified from Foundations of Chemistry by David Hanson