In the Classroom
Modeling Chemical Processes in Seawater Aquaria to Illustrate Concepts in Undergraduate Chemistry Gordan Grguric Marine Science Program, The Richard Stockton College of New Jersey, Pomona, NJ 08240;
[email protected] The importance of exposing undergraduate students to real-world chemistry has been discussed in various settings (1–5). This paper describes several topics from a recently introduced marine chemistry course at Richard Stockton College. The course focuses on modeling chemical processes in seawater aquaria and illustrates to the students the chemical principles behind these processes. Seawater aquaria have been proposed as excellent environments for development of analytical chemistry skills (6 ). In our course, these systems are used to teach the importance and applicability of concepts such as mass and charge balance in solution, acid–base equilibria, and chemical kinetics. Practical examples and empirical data from several large aquarium facilities are used to help the students visualize and apply the concepts in question. The course is open to our Chemistry, Environmental Studies, and Marine Science students, most of whom will have had a year of general and inorganic chemistry as well as mathematics through the first semester of calculus. The format of the course consists of one lecture and one computer lab session per week. During lectures, students are introduced to practical problems facing seawater aquarium facilities. Topics covered include determining the salts needed to prepare a given volume of artificial seawater, maintaining pH and alkalinity through controlled additions of chemicals, and predicting the type and the extent of disinfection by-products. Approaches to these problems are based on chemistry concepts to which students were introduced in their courses and now have a chance to use in a specific setting. The calculations involved in addressing aquarium chemistry questions can be tedious and time-consuming, so we decided to have students model their approaches to problems using Excel. This is facilitated by the weekly computer lab sessions in an electronic classroom, which enable the instructor to demonstrate models and provide each student with his or her own workstation. Such intensive use of computers in chemical education (spreadsheets or more specialized chemical software) has become much more common in recent years (7–10) and to us, it was shown to have multiple benefits. First, calculations can be repeated many times using different input data. This serves to divorce students from the inner mathematical workings of their models, so they can focus on the chemical meaning of results. Another benefit of this approach is that students become independent self-learners through the development and use of their own models. A survey of student questionnaires at the end of semester showed that the students found this way of learning extremely valuable. Below are descriptions of three exercises from the course, with the approaches and some items for discussion described in detail. One or more of these topics can be used in a variety of chemistry courses as practical illustrations of the chemical principles under study.
Exercise 1: Preparation of Artificial Seawater The six most abundant ions in seawater are Cl , Na+, SO4 , Mg2+, Ca2+, and K+ (Table 1). A number of aquaria that are located far from the ocean, or where uncontaminated seawater is not available locally, prepare their own artificial seawater by dissolving Table 1. Weight salts containing these ions. While seawa- Percentages of ter must contain a specific concentration of 6 Major Ions in Seawater each ion, an ion can only be added through Wt % a combination with its counterpart in a given Ion salt. Thus, a combination of salts has to be Cl 55.1 found that will produce a solution with speci- Na + 30.6 fied concentrations of the individual ions. SO 2 7.7 4 Our students are asked to develop and pro3.7 Mg 2+ gram in Excel an artificial seawater formu2+ C a 1.2 lation, by choosing which salts to use and 1.1 calculating their amounts. The approach K + suggested to them is to sort the six major ions by their weight percentage in salinity (Table 1) and to balance the least abundant ions first. That approach guards against “overshooting” an ion. An example of the calculations is shown in Table 2 and is elaborated below. First, the total mass of each ion needed is calculated from the batch volume and the desired salinity. Then, the least abundant ion is found (K+), and on the basis of its needed mass, the mass of its salt (in this case KCl) is calculated. Now K+ is balanced, and the mass of needed Cl decreases by the mass of Cl added through KCl. This process is repeated for each of the other ions, in order of their increasing abundance. Thus, Ca2+ is balanced next using CaCl22H2O, followed by Mg2+, which is balanced using MgCl26H2O. After SO42 is balanced using Na2SO4, the ions remaining are Na+ and Cl. 2
Table 2. Calculation of Mass of Ions and Salts to Make 10,000 L of Artificial Seawater of Salinity 35 g/kg Ion Cl
Na+
197.4
109.9
SO4 2
M g2 +
Ca2 +
K+
Total Needed/kg
Salt
27.7
13.2
4.2
Needed after Sequential Balancing/kg
KCl
193.7
CaC l2 ⴢ2H2 O
186.3
MgC l2 ⴢ6H2 O
147.9
Na2 SO4 NaC l
Mass of salt/kg 0.0
0.0 0.0 96.6
0.0
4.1 a
7.8 15.4 110.1
0.0
40.9
0.7
243.8
To t a l :
418.0
aCalculations
are done in order of the mass requirement of the ion, from lowest (K+) to highest (Cl ).
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In the Classroom
Their running tallies show that the masses needed are 147.9 kg and 96.6 kg, respectively. Next, NaCl is used to balance Cl, and the students are asked to calculate the mass of residual unbalanced Na+. This mass is less than 1% of the initially needed Na+, which shows that balancing Cl essentially balances Na+ as well. The goal is for the students to realize that since the six major ions account for more than 99% of seawater salinity, once the masses (or concentrations) of five of those ions are given, the sixth one is fixed by charge-balance. An interesting topic for discussion is to compare the total mass of all salts (Table 2) to the bulk salinity (for the example in Table 2: 35 g/kg × 1.02 kg/L × 10,000 L) and account for the discrepancies. As part of this exercise, students can be asked to recalculate the masses of salts using anhydrous forms. The results are then compared, and now the total mass of all salts is a little less than the bulk salinity. The difference is under 1%, explained by the unbalanced residual Na+ (Table 2). The above exercise allows great flexibility. For example, several variations of the artificial seawater recipe are possible, with the use of different salts and a different balancing sequence of ions. In each case, students have to employ the appropriate versions of the percent composition calculations, as well as the appropriate mass and charge balance calculations. Exercise 2: pH/Alkalinity Carbonate system equilibria are of fundamental importance in natural water systems, and students are exposed to those equilibria in their inorganic and analytical chemistry courses. Most traditional aquaria that host a large number of heterotrophic organisms exhibit a decreasing pH and alkalinity over time, and chemicals have to be added to maintain these parameters in their seawater range: the pH between 7.8 and 8.2 and alkalinity between 1 and 3 meq/L. Alkalinity of seawater is a measure of its buffering capacity and is defined as the sum of equivalents of negatively charged ions that would react with added H+. About 90% of seawater alkalinity is carbonate alkalinity, due to HCO3 and CO32. This provides an opportunity for revisiting the carbonate system equilibria from a water management point of view. The goal in this approach is twofold: (i) to determine the pH and alkalinity shifts when specified amounts of chemicals are added, and (ii) to determine the chemicals and their amounts needed to achieve a required shift in pH and alkalinity. In the lecture, students first practice how to calculate the concentrations of H+, OH, H2CO3, HCO3, and CO32 from a given pH and carbonate alkalinity. The four chemicals commonly used to adjust pH and alkalinity in aquaria are then introduced: NaHCO3, Na2CO3, NaOH, and HCl. The equilibria in question are discussed and a system of 8 equations is set up (eqs 1–8). These equations contain the equilibrium expressions (eqs 1–3) and mass balance expressions for each of the five chemical species (eqs 4–8). The knowns in eqs 1–8 are the initial concentrations of all species and the concentrations of chemicals added, expressed as c(A). The values of the three equilibrium constants will depend on temperature and salinity, and the following may be used for 20 °C and 35 g/kg salinity: K1 = 9.55 × 107, K2 = 6.76 × 1010, and Kw = 3.98 × 1014 (12, 13). The unknowns in eqs 1–8 are the final concentrations of the five species and variables X, Y, and Z, which measure shifts in the three equilibrium reactions. 496
+
H
F
K1 =
HCO3
H2CO3 +
H
F
F
(1)
F
CO32
F
(2)
Kw = [H+]F [OH]F
(3)
[H2CO3]F = [H2CO3]I + X
(4)
K2 =
HCO3 F
[HCO3 ]F = [HCO3 ]I + c(NaHCO3) + Y – X 2
2
(5)
[CO3 ]F = [CO3 ]I + c(Na2CO3) – Y
(6)
[H+]F = [H+]I + c(HCl) – X – Y – Z
(7)
[OH]F = [OH]I + c(NaOH) – Z
(8) +
Solving the system of eqs 1–8 in terms of [H ]F yields a fourth-order polynomial. After this polynomial is set up in Excel, students find the desired solution by the bisection method (14 ). This necessitates determining the proper constraints on [H+]F, which is done using chemical intuition. For example, the greatest possible [H+]F is given as [H+]I + c(HCl) + c(NaHCO3). After the value of [H+]F is determined with sufficient accuracy, the values of other unknowns can be calculated by back-substitution. We found at least three ways in which modeling the carbonate equilibria has educational value for our students. First, as students enter different chemicals and their amounts, they learn how each of the four compounds affects pH and alkalinity. This serves to break some commonly held misconceptions, in particular that at pH 8, adding NaHCO3 will maintain or even increase the pH. Initially, students also tend to underestimate the large effect of Na2CO3 additions on the pH when it is in the vicinity of 8. The second educational tool provided by the model is the qualitative and quantitative interpretation of shifts in the three equilibrium reactions. On the basis of the signs of variables X, Y, and Z, students can determine the direction in which the reaction proceeded. For example, a positive sign on X denotes a protonation of HCO3 to form H2CO3, whereas the negative sign denotes a dissociation of H2CO3 to HCO3. By interpreting the signs and magnitudes of X, Y, and Z, students can describe what happened in a tank after the addition of chemicals. They may express their answers by stating: “In every liter of this aquarium tank, A µmol of HCO3 dissociated into B µmol of H+ and C µmol of CO32.” This approach helps students to visualize the direction and extent of chemical reactions, especially when combined with and confirmed by their reasoning of what should be happening. To that end, the more intuitive examples such as additions of HCl or NaOH are analyzed first. When students gain confidence in interpreting the meaning of X, Y, and Z, less intuitive examples can be analyzed, such as additions of NaHCO3, Na2CO3, or combinations of chemicals. The third educational benefit of the model is that students can use it “backward” to determine what chemicals and in what amounts are necessary to bring pH and alkalinity to required values. The method here is one of trial end error, but is enabled by the nearly instantaneous solution of the system
Journal of Chemical Education • Vol. 77 No. 4 April 2000 • JChemEd.chem.wisc.edu
In the Classroom
A 1,000,000-L seawater aquarium exhibits a monthly drop in pH of 0.20 units and a monthly drop in alkalinity of 0.30 meq/L. Determine the chemicals and their monthly amounts needed to maintain a pH of 8.10 and an alkalinity of 2.30 meq/L.
One answer to the above question is 12 kg of NaHCO3 and 8.5 kg of Na2CO3. Other combinations of chemicals are also possible—for example, NaHCO3 and NaOH. After experimenting with their models, students realize that to reach any achievable pH and alkalinity, no more than two chemicals are needed. They also realize that there are situations when the final pH and alkalinity may be incompatible with the initial values and no solution exists. This situation may occur if one wants to raise the pH and significantly decrease alkalinity at the same time.
Concn / (µmol L1)
of equations provided by the computer. A practical question that can be answered by this approach is the following:
Time / s Figure 1. Trends in concentrations of Br (––––), HOBrTotal = OBr + HOBr (– – ), and BrO3 ( ) during exhaustive ozonation. Initial conditions are [O3] = 1 mM, [Br] = 57 µM, [HOBrTotal] = 0, and [BrO3] = 0. The pH is buffered at 8.0, and the numerical integration interval is 1 s.
Exercise 3: Ozone–Bromine Reactions Ozone is used for disinfection of many seawater aquaria. In such systems, O3 reacts with Br (present as a minor seawater ion or as an impurity), according to reactions 9–11. O3 + Br → O2 + OBr O3 + OBr → 2O2 + Br
(9)
2O3 + OBr → 2O2 + BrO3
(10)
(11)
Reactions 9–11 are irreversible under seawater treatment conditions and can be quantified by chemical kinetics, which is first order in all reactants (15). The rate constants are, respectively, 160/M/s, 330/M/s, and 100/M/s (15). In the lecture, rate laws for O3, Br, OBr, and BrO3 are constructed with active participation of students, providing them with an opportunity to revisit their knowledge of chemical kinetics. These laws are given in eqs 12–15.
d O3 = k1 O3 Br + k2 O3 OBr + 2k3 O3 OBr (12) dt
d OBr dt
d Br dt
= k1 O3 Br – k2 O3 OBr
(13)
have been used elsewhere to demonstrate chemical kinetics to undergraduate students (16, 17 ). To address concerns about BrO 3 accumulation in aquaria that use ozone for disinfection, students analyze how changes in ozonation parameters affect the amount of BrO3 produced. The parameters varied may include the ozone dose, contact time, the concentration of Br in seawater, or the pH of the medium. For example, cutting the ozone dose in half can decrease the amount of BrO3 produced almost four times. Students realize the large effect of pH on BrO3 production, due to the fact that only OBr, but not HOBr, reacts with O3. This effect is especially pronounced in the pH range of most aquaria (7.5–8.5), since the pKa for HOBr is 8.76 (15). The ozone–bromine kinetic model can be expanded to include ozone reaction with a model organic compound. Ozone reactivity with Cl, analogous to that with Br but with a much smaller rate constant, can also be included in the rate laws. This incremental approach stands in contrast to the approach taken to analyze carbonate equilibria and illustrates the difficulty of using chemical kinetics to thoroughly describe a complex chemical system. Conclusion
= k1 O3 Br – k2 O3 OBr – k3 O3 OBr (14)
d BrO3 dt
= k3 O3 OBr
(15)
The rate laws in eqs 12–15 are programmed in Excel and numerical integration is used to evaluate changes in concentration of O3, Br, OBr and BrO3 over time. Equilibration between OBr and HOBr is taken into account by specifying the pH of the medium. The first exercise for students is to determine the trends in concentrations of various Br species over time when a large ozone dose is introduced. An example of such conditions is shown in Figure 1. The case when O3 is not limiting shows a beginning reactant (Br) being converted to an intermediate (OBr) and then to a final product (BrO3). Other reaction sequences of this type
Our survey conducted at the end of semester showed that most students felt they learned or solidified a lot of their chemistry knowledge through the course. The students indicated that the relatively long time spent doing the mathematics necessary to solve the problems did not distract from the overall learning of chemistry. In fact, most students preferred to arrive at solutions through their individual efforts, rather than through group discussions. The class visit to one of the largest fish aquaria on the East Coast (the New Jersey State Aquarium in Camden, NJ) gave the students an opportunity to compare their class results with the actual aquarium data, including those on artificial seawater recipes, chemical additions to control pH and alkalinity, and ozonation conditions and byproducts. The students’ modeling results from homework and examinations were shared with the aquarium personnel, making a direct connection from chemistry in academe to chemistry in industry.
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In the Laboratory
Acknowledgments Development of this course was enabled by a Fellowship for Research in New Teaching and Learning Strategies from Richard Stockton College of New Jersey. I would like to thank Robert Fournier, Lisa Gainor, and the rest of the staff at the New Jersey State Aquarium for their dedication and support in making this course possible. Literature Cited 1. Walters, J. P. Anal. Chem. 1991, 63, 977A–985A. 2. Richard, L. H.; Hawkes, S. J.; Spencer, J. N.; Bodner, G. M. J. Chem. Educ. 1992, 69, 175–186. 3. Goulding, M. Sci. Am. 1993, 268(3), 114–120. 4. Harris, T. M. J. Chem. Educ. 1993, 70, 340–341. 5. Wilson, A. H. J. Chem. Educ. 1998, 75, 1176–1177. 6. Hughes, K. D. Anal. Chem. 1993, 65, 883A–889A.
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7. Earl, B. L.; Emerson, D. W.; Johnson, B. J.; Titus, R. L. J. Chem. Educ. 1994, 71, 1065–1068. 8. Bowater, I. C.; McWilliam, I. G.; Wong, M. G. J. Chem. Educ. 1995, 72, 31–34. 9. Machuca-Herrera, J. O. J. Chem. Educ. 1997, 74, 448–449. 10. Diamond, D; Hanratty, V. C. A. Spreadsheet Applications in Chemistry Using Microsoft Excel; Wiley: New York, 1997. 11. Gross, M. G.; Gross, E. Oceanography—A View of Earth, 7th ed.; Prentice Hall: Upper Saddle River, NJ, 1996; p 93. 12. Skirrow, G. In Chemical Oceanography, Vol. 2; Riley, J. P.; Skirrow, G., Eds.; Academic: New York, 1975; p 176. 13. Dickson, A. G.; Riley, J. P. Marine Chem. 1979, 7, 89–99. 14. Hoffman, J. D. Numerical Methods for Engineers and Scientists; McGraw-Hill: New York, 1992; pp 92–94. 15. Haag, W. R.; Hoigné, J. Environ. Sci. Technol. 1983, 17, 261– 267. 16. Ball, D. W. J. Chem. Educ. 1998, 75, 917–919. 17. Novak, I. J. Chem. Educ. 1998, 75, 1574–1575.
Journal of Chemical Education • Vol. 77 No. 4 April 2000 • JChemEd.chem.wisc.edu
