Dimensional Analysis Dimensional analysis is a strategy for performing conversions by multiplying by ratios that equal one. Basic Principles of Dimensional Analysis __________________________________________ __________________________________________ __________________________________________ The Process of Dimensional Analysis oSet up conversion ratios so that ___________ _____________________________________ Calculate Usain Bolt’s speed in miles per hour. He ran a 100 meter dash in 9.58 seconds ( 10.4 m/ s). Conversion factors: 1000 m = 1 km, 1.6 km = 1 mile, 10.4 meters ___ _____ _______ ______ x x x x . seconds = _____ miles hours Tips for Dimensional Analysis Always include your units and cross off the ones that cancel out so that you can double check your work, making sure you did not miss a step or invert any ratios. For some problems, the same unit may be used for more than one type of measurement. For these cases, you will need to include both the unit and what is being measured. = Some ratios are normally given in a conventional orientation, such as miles per gallon, so that the information can be more easily interpreted. For example a higher miles per gallon ratio means better fuel efficiency. However for problem solving purposes these ratios can and may need to be inverted. If a car gets 25 miles per gallon, it also _______________ __________________________________ . Solve the problem with your table partner: A car has a fuel efficiency of 20 miles per gallon and is used to drive 15,000 miles per year. Determine how many pounds of carbon are released into the atmosphere each year by the car. • Each gallon of gasoline burned releases 5 lbs of carbon dioxide. • Every lb of carbon dioxide contains 0.27 lbs of carbon Discuss with your table partner Determine the formula for percent change: One formula you will need to have memorized for the AP exam is the percent change formula. Determine the formula and solve the question below. (Consider what this term means and how you would find what percentage of the original the change represents.) The level of CO2 in the atmosphere was 317 ppm in 1958. It is currently 400 ppm. What was the percentage change in carbon dioxide during that time period? Fill in your answers on the next slide. The formula for percent change is: The atmospheric level of CO2 percent change from 1958 to present : Solutions and Dilutions A commonly used skill in a lab is to calculate the needed volume of a more concentrated stock solution for dilution to a desired concentration and volume. To do these calculations the following formula can be used: CsVs = Cf Vf Cs = concentration of the stock Vs = volume of the stock Cf = desired final concentration Vf = desired final volume Discuss with your table partner Rewrite the equation to solve for Vs Use this formula to solve the two problems on the following slide. 100 mL of 0.02 M Tris solution needs to be made from a 1 M stock. What volume of stock should be used and to what volume of distilled water should the stock be added? A liter of 0.1 M NaCl solution needs to be made from a 4 M stock. What volume of stock should be used and to what volume of distilled water should the stock be added? Types of Concentration Units Mass of Solute/Volume of Solution such as 0.5 mg NaCl/L Moles of Solute/ Volume of Solution such as 0.8 M NaCl/ L (Molarity) Mass of Solute/ Mass of Solution such as 0.6 mg NaCL/kg Discuss with your table partner Understanding the Formula: When you multiply a solution’s concentration (in mass per unit volume) times its volume, what are you solving for if concentration is in mass/volume? Explain why CsVs should equal CfVf. .