Laboratory Experiment pubs.acs.org/jchemeduc
Adsorption Kinetics and Isotherms: A Safe, Simple, and Inexpensive Experiment for Three Levels of Students Polly R. Piergiovanni* Department of Chemical and Biomolecular Engineering, Lafayette College, Easton, Pennsylvania 18042, United States S Supporting Information *
ABSTRACT: Adsorption kinetics and isotherms are taught to chemistry and engineering students and are important to understanding operations such as water pollution treatment, yet many students do not have the opportunity to perform a hands-on experiment that demonstrates the theory in a practical and tangible way. This paper describes an experiment that is inexpensive, safe, and visually conclusive and can be used for a variety of student audiences: non-science and non-engineering students, first-year engineering students, and upper-level engineering students. Adsorption kinetics and isotherms were examined through the dyeing of fabric. All students observed the dyed water becoming colorless, while the adsorbent darkens. Students used the spectrophotometer to measure dye concentrations as a function of time and found that the data followed the first-order process they learned in calculus. Upper-division students noted a systematic error in the first-order model and determined that a second-order model fits the process much better. Students in upper-level courses also developed a procedure to collect data and fit it to isotherms. Data can be obtained at different temperatures for a complete picture of the process. KEYWORDS: First-Year Undergraduate/General, Upper-Division Undergraduate, Chemical Engineering, Environmental Chemistry, Laboratory Instruction, Hands-On Learning/Manipulatives, Applications of Chemistry, Dyes/Pigments, UV-Vis Spectroscopy
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A
dsorption is one of the most common methods used to remove contaminants, especially dyes, from wastewater.1 Thousands of synthetic dyes are available to the textile industry, with over 70 million kilograms used annually.2 The dyeing process uses about 9 trillion gallons of water annually, and 10− 25% of the dye leaves the process with the water.2 A portion of the process water is recycled, but up to 20% of the dye is discharged as aqueous effluent. The dye industry is estimated to be responsible for 17−20% of industrial water pollution.2 To alleviate this problem, both the dyeing process and wastewater treatment process must be optimized. Fabric dyeing and wastewater dye removal are adsorption processes, and understanding the kinetics and thermodynamics of the two processes will allow dyes and adsorbents to be evaluated fairly. Experiments to help students understand adsorption have been published in this Journal.3−7 The experiments described in this paper were developed to introduce dye adsorption as wastewater treatment to three different audiences: non-science and non-engineering students, first-year science and engineering students, and upper-level engineering students. All students receive similar background information about the problem of dye pollution in wastewater and the various treatment options. The students also perform the same experiment; however, the level of scientific and mathematical background presented to each group before the experiment varies. © 2014 American Chemical Society and Division of Chemical Education, Inc.
BACKGROUND PRESENTED TO DIFFERENT STUDENT AUDIENCES
Non-Science and Non-Engineering Students
Second-year students in a course on the science and technology of indigo dye performed the experiment in the spring 2013 semester. Most of the students, primarily history, art, and government majors, had not taken math or chemistry since high school. The students found the mathematics of a firstorder differential equation intimidating. However, as future leaders in business and government, it is important that the students become aware of the dye pollution problem, its potential solutions, and also learn how chemistry and mathematics can be used to test hypotheses and predict results. To help the students understand the process, before lab they participated in a “Lego Adsorption” activity: groups of three students were given a 10 in. square Lego baseplate and about 100 (4 × 4) Lego bricks. During 10 s intervals, the students randomly placed Legos on the baseplate and then counted how many spots were filled during each interval. Eventually, no more Legos would fit. They discussed the process (placing Legos started out easy and became more difficult as Legos filled the baseplate, some holes were not filled because they were not 4 × 4, etc.) and compared it to dye adsorption. The students also created a plot and identified the driving force (simply the difference between the maximum number of available spaces and the current number of available spaces in this example) and Published: January 9, 2014 560
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on introduction helped them better understand what they later observed in lab.
limiting value (Figure 1). In 1984 a paper using statistical games to explain chemical kinetics was published in this
First-Year Science and Engineering Students
Seventy-five first-year science and engineering students have performed this laboratory over the past four years. Most were also enrolled in the first or second semester of calculus, so they understood first-order processes and knew how to solve the equations. In class, we discussed first-order processes they were familiar with (Newton’s law of cooling, for example) and defined the driving force for each (temperature difference). We also discussed the problem of water pollution and treatment options, including adsorption. Although the science and engineering students had a strong background in math and chemistry, they had less knowledge of dye adsorption models.1 Two models were presented: adsorption reaction models and adsorption diffusion models. Adsorption reaction models originate from chemical kinetics and are modeled as a pseudo first-order system.1,8 The rate of dye adsorption based on the adsorption capacity can be modeled as
Figure 1. The students modeled a first-order process using Legos by counting how many Legos could be placed on a baseplate in 10 s intervals and summing to obtain the cumulative number placed in 10 min. A 10 in. square baseplate has 256 “dots”, and each dot represented a binding spot. Each Lego required a square of 4 dots.
dqt
Journal.8 The author found the game technique to be especially useful for students with less mathematical knowledge, similar to the students in this course. Dye adsorption is similar to the “Lego Adsorption” process and follows a general first-order differential equation. The mathematical model and solution were presented to the students and then plotted using the Lego data (Figure 2).
dt
= k1(qe − qt )
(1)
where qt (mg dye/g adsorbent) represents the quantity of dye adsorbed at time t, qe (mg dye/g adsorbent) is the quantity of dye adsorbed at equilibrium, and k1 is the average value of the rate constant. Solving eq 1 with the initial condition that qt = 0 at t = 0 yields ln(qe − qt ) = ln qe − k1t
(2)
The second model, adsorption diffusion, assumes three steps: the dye diffuses across the external film surrounding the adsorbent, then diffuses into the pores, and then finally adsorbs onto the active site. This process can be modeled as a pseudosecond-order model:1,8 dqt dt
= k 2(qe − qt )2
(3)
Solving eq 3 with the initial condition that qt = 0 at t = 0 yields 1 1 = + k 2t qe (qe − qt )
Figure 2. A first-order model of the Lego adsorption data. Max represents the maximum number of dots on the baseplate (256), and number represents the number of dots filled at that time. The regression equation intercept is ln(max), resulting in an experimental maximum adsorption of 267 dots (4.5% error). The slope indicates the rate at which the Legos were added.
(4)
which can be algebraically rearranged to t 1 1 = + t qt qe k 2qe2
(5)
This form of the equation can be plotted without an estimation of qe. After this background presentation, students collected the data on dye removal.
Although the Lego model has limitations (for example, no reversibility, both zero and first-order kinetics are exhibited), it served as a useful tool to initiate a discussion on the link between a process and mathematics for students who were uncomfortable with their math skills. They were intrigued by the idea that an equation could demonstrate what they had just completed. The class also discussed other first-order processes that these students were familiar with (such as a cooling cup of coffee or learning a new skill) and defined the initial conditions, limiting values, and driving force for each process. After this background presentation and activity, students collected qualitative and quantitative data on dye removal. This hands-
Third-Year Science and Engineering Students
Upper-level students received the same introduction to adsorption kinetics as the first-year science and engineering students. Most of the students also have theoretical knowledge about isotherms, so they were reviewed briefly before the laboratory. The Freundlich isotherm is an empirical model3−5,8 qe = kCe1/ n
(6)
where qe represents the quantity of dye (mg/g) adsorbed at equilibrium, Ce represents the concentration of dye (mg/mL) 561
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Figure 3. Kinetic data obtained from dyeing silk fabric with red dye at 65 °C. Experimentally, the equilibrium dye adsorption concentration, qe was 3.4 mg dye/g fabric. The first- and upper-order models yield equilibrium dye adsorption concentrations of 4.5 and 3.7 mg/g, respectively. The firstorder rate constant, k1, was 0.0065 s−1 and the rate constant for the pseudo second-order model, k2, was 0.0023 g fabric/(mg dye s).
in the bulk fluid at equilibrium, and k and n are parameters that depend on the adsorbate and adsorbent. The equation can be linearized and the temperature dependent constants k and 1/n found by linear regression: ln qe = ln k +
1 ln Ce n
readily available. If an oven or water bath is available, data can be obtained at different temperatures, and the results can be compared. The kinetic experiments can be completed in less than an hour. Fabric is used as a model adsorbent. KoolAid adsorbs strongly to protein fabrics, such as wool and silk. Although it can stain cotton and linen fabric, the dye does not adsorb well. Any color of KoolAid can be used, but red and green have fewer particulates than blue, pink, or yellow colors. KoolAid is colored with three FD&C dyes, Red 40, Blue 1, and Yellow 5 (structures are provided in the Supporting Information). Other flavored drinks and foods are possible sources of the dyes. The quantity of dye in each packet of KoolAid is not published but varies little among packets (data not shown). Pure FD&C dyes (Roha (USA) Ltd., St. Louis, MO) were used to create a calibration equation provided to the students. White silk dupioni and optic white worsted wool suiting were purchased from VogueFabricsStore.com (Chicago, IL). Other silk and wool fabrics have been used with similar results. To perform the kinetics experiment, groups of one or two students were given beakers with 1−4 packets of KoolAid dissolved in 625 mL of a 4:1 water/vinegar mixture. A piece of white silk or wool was weighed, dampened with water, and then immersed in the solution. The students removed a 1 mL sample of liquid initially, and then every 2−5 min until the
(7)
Values of n greater than 1.0 indicate favorable adsorption. The Langmuir isotherm assumes a uniform surface where adsorption takes place at specific homogeneous sites in a monolayer. The isotherm is represented by the equation3−6,8
qe =
QbCe 1 + bCe
(8)
which can be linearized as 1 1 1 = + qe Q QbCe
(9)
The constant Q represents the maximum adsorbate that can be adsorbed onto the surface, and b is the isotherm constant.
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EXPERIMENTAL DETAILS A spectrophotometer is the only equipment required. The necessary materials (beakers, disposable cuvettes, silk or wool fabric, KoolAid, water, and vinegar) are inexpensive, safe, and 562
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Figure 4. Data obtained with different initial concentrations of dye on wool to determine isotherm parameters.
day, they returned to measure the final absorbance of the dye solution to calculate (Ce). The quantity of dye adsorbed on the fabric, qe, was calculated from a mass balance (eq 10). The adsorption capacity varies with fabric type (wool or silk) and the fabric processing and weave.
water was colorless (and the fabric was colored). The students measured the absorbance of the liquid samples with the spectrophotometer and used the calibration equation to convert the measurement to dye concentration. This provided concentration of dye in the water as a function of time, Ct, and a mass balance (eq 10) was used to calculate the quantity of dye on the fabric, qt (mg dye/g fabric).
qt = (Co − Ct )
V W
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HAZARDS The adsorbent, dye, and solutions used in the experiment present no hazards.
(10)
ANALYSIS OF RESULTS The experiments have been performed many times with different groups of students. Data collection was visual because the students can observe the solution becoming colorless (they line up the cuvettes as they collect the samples) as the fabric becomes darker. All students performed similar analyses, although the non-science and non-engineering students did the calculations using Excel together during class. Typical results for the adsorption kinetics of red KoolAid on silk are shown in Figure 3. The first graph shows the rate of dye adsorption as a function of time and the second graph shows a first-order fit of the data. All student groups were able to create these two plots and interpret the slope and intercept values. The intercept is related to the equilibrium adsorption concentration, or adsorption capacity (qe). A measure of the students’ accuracy could be determined by comparing their calculated value to the experimental value. The slope indicates the rate constant. First-year engineering students and upper-level students also created the third graph (Figure 3, bottom, right), showing the higher-order model fit. The first-order model appeared to fit−it has a coefficient of determination near 1.0−but the higherorder model was more accurate. The students concluded this by comparing the experimental value of the equilibrium adsorption concentration (qe) with the value predicted by the two models. The first-year engineering students discussed why engineers use mathematical models and completed several homework problems on model determination.9 This experiment provided another opportunity to model data and observe how different processes can be modeled with similar mathematical functions. Students with a strong background in chemical kinetics may understand why the higher-order fit is better.1,10 The higherorder model assumed three steps in the dyeing process: the dye diffuses across the external film surrounding the adsorbent, then diffuses into the pores, and then finally adsorbs onto the
where Co is the initial dye concentration (mg/mL), V is the volume of dye solution (mL), and W is the mass of the fabric (g). The aliquots removed for measurement were not returned to the beaker, which introduced a small amount of error (which students can discuss in their report). However, each value of qt was easily calculated at the correct volume when completing the calculations in a spreadsheet. Students could also calculate the quantity of dye removed with each sample and discuss the amount of error the method introduces. All three groups of students performed the same kinetics experiment, with one slight modification. The non-science and non-engineering students cut their fabric into six pieces, and removed one piece at various times (3 s, 1, 5, 20, 45 min, and 24 h). Although this introduced additional error (W was not constant), the visual impact was important. To minimize the error, the first five pieces removed should be small compared to the whole piece. The other two groups of students did not remove the fabric. The liberal arts course requires students to consider the societal and environmental impacts of the dyeing process. Thus, in addition to studying wastewater pollution and cleanup, the non-science and non-engineering students also performed a “Dye Desorption” experiment where they observed the rate that dye faded from different fabrics. After dyeing silk and wool with various colors of KoolAid, the students placed small pieces of fabric in hot water. Samples of the water were removed over an hour and the absorbance of the samples was measured with the spectrophotometer. The adsorption isotherm experiment took 24−48 h and was only performed by the third-year students. For 25 students, four packets of red KoolAid were added to 1 L of a 4:1 water/ vinegar mixture. Various dilutions were prepared (from undiluted to about 1:64) and 41 mL of the solution was distributed to each student. The students measured the initial dye concentration, added a known mass of fabric, covered the beaker, and placed it in an isothermal environment. The next 563
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and drew conclusions from graphs in a technical memo. The fabric was cut into pieces, so the students could remove one piece at various times. For most colors, the silk was tinted after just 3 s, which surprised the students. Silk dyed with the lemonade flavor, however, remained pale for an hour. The students were asked what would happen if the quantity of dye were doubled. After some thought, and some leading questions, they decided that the effect on the rate was hard to predict, but given ample time, the final color should be darker. Indeed, a quick experiment with two packages of lemonade confirmed their reasoning. The following week when desorbing the dye from the silk, the students noted that red dye faded more quickly than other colors (purple, a mixture of red and blue, also fades slightly). The students wrote papers after the experiments and correctly used words and phrases such as “adsorbent” and “driving force”. Many included the analogy with the Lego adsorption activity. Later, an exam question asked the students to explain a graph similar to Figure 1. All could identify the driving force on the graph and describe it (the difference in dye concentrations in solution and on the fabric) and 75% correctly defined what the axes represented. For the technical memo, the students were given a graph of adsorption data for four hypothetical dyes. Data on the dye toxicity and wastewater contamination was also created for the assignment. The students were to analyze the data and determine which dye should be manufactured. All students were able to determine which dye adsorbed most quickly and which dye had the highest equilibrium concentration. Most students (88%) used the desorption graph and wastewater contamination levels to support their recommendation. Finally, at the end of the semester, the students used the Web site PowToon.com to create a 1-min public service announcement to create awareness about the problem of dye pollution in the world’s waterways. After watching these powerful videos, it was clear that the students recognize the problem of dye pollution. Several students proposed solutions such as adding an adsorption unit using activated carbon filters or agricultural waste to remove the dyes before they enter the water. Although their proposals might not be economical or feasible, the students clearly showed they had understood the adsorption process.
active site. Research has indicated that the chemisorption mechanism is the rate controlling step.10 Later, upper-level chemical engineering students take a reaction engineering course, where the mechanisms behind various models are derived and explained. They can relate that information to what they discovered during this experiment. An example of the isotherms obtained for dyeing wool with red KoolAid is shown in Figure 4. The isotherm parameters can be calculated from the slope and intercept, and students confirmed that the adsorption of dye onto the fabric is a favorable process. The non-science and non-engineering students collected data on desorption of the dye from silk fabric. The results for four colors are shown in Figure 5. Red KoolAid is the least fast dye,
Figure 5. Students measured the quantity of dye desorbing from silk dyed different colors by measuring the quantity of dye accumulating in the water solution (data collected at 50 °C).
which the students could relate to as they had all experienced the surprise load of pink laundry. Desorption from the purple dye was primarily red colored (purple is a mixture of Red 40 and Blue 1). The chemistry of the dye-binding process is still being researched,11 but some differences between the dye molecules could be shown to the students. For example, Red 40 is a diazo dye, and has one less charged group than Blue 1, which has a triphenylmethane skeleton. The desorption data were fit to a first-order model (Figure 6). An higher-order model also fits the data (not shown), but this was not demonstrated to these students.
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First-Year Science and Engineering Students
ASSESSMENT OF STUDENT LEARNING
First-year engineering students performed the lab many times and analyzed the kinetic data to choose a model and estimated the equilibrium adsorption concentration and the rate constant. The students followed a procedure outlined in their textbook to do this.9 First, we discussed several possible models, plotted them in Excel, fitted a trendline, and calculated the coefficient of determination (R2). Class time and the book provided students insight on how to determine when R2 is useful and how to choose the appropriate model. The students also compared the experimental adsorption capacity (qe) with the value predicted by the model. Most students used Excel to plot the data and estimate the model parameters with little trouble, but many had difficulty with the units for qt, qe, and k. Student final reports were analyzed for the calculation and understanding of the model parameters. The average score on the lab reports was 81%, which is typical for reports in this course. This lab was a small portion of the entire course, so pre-lab questions on the adsorption process were not assigned and gains in student learning were not measured.
Non-Science and Non-Engineering Students
Non-engineering students performed the experiment using 10 different flavors of KoolAid, prepared graphs together as a class,
Figure 6. Red dye desorption also fits a first-order kinetic model. The y axis represents the quantity of dye remaining on the fabric. 564
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Third-Year Science and Engineering Students
Upper-level students who completed the experiment had no difficulties with the mathematics or the analysis. They were required to develop their own procedure to create the isotherms, which sometimes required several trials to collect the correct data. The students commented that developing their own protocol led to a better understanding of isotherms.
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FUTURE WORK This set of laboratory experiments will continue to be used in the various courses. In addition, the experiment will be used as an outreach activity for middle-school students. These students will collect the samples, measure their absorbance with the spectrophotometer, and create a plot showing the disappearance of the dye from the water. They will create a PowToon public service announcement for their final project.
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ASSOCIATED CONTENT
S Supporting Information *
Detailed laboratory procedure, student handouts, and photos of the experiment. 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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REFERENCES
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