How Is the Freezing Point of a Binary Mixture of Liquids Related to the

Laboratory Experiment pubs.acs.org/jchemeduc

How Is the Freezing Point of a Binary Mixture of Liquids Related to the Composition? A Guided Inquiry Experiment Sally S. Hunnicutt* Department of Chemistry, Virginia Commonwealth University, Richmond, Virginia 23284-2006, United States

Alexander Grushow Department of Chemistry, Rider University, Lawrenceville, New Jersey 08648-3099, United States

Rob Whitnell Department of Chemistry, Guilford College, Greensboro, North Carolina 27410-4108, United States S Supporting Information *

ABSTRACT: The principles of process oriented guided inquiry learning (POGIL) are applied to a binary solid−liquid mixtures experiment. Over the course of two learning cycles, students predict, measure, and model the phase diagram of a mixture of fatty acids. The enthalpy of fusion of each fatty acid is determined from the results. This guided inquiry experiment, which was developed as part of the POGIL-PCL (Physical Chemistry Laboratory) Project and tested at multiple institutions, relies on “green” materials and can be carried out by students using simple or sophisticated apparatus. KEYWORDS: Upper-Division Undergraduate, Physical Chemistry, Inquiry-Based/Discovery Learning, Phases/Phase Transitions/Diagrams, Solutions/Solvents, Laboratory Instruction

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BACKGROUND The physical chemistry laboratory course often includes an experiment in which cooling curves for a solid mixture are used to generate a solid−liquid phase diagram. The data are then manipulated by students to find the enthalpy of fusion of both solids in the mixture. In this paper we describe a guided inquiry variation of this experiment that is also “green”. The experiment was developed as a part of the POGIL-PCL (process oriented guided inquiry learning-physical chemistry laboratory) Project.1 POGIL-PCL experiments2 require students to work in teams to collect data, which is subsequently pooled and analyzed. Students make predictions regarding the experimental outcomes and compare their data and results to their predictions. Mathematical models are introduced after students make some preliminary measurements in order to explain and further understand their subsequent refined measurements and results. Numerous solid−liquid phase diagram experiments have been published.3,4 Some of the earliest experiments focus on the lead−tin diagram,5 while more recently published experiments use organic mixtures for the phase diagram.6,7 At least 15 different mixtures8 could be formed from six different organic compounds; the mixtures form eutectics in experimentally accessible temperature ranges, and the compounds are reasonably priced, available, and safe. Previous work has emphasized the variety of experimental techniques used to measure cooling or heating curves, including differential scanning calorimetry,9 polarizable microscopy,10 commercial instrumentation,11 and the use of spreadsheets12 to generate the phase diagram. The objective of most of these verification © XXXX American Chemical Society and Division of Chemical Education, Inc.

experiments is to generate the phase diagram and determine the enthalpies of fusion for the two compounds in the mixture as a way to demonstrate the thermodynamics equations associated with solid−liquid mixtures. Two previously described experiments address the potential for forming intermediate compounds formed between the main components of the mixture. Melts of hydroquinone and bis-[N,N-diethyl]-terephthalamide9 form a third compound, giving rise to two eutectics in this mixture, which is used to introduce students to the topics of molecular recognition and self-assembly. Two intermediate compounds form in mixtures11 of phenol and t-butanol, and scientists disagree over the specifics of the formation. The phase diagram experiment involving this mixture is used to give students a more researchlike, open-ended experience. The experiment described in this paper is based on mixtures of aliphatic fatty acids. Such mixtures are “green” as the fatty acids, stearic and lauric acid, are very safe to handle, inexpensive to purchase, and inexpensive to dispose of. Fatty acids were proposed13 for use in the general chemistry laboratory for the determination of the molar mass of an unknown fatty acid based on colligative properties due to the fatty acids’ green profile. Mixtures of fatty acids melt at temperatures below 100 °C and at or just above room temperature. They have a variety of useful applications including soaps and phase change Received: June 16, 2017 Revised: August 23, 2017

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DOI: 10.1021/acs.jchemed.7b00409 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

Laboratory Experiment

materials. Mixtures of fatty acids that differ by four or more carbons14 in their aliphatic chains do not form compounds, but mixtures of fatty acids that differ by two carbons (for example, lauric and myristic acid) do form compounds that melt incongruently. Thus, eutectics and peritectics could both be introduced to students by selecting the correct pair of fatty acids. The experiment described in this paper is the first to use mixtures of fatty acids for a physical chemistry experiment that develops a solid−liquid phase diagram. In addition, the solid− liquid phase diagram experiment with mixtures of fatty acids is particularly well-suited for a guided inquiry experiment. The experiment is highly reproducible, so that a student or pair of students may collect data reliably in one or two lab periods that reveals part of the phase diagram. With part of the diagram constructed, students have the opportunity to predict the appearance of the rest of the diagram. Students from a whole class can then pool their data to build a richer, denser set of data for analysis. Figure 1 diagrams the POGIL-PCL experiment framework.2 The title of the experiment described here is “How Is the

Box 1. Process and Content Objectives Process objectives Students will be able to 1. linearize a relationship; and 2. identify the dependent and independent variables in a linear relation and relate these variables to measurable quantities in the lab; and 3. locate the desired properties from a linearized, graphed relationship using the slope and intercept and the content outcomes are objectives that are specific to solid−liquid mixtures. Content objectives Students will be able to 1. choose experimental parameters that allow determination of the phase diagram of a mixture of solids; and 2. predict the freezing point of a mixture; and 3. connect the freezing points of mixtures of solid A with solid B added as the solute to mixtures of solid B with solid A added as the solute; and 4. define and label the components of a solid−liquid phase diagram, including the eutectic point. of a melt and visually determine the temperature at which the first persistent solid appears.

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HAZARDS Students should wear personal protective equipment when conducting this experiment. Both lauric and stearic acid exhibit minimal reactivity or fire hazard. The solids should not be heated to temperatures well above their melting points. Lauric acid should not be ingested and is a skin irritant, and stearic acid is a milder irritant. Neither fatty acid is associated with chronic health effects. Other fatty acids that could be used in this experiment, such as myristic or capriolic acid, have similar hazards. If the solids are heated in test tubes immersed in water baths, care should be taken when using heated glassware. To dispose of the fatty acids after the experiment is completed, students can remelt the solids and pour them into a separate glass waste container. Hot, soapy water removes any remaining solidified fatty acid from the test tubes.

Figure 1. POGIL-PCL experiment template. POGIL-PCL experiments include multiple data−think cycles as shown in the middle of the figure and discussed in the text.

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Freezing Point of a Binary Mixture of Solids Related to the Composition of the Mixture?”. The content objectives for this guided inquiry experiment are similar to those of the previously published experiments: students use cooling curves to determine the phase diagram for a solid−liquid mixture and the enthalpies of formation of two fatty acids. The experiment also includes important process skills that move the experiment beyond verifying the validity of thermodynamics relationships. Box 1 lists the specific process (1−3) and content (4−7) objectives. The students make reasoned predictions regarding the melting points of the mixtures and the general appearance of the phase diagram, and they work together with the instructor to design the collection of data. In addition, the experiment is carried out by multiple groups of students, who must pool their data to determine if their predictions are correct. These objectives help students develop their critical thinking and teamwork skills. The experiment (and an Instructor’s Handbook, which includes student data and the learning objectives) is given in the Supporting Information. The experiment is based on the simplest form of data collection: students record the temperature

LABORATORY ACTIVITY The experiment is described below using the framework shown in Figure 1. The experiment is done twice. In the first cycle the focus is qualitative: How does adding a second solid affect the freezing (melting) point of the first solid? In the second cycle the focus is quantitative: How do we model solid−liquid mixtures, and what physical parameters can we determine from the model? Qualitative Cycle: Pre-Experiment Questions and Predictions

Students begin this experiment by individually answering the pre-experiment questions (Box 2) in their laboratory notebooks before coming to class. Their answers are then shared when the class meets. An informal sampling of faculty who have used this experiment report that about half of the students correctly state that the melting point of the mixture is less than the melting point of the pure solid. Significant numbers of students give the melting point as a mass- or mole-weighted average of the melting points of lauric and stearic acid. This reasoning leads them to incorrectly predict that the melting point of 1 g of stearic and 5 g of lauric acid will have a higher melting point B




instructors could substitute a different experimental technique for the one described here.

Box 2. Pre-Experiment Questions

Qualitative Cycle: Thinking about the Data

1. Use the NIST Chemistry Webbook (http://webbook. nist.gov/chemistry/) to look up the formula, molar mass, structure, and melting points of lauric and stearic acids. Draw the structures of the compounds in your lab notebook. 2. Suppose 1 g of lauric acid is added to 5 g of stearic acid. Predict the temperature at which this mixture will begin to melt, and justify your answer. 3. Now suppose 1 g stearic acid is added to 5 g of lauric acid. Predict the temperature at which this mixture will begin to melt, and justify your answer.

Students combine their data into one spreadsheet, and subsequently they discuss the results using the “thinking about the data” questions (Table 1) as a guide. Working together, they construct a graph (Figure 2) of mole fraction of lauric acid versus freezing (melting) point temperature. This step reinforces for the students that the lauric acid/stearic acid mixture is part of the same system regardless of which solid is added (i.e., lauric added to stearic acid or stearic added to lauric acid). Using data from the whole class opens discussion of reproducibility, units used to report results, and, not infrequently, errors in transcription or measurement. At this point in the experiment, insufficient data has been collected to determine the eutectic point temperature or mole fraction. Students predict the eutectic point by examining their temperature versus mole fraction graph (Figure 2). Some students assume that the eutectic occurs at a mole fraction of 0.5, while others extend the initial phase lines in Figure 2 and predict that the eutectic point will be found at a mole fraction of about 0.75. Further discussion helps to clarify for students that the solid that first begins to freeze is the solvent even where, as is the case in the lauric acid−stearic acid mixture, the mole fraction of stearic acid is between about 0.5 and 0.25 (see Box 1, objectives 5−7).

than 43.2 °C, the melting point of lauric acid. A few students recall that melting points were used in organic chemistry laboratory to determine the purity of their synthesized compounds, and they predict a lower temperature than the melting point of the pure compound (but not a specific value). Occasionally students will use colligative properties to either calculate a predicted value for the melting point or to justify their reasoning. Experimental Protocol

In the first experiment cycle, students work in pairs to find the freezing points of either pure lauric or pure stearic acid and then of three mixtures of the two acids. The second solid is added in predetermined increments to the first. Half of the students in the class begin with lauric acid, and the other half begin with stearic acid. The general protocol as written in Box 3 uses the simplest method for measuring freezing points, but

Quantitative Cycle: Pre-Experiment Questions and Prediction

Students considered the effect on freezing (melting) of adding a solute into a solvent in the first cycle, but the emphasis was qualitative. In the second cycle the students repeat the experiment, but they collect the data needed to complete the phase diagram and to find the enthalpy of fusion of each fatty acid according to eq 1

Box 3. Experimental Protocol General protocol (Read entire protocol before starting the experiment) The following protocol will be used for the measurement of all melting points in this experiment. The temperature of a cooling binary liquid mixture will be monitored using a digital thermometer. Instructions for using the thermometer will be provided. 1. Set up the digital thermometer and associated software to record the temperature once per second. 2. Add approximately 5 g of pure solid (select a fatty acid) to a tube; obtain an accurate mass of the solid. Use weighing paper or a weighing boat when determining the mass of the fatty acid. Insert the thermocouple in the tube, and clamp the tube in a beaker of boiling water. 3. Begin collecting temperature data once the solid has melted. Use tongs to remove the tube, and clamp the tube to a ring stand. Vigorously agitate the cooling solid using a metal wire. Watch the tube to determine the temperature at which solid first begins to precipitate, and record that temperature. You can continue to record the temperature until most of the liquid has solidified, but this is not necessary. 4. Add the required mass of the second fatty acid to your tube (after accurately determining its mass), and repeat #3. 5. Repeat #4 as needed for each experiment below. 6. To dispose of the fatty acid mixture, remelt the mixture. Scrubbing the tube with hot soapy water removes solidified fatty acid.

⎛ 1 1⎞ R lnXA = Δfus,A H ⎜⎜ − ⎟⎟ * T⎠ ⎝ Tfus,A

(1)

In eq 1, R is the gas constant (in J K−1 mol−1), XA is the mole fraction of component A, Δfus,AH is the enthalpy of fusion of component A (in J mol−1), T*fus,A is the normal melting point of A (in K), and T is temperature (in K). As in other POGIL-PCL experiments,2 students first answer a few pre-experiment questions to prepare them for this second cycle. They determine the appropriate independent and dependent variables and rearrange eq 1 so that it is plotted to give the enthalpy of fusion as a result. The objective here is for students to learn how collected data may be modeled to determine a desired parameter rather than to derive the equation or construct the relation from the data. In addition, the students must decide which data to collect (the mole fractions of the mixtures for which the freezing point will be determined). A method suggested by some students is to change the mass of each solid for each mixture, which of course would take much longer to complete and lead to errors (due to cleaning out the tubes between each measurement of the freezing point). A discussion of experimental design for efficiency and accuracy can lead students to use the addition method from the first part of the experiment (see Box 1, objective 4). Thinking about the Data: Quantitative Cycle

The students pool data (see Figure 3) to plot the phase diagram. Students who opted to begin with lauric acid and then C




Table 1. Thinking about the Data Questions for Cycle One with Typical Student Responses Thinking About the Data Questions

Typical Student Responses

1. Use your graphs of temperature versus time and your visual determination of the temperature when solid first precipitates to determine the freezing points of the pure solids and the mixtures. 2. Share your results with the class by recording the freezing points for each mixture in a common spreadsheet. Repeat measurements if needed. 3. How does the addition of a second solid affect the freezing point of the first solid? The class must come to consensus on an answer.

Data shown in Figure 2.

Students recall that an impurity will depress the freezing point of a solid (from organic chemistry laboratory) or that rock salt is used to lower the freezing point of water. See Figure 2.

4. Determine the mole fraction of lauric and stearic acid for each of the “mixtures” for which a melting point was determined. Add the mole fractions to your spreadsheet. Is it important to report mole fraction in terms of lauric acid or stearic acid? 5. Construct a graph with the mole fraction of lauric acid on the x-axis and melting point on the y-axis. How many points are on your graph? Predict the general appearance of a graph freezing point versus mole fraction of lauric acid from 0 to 1. Go to predict the freezing point temperature of a mixture with a mole fraction of lauric acid of 0.70. The whole class will generate a consensus prediction. You will use this prediction to determine which mixtures to investigate in Part Two (#11 below). 6. Which fatty acid is the solvent in each of the mixtures you studied? Which solid precipitates first in each mixture? State your reasoning.

Some students predict that the freezing point data will “connect” where the mole fraction is 0.5, and others will extrapolate the two data sets so that they meet at XLA = 0.5.

Many students begin with the assumption that the solvent is in excess. The instructor facilitates a discussion so that students recognize that, in mixtures, it is the solvent whose melting/freezing point is changed by the presence of a second compound.

Figure 2. Partial phase diagram for stearic acid and lauric acid determined by a class of 16 students in the first cycle of the experiment.

Figure 4. Determination of the enthalpy of fusion of stearic acid from the stearic acid−lauric acid phase diagram. Circles are student data pooled from one class, and squares are from ref 14. In this case the student results give ΔfusH = 52 ± 1kJ mol−1 while the data from ref 14 give ΔfusH = 55 ± 2kJ mol−1.

increase as the mole fraction of lauric acid drops below about 0.85. However, the discussion from the first part of the experiment eventually makes it clear to the whole class that these mixtures are part of a continuum, not two separate systems. The students go on to determine the enthalpies of fusion for lauric and stearic acid using eq 1 as shown in Figure 4 (see Box 1, objectives 1−3). Because of the prior discussion, most students correctly choose which points from the phase diagram must be used to determine the enthalpies of formation of the stearic and lauric acid. The students clearly comprehend that the solvent is the component on either side of the eutectic that freezes out first as a mixture is cooled (see Box 1, objectives 4−7).

Figure 3. Phase diagram for lauric acid and stearic acid. The squares are data collected by one class of students, and the circles are from ref 14. Note that student data appears to depress the temperature of the liquid to solid phase transition. This is likely due to the visual determination of the appearance of solid, especially compared to determination of the freezing temperature using differential scanning calorimetry.

measure freezing points of mixtures with added stearic acid are often surprised when the freezing temperature begins to D



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IMPLEMENTATION This experiment was developed as part of the POGIL-PCL project.1 As such, it was tested at a POGIL-PCL workshop with faculty participants, who gave important feedback leading to the qualitative−quantitative cycle structure of the experiment. Next, a written copy of the experiment, with the instructor handbook, was reviewed by three different faculty members. Their comments were incorporated into the documents. Ultimately, the experiment was tested as written in three different physical chemistry laboratory classes outside of the author’s home institution. Since the reviews and beta-testing, at least five additional faculty members at five different institutions have used this experiment with their students, who were able to obtain similar results. The experiment was done with students in classes ranging in size from 4 to 16 students; at the first author’s institution, the experiment has been done for many semesters with 4−6 sections of 16 students each semester. Classes as small as four students can readily gather enough data to perform the phase diagram analysis. More students allow for both more points on the phase diagram and checks on reproducibility of the experiments. In most cases, students wrote journal-like reports and maintained standard laboratory notebooks, using answers to the questions as the basis for their writing.

ible alternative to many other two-component systems commonly used for this experiment. Second, this guided inquiry experiment promotes student learning because it emphasizes inquiry, prediction, and decision-making in the context of learning about the thermodynamics of mixing and of solutions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.7b00409. Student experiment handout (PDF, DOCX) Instructor handbook for experiment (PDF, DOCX)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Sally S. Hunnicutt: 0000-0001-8714-4434 Alexander Grushow: 0000-0002-5570-1459 Rob Whitnell: 0000-0002-6525-7750 Notes

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The authors declare no competing financial interest.

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CONCLUSION As discussed previously,2 POGIL-PCL experiments are best described as structured or guided inquiry15,16 where students follow an apprenticeship model of research. This model is clearly evident in the currently described experiment. Students make two important predictions, which are tested in the laboratory, and they make critical decisions about how to carry out the experiments. Students model data using an equation that they linearize, and the data analysis is introduced at a point in the experiment where it is most appropriate, after collecting some preliminary data. Pooling data has two advantages. It provides a larger data set for analysis than could be obtained by a student or pair of students in the allotted time. Data pooling also reinforces the meaning of reproducibility by allowing some measurements to be repeated by different students. The determination of a phase diagram is a sufficiently flexible enough topic that instructors can choose to use modern technologies, such as a differential scanning calorimeter, or the least expensive technology, such as a thermometer, for measuring cooling curves. The chemical system also adds flexibility because instructors could select fatty acid mixtures that form peritectics and eutectics rather than just simple eutectics. The research of Costa et al. provides several examples,14 and students in our lab courses found the eutectic and peritectic points for several of the mixtures that agreed with these prior results. However, faculty members who use this experiment found that mixtures that form a simple eutectic, such as lauric/stearic acids, are more than sufficient to achieve the given content and process objectives. The determination of a solid−liquid phase diagram is a ubiquitous experiment in the physical chemistry laboratory curriculum for good reason: It provides a powerful laboratory demonstration of thermodynamic principles that students often find opaque after exposure to these concepts in the classroom. The POGIL-PCL version of this experiment as described here is a significant improvement on previous versions for two reasons. First, the use of fatty acid mixtures provides an inexpensive, safe, reliable, and reproduc-

ACKNOWLEDGMENTS This work was funded by NSF-TUES #1044624. REFERENCES

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How Is the Freezing Point of a Binary Mixture of Liquids Related to the

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