Laboratory Experiment pubs.acs.org/jchemeduc
A Discovery Chemistry Experiment on Buffers Suzanne E. Kulevich,* Richard S. Herrick, and Kenneth V. Mills Department of Chemistry, College of the Holy Cross, Worcester, Massachusetts 01610, United States S Supporting Information *
ABSTRACT: The Holy Cross Chemistry Department has designed and implemented an experiment on buffers as part of our Discovery Chemistry curriculum. The pedagogical philosophy of Discovery Chemistry is to make the laboratory the focal point of learning for students in their first two years of undergraduate instruction. We first pose questions in prelaboratory sessions that serve as the focus for discussion and that guide inquiry in the lab. We then use the experimental results to guide the lecture-hall discussion and discovery of chemical principles. In this experiment, students first discover the Henderson−Hasselbalch equation using pooled student data for three buffers. Students also discover the qualitative effects of buffers by examining the influence of the addition of a strong acid, a strong base, or water on the pH of a buffered solution versus that of nonbuffered solutions. Using their pooled results and knowledge of titration curves discovered in the previous lab, students gain a qualitative and quantitative understanding of buffers and report increased confidence in making buffered solutions. KEYWORDS: First-Year Undergraduate/General, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Inquiry-Based/Discovery Learning, Acids/Bases, pH
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There are many reports of laboratory and classroom exercises that focus on various aspects of buffers. Topics covered include buffer capacity,15−18 buffer preparation,19,20 the Henderson− Hasselbalch equation and it is appropriateness for use,19,21−26 analogies to promote understanding,27 classroom demonstrations of buffers,28−30 and the use of biological buffers.31 One report describes an experiential lab in which students prepare various acetate buffer solutions and study the effect of dilution or addition of strong acids or bases.32 Although components of that exercise resemble our experiment described below, we extend the analysis to multiple buffer systems covering a large pH range, incorporate the methods of data-pooling and graphical analysis that are central tenets of our Discovery pedagogy, and assess student learning. In addition, we find that employing both acidic and basic buffer systems is crucial in demonstrating the generality of the discovery, that comparing raw data and transformed plots is important to developing students’ analytical skills, and that incorporating discussions of a prior experiment on titration curves provides a comprehensive learning experience for the student. We also find that approaching the problem of buffers as a guided-inquiry exercise increases student engagement with the material and is a more modern pedagogical take on time-tested experiments. We report a laboratory-based guided-inquiry experiment that introduces students to many aspects of buffers. The experiment builds on student understanding of chemical equilibria, acid− base chemistry, and titration curves. Concepts that are explored in the experiment include (1) preparing buffers, (2) buffer range, (3) buffer capacity, (4) buffer chemistry, and (5) the law of mass action. Processes utilized include (1) data pooling, (2)
he Holy Cross Chemistry Department has developed a laboratory-based guided-inquiry curriculum for our foursemester general and organic chemistry sequence that we call Discovery Chemistry, as described in this Journal.1−6 We have recently reported on density, reaction kinetics, and electrochemistry7−9 experiments along with several organic experiments.10−13 A key aspect of Discovery Chemistry is the pooling of student data, which creates a large data set to facilitate the use of graphical analysis. This analysis is the basis for detailed in-class discussion and introduces students to chemistry in a way that emphasizes the centrality of experimentation and the inquiry-based nature of science. Successful discovery experiments work best when complex topics are explored that span multiple concepts, processes, and techniques, leading to a rich postlaboratory discussion experience. Buffers are a crucial concept in the curriculum for general chemistry, analytical chemistry, and biochemistry. The molecular explanation for buffered systems, as well as their calculations and manipulations, are often a particularly difficult topic for students because the understanding of buffers has multiple levels of complexity.14 Mastering buffers requires a strong understanding of fundamental acid−base chemistry and chemical equilibrium, the ability to identify information required to solve a quantitative problem, and the skill to apply algebraic methods to compute an answer. In addition, students often report a disconnect between practical and theoretical understandings of the concept.14 A thorough understanding of the derivation, utility, and limitations of the Henderson−Hasselbalch equation, as discovered in this experiment, helps to tie together the qualitative and quantitative aspects of buffers. © 2014 American Chemical Society and Division of Chemical Education, Inc.
Published: July 14, 2014 1207
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First, students obtain separate 0.5 M solutions of their acid and conjugate base. They prepare mixtures of their acid and conjugate base, using volumetric glassware, in volume ratios of 1:1, 5:1, 10:1, 1:5, and 1:10. We believe it is good practice for students to use volumetric glassware to make dilutions, an important skill with which novice chemists often struggle. However, we do not have the students make the initial solutions, both to improve data quality and to avoid having students handle concentrated acids and bases in an introductory lab setting. They calibrate a Fisher Scientific Accumet Research AR10 pH meter and record the pH of each solution. This is a standard laboratory pH meter, and less expensive models would likely be a good substitute. Students are directed to use their data to plot pH as a function of molar ratio (Supporting Information Figure S2) and observe that there is not a linear relationship. During in-lab conversations, they are directed to consider a plot of pH as a function of the base-10 log of the ratio (Figure 1), which results
graphing, (3) applying equations derived from theory to experimental data, and (4) connecting data analysis with fundamental molecular understanding of buffers. This multipronged approach is applied to three buffer systems: acetic acid/acetate, TrisHCl/Tris, and ammonium/ammonia. Students observe and graph the properties of their assigned buffer system, learn from pooled data how buffer systems with different pKa values behave, and practice careful calculations derived from acid−base equilibria. This path of learning leads from simple observations to a comprehensive understanding of buffers and their uses. The prelaboratory discussion and experimental work is completed in a 4 h laboratory period.
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PRE-LABORATORY DISCUSSION Before beginning this Discovery Chemistry exercise, students have studied acids and bases including strong acids and bases and weak acid−base equilibria. In the previous week’s experiment, pairs of students generated titration curves for mono-, di-, or triprotic acids.33 These data serve as the focus for subsequent lecture discussion, and representative curves are shown as Supporting Information Figure S1. From this exercise students discover the general shape of the titration curve and note changes due to the strength of the acid. They learn the meaning of pKa and how to interpolate the pKa from the titration curve of a weak acid and, thus, estimate the relative strength of the acid. They also observe that the pH does not change significantly on addition of strong base until close to the equivalence point. In the prelaboratory discussion for the buffer experiment, students are shown their acetic acid titration curve from the previous week. We return to an observation about weak acid titration curves that was not fully answered: Why does the pH change so little in the intermediate region of the titration curve (i.e., from about 10% to 90% of the titration of each weak acid proton)? We then set the discovery questions, based on observations from the preceding week: What is the nature of the acid−base equilibrium in the buffering region, and can we find a graphical way to more easily estimate the pKa and strength of an acid? For the first question, students speculate why the system is resistant to pH change in the buffering region and if this might be different than the reason that pH changes little after the final equivalence point is reached. We also ask students what they might expect to observe when we add a strong acid or base to water or to a buffered system or when we significantly dilute a solution of acid, base, or a stoichiometric mixture. The ideas from the students are listed on the board, recorded by the professor, and used as the basis to begin the postlaboratory discussions. This sets the stage for experimental discovery, to be followed by both graphical analysis, and an examination of the relevant acid−base equilibrium reactions that describe buffered systems.
Figure 1. Data from pairs of students showing best-fit line using linearleast-squares regression for ammonium/ammonia (seven pairs of students), TrisHCl/Tris (seven pairs of students), or acetic acid/ acetate (six pairs of students). With standard error from the regression analysis the equations of the lines are y = (0.96 ± 0.02)x + (9.17 ± 0.01), y = (0.99 ± 0.03)x + (8.16 ± 0.02), and y = (1.04 ± 0.01)x + (4.76 ± 0.01), respectively. Students prepare mixtures of 0.5 M acid and 0.5 M conjugate base solutions using volumetric glassware and measure the pH of the resulting solutions.
in a linear relationship with a slope equal to one. This allows for derivation of the Henderson−Hasselbalch equation in class, both by graphical analysis and by derivation of the equation from the Ka expression. In-class lectures use this equation to help students learn how to prepare buffers and how to evaluate the relative population of acid and conjugate base using these three acids as examples. (Instructors also discuss the limitations of the Henderson−Hasselbalch equation in lecture, drawing on examples from the titration curve analysis from the previous lab where the small x approximation is not valid.) In the second part of the experiment, students add concentrated HCl or NaOH to water and to a 1:1 molar mixture of their acid/conjugate base pair (Figure 2). They record the initial and final pH of each solution. They plot the data as instructed, creating separate lines for the water and buffer solutions. If instructors have time, they might consider testing different ratios of acid/conjugate base pairs to help discover the concept of buffer capacity.
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EXPERIMENTAL WORK Students work in small groups and are assigned one of three systems: acetic acid/acetate, TrisHCl/Tris, or ammonium/ ammonia. These are chosen so that students can learn the generality of their observations and be able to rank the strength of the acids. The discussion in the manual is intentionally vague, and the provided details are only enough to allow students to safely perform the experiment. This allows for the student and instructor to interact and discover the concepts together, both in the lab and in pre- and postlab discussions. 1208
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We conducted an assessment quiz before the initial prelab discussion and before the prelab discussion the following week.34 The questions and student responses are reported in Table 1. Table 1. Student Assessment Data from a Before and After Survey, 2013 Answersa
Question 1. On 10-fold dilution of a strong acid, the pH will:
2. On 10-fold dilution of a buffered solution, the pH will:
Figure 2. Data from seven pairs of students showing the addition of concentrated HCl or NaOH to a stoichiometric mixture of ammonium/ammonia or to distilled water. Lines are added to guide the eye. The initial pH of water is reported as 7 for all student pairs. Representative data for the other two systems are given as Supporting Information Figure S3. Students make two separate 20 mL solutions by combining 10 mL of 0.5 M acid and 10 mL of 0.5 M conjugate base. They measure the pH of each solution, then add 10 mL of 0.1 M HCl to one solution and 10 mL of 0.1 M NaOH to the other, mix, and measure the pH again. They also add 10 mL of 0.1 M HCl to 20 mL of water in one beaker and 10 mL of 0.1 M NaOH to 20 mL of water in another beaker and measure the pH of each.
3. If one adds a small amount of strong base to a buffered solution, the pH will:
4. To have a solution that is considered a buffer, one must have
In the third part of lab, students perform 10- and 100-fold serial dilutions of their solutions of acid, conjugate base, or the stoichiometric mixture. We find that students often struggle with dilutions both conceptually and in the lab and can benefit from a review of this useful laboratory technique. Students measure the pH of each initial solution and after each of the dilutions and graph their data as in Figure 3.
5. The pH of a buffer solution
6. How confident are you that you could create a buffer?
Prelabb,c
Postlabc
Increase
43%
84%
Decrease Stay about the same Increase
54% 3% 10%
11% 5% 4%
Decrease Stay about the same Increase slightly
11% 79%
10% 87%
73%
82%
5%
4%
16% 6%
16% 0%
43%
71%
30%
19%
27%
11%
9%
1%
7%
8%
Increase by a large amount Decrease slightly Decrease by a large amount A weak acid/conjugate base pair A strong acid/conjugate base pair A mixture of a strong acid and strong base Is always equal to pH 7 Depends on the pKa of the acid Depends on the ratio of base to acid Both b. and c. Not very confident
11%
14%
72% 61%
77% 4%
Somewhat confident Confident Very confident
31% 7% 1%
40% 45% 11%
a
Correct answer in bold. bMost popular answer in bold italics for preand postlab surveys. cNumbers might not equal 100% due to rounding. 140−143 respondents per question.
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HAZARDS Acetic acid (CAS # 64-19-7) is corrosive and flammable; sodium acetate (CAS # 127-09-3), ammonium chloride (CAS # 12135-02-9), Tris (CAS # 77-86-1), and Tris−HCl (CAS # 1185-53-1) are irritants; aqueous ammonia (CAS # 7664-41-7) is toxic, corrosive, and a lachrymator; aqueous HCl (CAS # 76447-01-0) is corrosive and toxic. Sodium hydroxide (CAS # 1310-73-2) is corrosive, causes skin burns, and is harmful or fatal if swallowed or inhaled. Safety glasses and gloves must be worn.
Figure 3. Data from seven pairs of students showing the influence of dilution on a solution of ammonia, ammonium, or a stoichiometric mixture. Students are instructed to connect their single measurements to guide the eye; the lines above connect a point of the average value for each measurement. Representative data for the other two systems are given as Supporting Information Figure S4. Students add 10 mL of 0.5 M acid to 10 mL of 0.5 M conjugate base and mix. They pipet 5 mL of this solution into a 50 mL volumetric flask and bring to volume with water. They transfer this solution to a beaker and repeat the 10fold dilution. The same two dilutions are performed with the 0.5 M acid and 0.5 M conjugate base solutions, and the pH of each solution is measured with the pH meter.
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POSTLAB DISCUSSION (INTERPRETATION OF RESULTS) This experiment is well received by students, mostly likely due to its experiential learning element.35 Students discover the Henderson−Hasselbalch equation by making and testing buffer solutions of various component ratios rather than simply 1209
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empirically. They see that the linear relationship obtained is based on the Henderson−Hasselbalch equation, and they discover how to use the equation to answer questions about buffers. We also direct discussions using balanced chemical equations that require students to reflect on the relationship between Le Chatelier’s principle, the common ion effect, and buffered systems. These concepts are subsequently reinforced the following week during a lab that utilizes solubility and complex-ion formation equilibria. The concepts and their applications are also reinforced with follow-up problem sets and exam questions that focus on the analysis of lab data, the use of the chemical concepts to perform practical calculations relating to pH prediction and buffer preparation, and more in-depth thought questions that require students to apply what they have learned in the lab and lecture to new and more complex problems on their own.
memorizing an equation. By plotting their results, they observe mathematical trends and see linear relationships. They discover that buffer solutions resist pH change when diluted or treated with strong acid or base while working with modern digital pH meters. Via this concrete, hands-on experience, students observe that although buffered systems change pH with manipulation, they resist large changes in pH. Subsequent lectures begin with reflective observation and remind students of the qualitative aspects of buffers. These ideas are reinforced by examination of the pooled data and graphs for the three buffer systems. As part of learning how to manipulate equations, the discussion returns to the weak acid titration curves from the previous week’s experiment. During that titration experiment, students were told that the pKa can be estimated by the pH at the half-equivalence point for conditions under which the small x approximation is valid and interpolated from their curve to estimate the pKa and the relative strength of the acid. This week, using the plot that allows them to discover the Henderson−Hasselbalch equation, students learn how to use an equation based on a linear best-fit line to more accurately calculate the pKa. This week’s data also allow students to interpret the shape of their weak acid titration curves in the following four areas. First, using the previous week’s data, students observe that the pH does not vary much in the region near the half-equivalence point. During the discussions that follow the buffers lab, we return to these titration curves and discuss what species were in solution in these regions and why they would or would not make a buffer. We also make reference to our titration curve with HCl and ask students to consider why, although the pH does not change near the half-equivalence point, this solution does not constitute a buffer. As part of this thought exercise, students are asked to write the balanced equations for both the neutralization and resultant equilibrium reactions for strong and weak acids. Second, the combination of the two weeks of laboratories also allows for a graphical appreciation of buffer capacity. We connect our lecture discussion about buffer capacity to the observation of the curvature of the titration curve outside of the buffering range. Students learn why the base to conjugate acid ratios of 1:10 and 10:1 are commonly used as the lower and upper limits for use of the Henderson−Hasselbalch equation. Third, from the dilution experiment, we discuss the balance between the concentration of the buffer and its ability to resist changes in pH. This allows for a segue into methods for preparation of a buffer, noting that students have prepared buffers in both weeks: titrating a weak acid with a strong base in week one when making a titration curve and mixing solutions of acid and conjugate base in week two. Finally, we link the regions of the titration curves that students find most surprising, such as the shallow inflection points for relative strong weak acids or conjugate bases, with the limitations of the assumptions behind the Henderson−Hasselbalch equation. This period of discernment is important in building a foundation that is then used for abstract conceptualization. In this last crucial phase of discussion, students learn how to manipulate chemical equilibria to generate equations that explain the quantitative results obtained in lab. Students are expected to be able to write all of the relevant chemical equations that describe both the neutralization and subsequent equilibrium reactions and connect these symbolic chemical equations to the quantitative relationships they observed
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CONCLUSION Our assessment data suggest that when students prepare and manipulate buffers and make thoughtful use of graphical analysis, their understanding of topics related to acid−base equilibrium and their confidence with preparing buffered systems improve (Table 1). Using three separate systems allows students to make discoveries with their own data and generalize with class data. The lab experience creates both a concrete and a qualitative picture of the concept of a buffer. This reflective discovery allows students to tackle difficult buffer questions (see Supporting Information) and apply their qualitative and quantitative understanding of buffered systems to future courses.
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ASSOCIATED CONTENT
S Supporting Information *
Student lab manual; instructor prep notes, including CAS numbers and hazards; student data sheet; sample postlab follow-up exercises and exam questions; Figures S1−S4. This material is available via the Internet at http://pubs.acs.org.This material is available via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We gratefully acknowledge the assistance of Jane Jennette, Jamie Herrick, Maria Fistik, and Elizabeth Landis. This material is based upon work supported by the National Science Foundation under grants MCB-0950245 and MCB-1244089 (K.V.M.), by a Henry Dreyfus Teacher-Scholar Award (K.V.M.), and by a Petroleum Research Fund grant 51085UR3 (R.S.H.).
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