Chemistry Boyle’s Law Pressure-Volume Relationship in Gases MATERIALS AND RESOURCES ABOUT THIS LESSON n this lesson, students will use a gas pressure data EACH GROUP collection system to collect pressure and volume data collection device I data pairs that can then be analyzed for their gas syringe, 20 mL mathematical relationship. The data collection is quick sensor, gas pressure and easy, and students typically get excellent results. OBJECTIVES Students will: • Use a gas pressure sensor and a gas syringe to measure the pressure of an air sample at several different volumes. • Determine the relationship between pressure and volume of the gas. • Describe the relationship between gas pressure and volume in a mathematical equation. • Use the results to predict the pressure at other volumes. LEVEL Chemistry Copyright © 2015 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. i Boyle’s Law – Chemistry TEACHER PAGES NEXT GENERATION ASSESSMENTS SCIENCE STANDARDS • AP Style Question: Gas Laws • Topic Assessment: States of Matter REFERENCES ANALYZING AND USING MATHEMATICS DEVELOPING AND INTERPRETING DATA USING MODELS Adapted from “Experiment 6: Boyles Law, Pressure- Volume Relationship in Gases.” Chemistry with Vernier, Vernier Software & Technology, 2008. Used with permission. ENERGY AND MATTER SCALE, PROPORTION, CAUSE AND EFFECT AND QUANTITY PS2: FORCES AND INTERACTION CONNECTIONS TO AP APAP CHEMISTRYCHEMISTRY 2 2.A.2 The gaseous state can be effectively modeled with a mathematical equation relating various macroscopic properties. A gas has neither a definite volume nor a definite shape; because the effects of attractive forces are minimal, we usually assume that the particles move independently. *Advanced Placement® and AP® are registered trademarks of the College Entrance Examination Board. The College Board was not involved in the production of this product. Copyright © 2015 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. ii Boyle’s Law – Chemistry TEACHER PAGES COMMON CORE STATE STANDARDS (LITERACY) RST.9-10.3 (MATH) HSF-LE.A.2 Follow precisely a multistep procedure when Construct linear and exponential functions, including carrying out experiments, taking measurements, or arithmetic and geometric sequences, given a graph, a performing technical tasks, attending to special cases description of a relationship, or two input-output pairs or exceptions defined in the text. (include reading these from a table). (LITERACY) RST.9-10.7 (MATH) HSF-LE.B.5 Translate quantitative or technical information Interpret the parameters in a linear or exponential expressed in words in a text into visual form (e.g., a function in terms of a context. table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into (MATH) HSS-ID.B.6A words. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (LITERACY) WHST.9-10.1 Fit a function to the data; use functions fitted to data Write arguments focused on discipline specific to solve problems in the context of the data. Use content. given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential (MATH) HSN-Q.A.2 models. Define appropriate quantities for the purpose of descriptive modeling. (MATH) HSS-ID.B.6C Represent data on two quantitative variables on a (MATH) HSA-CED.A.2 scatter plot, and describe how the variables are related. Create equations in two or more variables to represent Fit a linear function for a scatter plot that suggests a relationships between quantities; graph equations on linear association. coordinate axes with labels and scales. (MATH) HSS-ID.C.8 (MATH) HSA-CED.A.4 Compute (using technology) and interpret the Rearrange formulas to highlight a quantity of interest, correlation coefficient of a linear fit. using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. Copyright © 2015 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. iii Boyle’s Law – Chemistry TEACHER PAGES TEACHING SUGGESTIONS his activity provides a quick and simple LABQUEST KEYSTROKES way for students to develop and explore the 1. To start the experimental setup: relationship between gas pressure and volume, T a. Connect the gas pressure sensor to your data otherwise known as Boyle’s law. The use of a data collection device. collection device simplifies the data gathering process and allows students to focus on the development b. Adjust the volume of the syringe to 20 mL and understanding of the mathematical model that before connecting to the sensor. underlies this relationship. c. Choose “New” from the “File” menu. Boyle’s law describes that for a fixed quantity of gas 2. To set up the data-collection mode: the pressure and volume are inversely proportional. a. On the “Meter” screen, select “Mode.” While students may be familiar with linear graphs that Change the mode to “Events with Entry.” show a positive sloping, direct linear relationship, the negatively sloping curve generated by this inverse b. Enter the Name (“Volume”) and Units function and the subsequent manipulation required to (“mL”). Select “OK.” linearilize it may be new. Because the data collection 3. To collect data pairs. is so quick, you should spend time focusing on the development and utilization of the mathematical a. Move the piston so the front edge of the model so eloquently established by this real-wold data. inside black ring (Figure 2) is positioned at the specified line on the syringe. Hold the If your students need a refresher on the types of piston firmly in this position until the pressure relationships and their corresponding graphs, see the value displayed on the screen stabilizes. Middle Grades lesson, “Happiness is a Straight Line,” for discussion points and examples. b. Tap “Keep” and enter the gas volume (in mL) on the screen. Remember, to add 0.8 mL to the volume of the syringe for the total volume to account for the small volume of trapped air in the connection port. Select “OK” to store this pressure-volume data pair. c. Continue this procedure using each syringe volumes remembering to add the 0.8 mL to each volume before entering. d. Stop data collection by tapping the red square. Copyright © 2015 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. iv Boyle’s Law – Chemistry TEACHER PAGES TEACHING SUGGESTIONS (CONTINUED) 4. To test different curve fits to the data: 6. To calculate regression statistics and to plot a best fit regression line on the graph: a. Choose “Curve Fit” from the “Analyze” menu. a. Choose “Graph Options” from the “Graph” menu. b. Test the direct hypothesis with “Linear Regression” where x is the volume and y is b. Select “Autoscale from 0”, and select “OK.” the pressure. c. Choose “Curve Fit” from the “Analyze” c. Test the inverse hypothesis with “Power as menu. the Fit Equation.” [this should provide the d. Select “Linear” as the Fit Equation. The better fit]. linear-regression statistics for these two data 5. To linearize the data by graphing pressure vs. columns are displayed in the form reciprocal volume: y = mx + b a. Tap the “Table” tab to display the data table. where b. Choose “New Calculated Column” from the x = 1/volume “Table” menu. y = pressure c. Enter the Name (“1/Volume”) and Units m = a proportionality constant (“1/mL”). Select the equation, “A/X”. Use b = y-intercept “Volume” as the column for X, and “1” as the value for A. e. Select “OK.” d. Select “OK.” Because the relationship between pressure and volume is an inverse relationship, the graph of pressure vs. 1/ volume should be direct; that is, the curve should be linear and pass through (or near) the origin. The slope of the line is equal to the proportionality constant k as established by Boyle’s law, PV = k. Copyright © 2015 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. v Boyle’s Law – Science ANSWER KEY DATA AND CALCULATIONS Table 1. Volume vs. Pressure Constant, k Volume (mL) Pressure (kPa) (P/V)(P × V) 5.8 175.9 30.3 1020 7.8 131.4 16.8 1025 9.8 105.1 10.7 1030 11.8 87.0 7.37 1027 13.8 74.4 5.39 1027 15.8 65.1 4.12 1029 17.8 57.6 3.24 1025 19.8 52.0 2.63 1030 Copyright © 2015 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. vi Boyle’s Law – Science ANSWER KEY PROCESSING THE DATA 1. If the volume is doubled from 5.0 mL to 10.0 mL, 7. What experimental factors are assumed to be what does your data show happens to the constant in this experiment? pressure? Show the pressure values in your The number of gas particles (n) and the answer. temperature (T) remain constant in this If the volume is doubled, the pressure decreases experiment. by approximately half. 8. One way to determine if a relationship is inverse 2. If the volume is halved from 20.0 mL to 10.0 or direct is to find a proportionality constant, k, mL, what does your data show happens to the from the data. If this relationship is direct, pressure? Show the pressure values in your k = P/V; if it is inverse, k = P × V. answer. Based on your answer to Question 4, calculate If the volume is halved, the pressure doubles. k for the seven ordered pairs in your data table (divide and multiply the P and V values).