The Great Gas Plot. Using Balloons and Graphs to Analyze Relationships

Transcription

1 Chemistry The Great Gas Plot Using Balloons and Graphs to Analyze Relationships MATERIALS AND RESOURCES EACH GROUP baking soda balance 8 balloons 8 clamps, balloon funnel, powder graduated cylinder, 1000 ml marker, Sharpie pan, overflow plate, plastic syringe, 60 ml vinegar weigh boats bucket ABOUT THIS LESSON This activity is an essential lesson that delineates the significance of graphs, the importance of relationships, and the underlying conditions of those relationships. This lesson also develops concepts of limiting reactants and yield in chemical reactions. OBJECTIVES Students will: Use balloons to capture the carbon dioxide gas produced in a chemical reaction and measure their volume using water displacement Graph the data collected and determine equations for lines of best fit Analyze the graph to make inferences and draw conclusions about the conditions of a relationship between two quantities T E A C H E R P A G E S LEVEL Chemistry i

2 NEXT GENERATION SCIENCE STANDARDS CONNECTIONS TO AP* AP CHEMISTRY 2 PLANNING/CARRYING OUT INVESTIGATIONS PATTERNS ANALYZING AND INTERPRETING DATA CAUSE AND EFFECT 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. PS1: MATTER ACKNOWLEDGEMENTS Sharpie is a registered trademark of Sanford L.P., A Newell Rubbermaid Company. AP CHEMISTRY 3 A.2 Quantitative information can be derived from stoichiometric calculations that utilize the mole ratios from the balanced chemical equations. The role of stoichiometry in real-world applications is important to note, so that it does not seem to be simply an exercise done only by chemists. T E A C H E R P A G E S C.1 Production of heat or light, formation of a gas, and formation of a precipitate and/or a color change are possible evidences that a chemical change has occurred. C.2 Net changes in energy for a chemical reaction can be endothermic or exothermic. *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. ii

3 COMMON CORE STATE STANDARDS (LITERACY) RST Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text. (LITERACY) RST Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words. (MATH) S-ID.6C Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a linear function for a scatter plot that suggests a linear association. (MATH) S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. ASSESSMENTS (LITERACY) W.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (MATH) A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (MATH) F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. (MATH) F-LE.5 Interpret expressions for functions in terms of the situation they model. Interpret the parameters in a linear or exponential function in terms of a context. (MATH) N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. The following types of formative assessments are embedded in this lesson: Assessment of prior knowledge Guided questions during the activity Design of experiment and data collection The following additional assessments are located on our website: Chemistry Assessment: States of Matter Chemistry Assessment: Reactions 2011 Chemistry Posttest, Free Response Question Chemistry Posttest, Free Response Question 1 and Question Chemistry Posttest, Free Response Question Chemistry Posttest, Free Response Question 3 T E A C H E R P A G E S iii

4 TEACHING SUGGESTIONS In this activity, students generate gas inside balloons via a chemical reaction to collect and graph data that allows relationships between quantities of reactants and products to be explored. This activity uses chemistry concepts to highlight the big picture in science, understanding and exploring relationships. Although the chemical reaction used is common and familiar to students, the method for capturing the gas produced is visually engaging and allows for immediate qualitative analysis and comparison during the investigative process. The accuracy of the data collected is dependent on students ability to completely capture and effectively measure the volume of carbon dioxide gas generated in eight different reactions using different quantities of baking soda and a fixed quantity of vinegar. Significant student error can be introduced during both gas collection and volume measurement by water displacement, so careful attention must be paid to each process. Students may need assistance performing the techniques described in the Procedure. You may choose to demonstrate this process or have students practice at their stations using distilled water and an extra, expendable balloon. Additionally, you might advise students to start with the 4.0-g baking soda balloon and work down to the 0.5-g balloon. This allows for students to refine their technique before experimenting with the smallest quantities of baking soda, where student error such as spills or gas leaks have the greatest impact on results. In discussing the lab design, you should ask leading questions that enable students to understand procedures, collect the data, construct the graph, and thoroughly analyze the graph for relationships and the significance of the change in relationships. Some examples of leading questions include: How will you measure the volume of the gas produced? Why is it important to capture all the gas and not allow some to escape into the environment? What happened to the amount of baking soda and the amount of vinegar in each of the trials? What does a linear relationship tell you about the amount of gas and the corresponding amount of baking soda? If you triple the amount of baking soda, will that result in three times as much carbon dioxide? Why or why not? What does a horizontal line tell you about the relationship between the two variables? How does the chemical equation help us to explain why the shape of the graph changed from a line with a positive slope to one that is horizontal? Analysis Question 6 prompts students to compare the sequence of balloons sketched in Question 1 with their graphical representation from Question 3. The picture and graph in Figure A and Figure B are examples of what students may produce for such a comparison. Some students are likely to create a sequence in which balloons are put in a line in order of increasing volume. The exact representation is less important than practicing the skills of looking for patterns and organizing data. Both the arrangement, or resulting sketch, and the graph generated show that up to a point, increasing the amount of baking soda increases the amount of CO 2 produced. The sketch provides information about how the data was collected by using illustrations of the balloons, whereas the graph allows for quantitative analysis that cannot be accurately done with the sketch. T E A C H E R P A G E S iv

5 TEACHING SUGGESTIONS (CONTINUED) Figure A. Sequence of balloons T E A C H E R P A G E S Figure B. Volume of gas vs. mass of baking soda v

6 TEACHING SUGGESTIONS (CONTINUED) Students explaining why the direct proportionality shifts to show no relationship after a certain mass of baking soda will arrive at the concept of limiting reactants. At small-enough masses of baking soda, the reaction proceeds until the baking soda has completely reacted, limiting the amount of CO 2 produced. At large-enough masses of baking soda, the acetic acid in the vinegar reacts completely and limits the amount of CO 2 despite the presence of more baking soda. The relationship between mass of baking soda and volume of carbon dioxide produced is conditional, as it remains a direct relationship only so long as there is enough vinegar to react completely. In the Going Further piece, students can extend concepts of stoichiometry and limiting reactants into a computational exploration of the ideal gas law and constant. There is also an option for students to apply stoichiometric skills to design a solution for a problem established by the teacher. The second option requires additional lab time and reinforces the techniques introduced in the original investigation. T E A C H E R P A G E S vi

7 DATA AND OBSERVATIONS Mass of Baking Soda Added (g) Table 1. Measuring Displacement Volume of Vinegar Added (ml) Volume of Water Displaced (ml) ANALYSIS On your lab table, arrange the balloons in a logical sequence that establishes a correlation between the volume of gas produced and the amount of baking soda used. Sketch, label, and create a caption for the relationship depicted by your arrangement in the space provided. See Figure A. A N S W E R K E Y Figure A. Correlation between volume of gas and amount of baking soda Copyright 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at vii

8 ANALYSIS (CONTINUED) 2. In Table 1, label the Volume of Water Displaced column as Volume of CO 2 Produced, as well. State your reasoning for why those two measurements are the same. The balloon captures all of the carbon dioxide evolved by the reaction. The volume of the balloon is equal to the volume of water displaced, thus reflecting the volume of CO 2 produced. 3. Use a graphing program to plot a graph of the volume of carbon dioxide gas produced versus the mass of baking soda. a. Provide axes labels and include units along with the title. b. For any and all regions of the graph that appear to be linear, perform a linear fit on the data using the program s curve-fitting function. Be sure to display and record the equation(s) for the line of best fit in y = mx + b format. See Figure B. 4. Compare your graph to the arrangement you sketched in Question 1. Explain how both representations are useful to the experimenter. Be sure to offer at least one way that each representation provides information the other does not. Both representations show a relationship between the mass of baking soda and the volume of carbon dioxide produced. The graph provides numerical data from which the slope and universal gas constant can be calculated. The horizontal part of the graph, where slope is essentially zero, shows that at some point adding more baking soda does not continue to increase the yield of carbon dioxide. The arrangement of the balloons provides a quick, qualitative analysis of the relationship between the amounts of product in each reaction. It allows the experimenter to physically organize and sort experimental data using the direct method of carbon dioxide capture rather than a secondary measurement, such as the displacement of water. A N S W E R K E Y Figure B. Volume of gas vs. mass of NaHCO 3 Copyright 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at viii

9 CONCLUSION QUESTIONS 1. On your graph, you should notice an obvious change in the relationship that exists between the amount of baking soda added and the volume of gas produced. Cite where this occurs and explain how the relationship changed even though the amount of baking soda was increasing and the amount of vinegar remained constant. Justify your explanation. The volume of gas produced increased with the amount of baking soda for masses less than 2.5 g. The data shows that from 2.5 g to 4.0 g there is not a significant change in the volume of carbon dioxide produced, and the slope is essentially zero. There are two reactants needed to produce carbon dioxide, baking soda and vinegar. As the amount of vinegar is not increasing, this change in the relationship indicates the point at which the active ingredient in vinegar has run out and is limiting the amount of product the reaction can yield. 2. The reaction between vinegar and baking soda caused a change in the temperature of the balloon. Based on your observations, justify whether the reaction is exothermic or endothermic. The reaction is endothermic. This was evident from the decrease in temperature of the solution as the reaction absorbed heat from its surroundings. Reactions that absorb heat are endothermic, as opposed to exothermic reactions which release heat. 3. A student measured the volume of the balloon by displacement without allowing the balloon to return to room temperature. Describe the effect this would have on the volume of the balloon. Justify your answer. This prompt is designed to make students think about the scale of the factors involved in this error. Gas laws indicate that when moles and pressure are held constant, as they are in this investigation, the volume of the gas is directly proportional to the temperature. By this law, a cooler sample of gas would result in a smaller volume, displacing less water than would a room temperature sample. However, it is worth noting that gas calculations are always done with temperature on the Kelvin scale. For example, the difference between 395 K and 398 K will not make a significant difference to the volume of gas in the balloon. Additionally, the latex of the balloon absorbs a marginal amount of heat when it relaxes, or is less stretched. However, this amount of energy will have a negligible impact on the temperature and volume of the gas. A N S W E R K E Y Copyright 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at ix

10 GOING FURTHER PART I: PROBLEM-SOLVING CHALLENGE The balanced equation for the reaction that took place in the balloon is HC 2 H 3 O 2 + NaHCO 3 NaC 2 H 3 O 2 + H 2 O + CO 2 3. Plot a graph of liters of CO 2 versus moles of CO 2. Using the ideal gas law, PV = nrt 1. Calculate the number of moles of each reactant placed into each balloon given that the average molarity of household vinegar is 0.82 M. See Table A. Mass (g) Table A. Reactants Added Baking Soda Moles (mol) Volume (ml) Vinegar Moles (mol) For each balloon, use stoichiometry to calculate the moles of carbon dioxide gas produced. See Table B. Table B. Carbon Dioxide Produced Baking Soda (mol) Vinegar (mol) Carbon Dioxide (mol) arrive at an average experimental value of the ideal gas constant, R, through graphical analysis. Show any relevant calculations and cite the sources for data pertaining to variables not collected in the lab. The ideal gas law can be rewritten as RT V = n æ ö ç çè P ø Students will need a barometric pressure and a room temperature. For the purposes of this calculation, 1.0 atm and 298 K are assumed. Latm R = mol K æ1.0 atmö R = L/mol ç çè 298 K ø 298 K R æ ç ö = L/mol çè1.0 atmø RT L/mol P = A N S W E R K E Y Copyright 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at x

11 GOING FURTHER (CONTINUED) Table C. Carbon Dioxide Produced Volume Produced (L) Moles Produced (mol) A N S W E R K E Y Figure C. Liters vs. moles of CO 2 Copyright 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at xi

12 Chemistry The Great Chemistry Gas Plot The Great Gas Plot Using Balloons and Graphs to Analyze Relationships MATERIALS baking soda balance 8 balloons 8 clamps, balloon funnel, powder graduated cylinder, 1000 ml marker, Sharpie pan, overflow plate, plastic syringe, 60 ml vinegar weigh boats bucket Data collected in scientific investigations is often graphed and analyzed to establish meaningful relationships between variables such that explanations can be constructed and predictions made. In all science, understanding the effect of material quantities on various outcomes is essential, such as seen in the following scenarios. A chemist or chemical engineer optimizes a process to synthesize durable substances from less expensive, readily available materials. A biologist investigates the effects of nutrient availability on the life cycle or growth potential of an organism. A geologist studies how ph levels in rainfall affects the weathering of exposed rock, which can be linked back to certain automobile emissions. An environmentalist evaluates the impact of leakage from a previously capped oil well on the biodiversity and health of plants in the area. A physicist explores mechanisms for storing solar or geothermal energy through processes involving phase changes or other reversible reactions. In this experiment, you will be exploring the specific relationships between quantities of reactants and products involved in the chemical reaction between vinegar and baking soda. A successful outcome in this experiment is dependent on replicable data collection and your ability to construct and analyze a graph. Clear thought processes and well-written responses contribute to your success in this task. PURPOSE In each trial of this experiment, you will use balloons to capture the gas generated by the reaction. A graph of the volume of gas produced versus the amount of baking soda reacted will be plotted and analyzed to make inferences and draw conclusions about conditions that affect the relationship between these two quantities. 1

13 SAFETY ALERT!» Goggles are required throughout this activity.» If the vinegar is splashed on exposed skin, flush with water and notify your teacher.» Wash your hands at the end of this activity. PROCEDURE To ensure as much air is removed from the balloon as is possible, carefully point the syringe downward and pull up on the plunger. If there is any air left in the balloon, bubbles should rise through the vinegar loaded in the syringe. 1. Label eight balloons with a quantity of baking soda, NaHCO 3, in 0.5-g increments, starting with 0.5 g and continuing until the last balloon is labeled with 4.0 g. 2. Using an electronic balance, measure out the required quantity of baking soda corresponding to each balloon. 3. Carefully transfer the baking soda into the appropriately labeled balloon using a funnel. Repeat this process until you have placed the appropriate quantity of baking soda in each of the labeled balloons. 4. Add water to the large container until it is mostly full. Carefully place the container filled with water inside the overflow pan. Slowly fill the remainder of the container with water. Take care not to spill any water into the overflow pan. 5. Obtain a sample of vinegar and load it into the syringe. To do so, completely compress the plunger on the syringe, place the tip of the syringe below the surface of the vinegar, and then pull up on the plunger until the syringe contains more than 30 ml of vinegar. Carefully push the plunger in until the syringe contains exactly 30 ml of vinegar. 6. Select one of the labeled balloons and stretch the neck of the balloon over the lower barrel of the syringe. Before releasing the balloon, squeeze as much air as possible out of the balloon. Make sure the balloon is secured tightly around the barrel of the syringe. 7. Push the plunger down and deliver all 30 ml of vinegar into the balloon. Take care to not push any of the air out of the syringe only depress the plunger enough to deliver all of the vinegar into the balloon. 2

14 PROCEDURE (CONTINUED) 8. Working with a partner, carefully twist the balloon, restricting its neck as close to the syringe as possible. Snap the balloon clip closed around the neck, trapping the gas in the balloon. For added insurance against a leak, tie a knot in the neck of the balloon. 9. Shake the balloon and allow the vinegar and baking soda to react. Continue shaking until the balloon returns to room temperature. 10. Place the balloon in the container filled with water and carefully press down with a flat object until the balloon is completely submerged and the flat object is sitting firmly against the top of the container. 11. Carefully remove the balloon and the container from the overflow pan. Measure the amount of water that overflowed into the pan and record this value in your data table. 12. Pour the water from the overflow pan back into the container, and then place the container back inside the overflow pan. The water should completely refill the container unless some was spilled. 13. Repeat Step 4 through Step 12 until you have measured the volume of water displaced by all eight balloons. 3

15 DATA AND OBSERVATIONS Mass of Baking Soda Added (g) Table 1. Measuring Displacement Volume of Vinegar Added (ml) Volume of Water Displaced (ml) ANALYSIS 1. On your lab table, arrange the balloons in a logical sequence that establishes a correlation between the volume of gas produced and the amount of baking soda used. Sketch, label, and create a caption for the relationship depicted by your arrangement in the space provided. 4

16 ANALYSIS (CONTINUED) 2. In Table 1, label the Volume of Water Displaced column as Volume of CO 2 Produced, as well. State your reasoning for why those two measurements are the same. 3. Use a graphing program to plot a graph of the volume of carbon dioxide gas produced versus the mass of baking soda. a. Provide axes labels and include units along with the title. b. For any and all regions of the graph that appear to be linear, perform a linear fit on the data using the program s curve-fitting function. Be sure to display and record the equation(s) for the line of best fit in y = mx + b format. 4. Compare your graph to the arrangement you sketched in Question 1. Explain how both representations are useful to the experimenter. Be sure to offer at least one way that each representation provides information the other does not. 5

17 CONCLUSION QUESTIONS 1. On your graph, you should notice an obvious change in the relationship that exists between the amount of baking soda added and the volume of gas produced. Cite where this occurs and explain how the relationship changed even though the amount of baking soda was increasing and the amount of vinegar remained constant. Justify your explanation. 2. The reaction between vinegar and baking soda caused a change in the temperature of the balloon. Based on your observations, justify whether the reaction is exothermic or endothermic. 3. A student measured the volume of the balloon by displacement without allowing the balloon to return to room temperature. Describe the effect this would have on the volume of the balloon. Justify your answer. 6

18 GOING FURTHER PART I: PROBLEM-SOLVING CHALLENGE The balanced equation for the reaction that took place in the balloon is HC 2 H 3 O 2 + NaHCO 3 NaC 2 H 3 O 2 + H 2 O + CO 2 1. Calculate the number of moles of each reactant placed into each balloon given that the average molarity of household vinegar is 0.82 M. 2. For each balloon, use stoichiometry to calculate the moles of carbon dioxide gas produced. 7

19 GOING FURTHER (CONTINUED) 3. Plot a graph of liters of CO 2 versus moles of CO 2. Using the ideal gas law, PV = nrt Rearranging the ideal gas law into y = mx + b format may prove useful. arrive at an average experimental value of the ideal gas constant, R, through graphical analysis. Show any relevant calculations and cite the sources for data pertaining to variables not collected in the lab. PART II: ENGINEERING CHALLENGE Your teacher will provide you with a circular object of a given size. In the same manner as this activity, your challenge is to fill a balloon that has the exact volume to perfectly fit within this object. You can use your experience with this activity, the data collected, and the graph produced along with useful calculations and analysis of the activity. You are expected to determine the necessary amounts of reactants, explain your procedures and process, and calculate the exact volume of your balloon before reacting and testing its exact fit through the given object. 8