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New Software Application and Case Study That Simplify Teaching Complex Chemical Solubility and Equilibria
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New Software Application and Case Study That Simplify Teaching Complex Chemical Solubility and Equilibria
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Journal of Chemical Education

Cite this: J. Chem. Educ. 2022, 99, 2, 526–530
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https://doi.org/10.1021/acs.jchemed.1c00887
Published January 6, 2022

Copyright © Published 2022 by American Chemical Society and Division of Chemical Education, Inc. This publication is available under these Terms of Use.

Abstract

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Chemical solubility and equilibria are paramount for understanding everyday systems. Recent events have led to more interest by the general public in chemical equilibria that occur in drinking water systems. This presents a great opportunity to increase student interest and engagement in the more complicated aspects of chemical equilibria. Shiny Apps allow exploration of complex equilibria without requiring that students (or instructors) get buried in the minutia. The application presented here, https://bazilio.shinyapps.io/LeadSolubilityCaseStudy/, can be used for instruction in chemistry or environmental science and only uses an internet browser such as Safari or Chrome; it is compatible with mobile browsers. Students are assigned a case study on the Flint, Michigan Water Crisis which guides them through lead sulfate, chloride, phosphate, and hydroxide equilibria, using the app to explore their intuitions about this complex chemical system.

This publication is licensed for personal use by The American Chemical Society.

Copyright © Published 2022 by American Chemical Society and Division of Chemical Education, Inc.

Overview

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This technology report describes a Shiny App (1) for use in teaching multiple chemical equilibria. Shiny Apps provide an intuitive, graphical user interface for students to interact with R (2) code and have been used previously for simulations of analytical chemistry content. (3−5) This app was designed to supplement a solubility case study (Supporting Information) which examines the recent Flint Michigan water crisis (where extremely high concentrations of lead were found in the drinking water and in children’s blood) in terms of chemical equilibria. The exercise builds on an infographic from Compound Interest (6) which shows a brief overview of a few of the chemical factors involved: disinfection byproducts, chloride to sulfate ratios, and orthophosphates for corrosion control. A high ratio of chloride to sulfate ions results in more corrosion of lead pipes due to Le Châtelier’s principle and lead ion complexation, and the first question in the exercise examines the relevant chemical equilibria to this effect. The second question focuses on lead phosphate solubility and why orthophosphate is used as a corrosion inhibitor. The third question introduces lead hydroxide and phosphate equilibria and aims to show that these systems cannot be ignored. Question four directs students to use the app to quantitively demonstrate the importance of considering multiple equilibria. The equilibria considered are not comprehensive of the complex equilibria at play in drinking water but rather select equilibria chosen to demonstrate the course material.

Lead in Drinking Water

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The Compound Interest infographic briefly explains some of the factors that led to high levels of lead (Pb) in the Flint, MI, drinking water. In April 2014, the city of Flint stopped purchasing treated Lake Huron water from Detroit and started treating water from the nearby Flint River in an effort to save money. High levels of lead were subsequently found in the water and in children’s blood, and the city returned to purchasing water from Detroit in October 2015. (7) The US Environmental Protection Agency set a lead action level (AL) above which utilities must take prescribed actions, including educating the public and replacing lead service lines; the 90th percentile lead level must be less than 15 μg/L. A trigger level (TL) was set recently in an update to the rule. If the 90th percentile lead level is greater than 10 μg/L and less than or equal to 15 μg/L, “additional planning, monitoring, and treatment requirements” are triggered. (8)
Lead may be present in drinking water systems in legacy lead service lines, lead solder, or lead-containing brass fixtures. Water utilities typically practice corrosion control to lessen the breakdown of the lead-containing plumbing and transport of released Pb to the consumer. Orthophosphate is a widely used corrosion inhibitor. Orthophosphates mitigate Pb release by many pathways, including forming sparingly soluble Pb–P-containing solids (“scales”), and forming non-Pb-containing scales that act as barriers between Pb-containing scale and water. (9) In water systems, the low solubility Pb-containing corrosion products may include lead(IV) oxide (PbO2) and hydrocerussite (Pb3(CO3)2(OH)2, and at high pH and with sufficient dissolved inorganic carbon, lead orthophosphate (Pb3(PO4)2) and hydroxylpyromorphite (Pb5(PO4)3OH). For simplification, Pb3(PO4)2 is the only Pb–P-containing sparingly soluble solid considered in calculations for the exercise.

How to Use the App

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The Flint Water Crisis Case Study can be assigned as homework or can be completed in groups during class. Initial questions prompt the students to make predictions about the behavior of this chemical system based on their chemical intuitions and series of equilibrium reactions. Students then click on the link in question 3 which opens the app in an internet browser on their computer or mobile device. Once on the page, they may select a pH and the equilibria to use, click update, and click through the three tabs to see the results. Follow-up questions encourage the students to compare the quantitative results from the app with their qualitative predictions. The instructor then facilitates follow-up discussions in class to answer questions and emphasize key points.
The exercise uses the Flint Crisis as a case study because students are likely familiar with the crisis due to its relatively recent occurrence and the extensive media coverage it has received. Past research has shown that students value and are motivated by the inclusion of socioscientific discussions in chemistry coursework. (10) Once connections are made, there may be discussion on water chemistry and legacy lead pipes in the United States. A survey conducted in 2013 estimates that 6.1 million lead-containing service lines are currently present in US community water systems. (11) The social impacts of water contamination, and their disparate effects on communities of color, have resulted in several recent publications in the chemical education literature on pedagogical activities driven by this case study. Examples include community-learning laboratory experiments in which students test local water supplies (12,13) and classroom activities that connect chemistry instruction with social and environmental justice. (14−16)ChemMatters also published a Teacher’s Guide for conceptual K–12 instruction on the chemistry of the Flint water crisis, (17) but we are unaware of any tools that allow students to explore the quantitative relationships between the complex chemical equilibria involved. This application could be used as a stand-alone module or as a quantitative complement to the previously published activities.

Application Details

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Chloride to Sulfate Ratio

The first problem of the solubility case study examines the relevance of the change in the chloride to sulfate mass ratio. A high chloride to sulfate mass ratio (CSMR) increases lead and copper corrosion, and CSMR levels greater than ∼0.6 have been linked to greater lead solder corrosion. (18) Sulfate forms a sparingly soluble lead precipitate (PbSO4) while chloride forms soluble lead complexes (e.g., PbCl+, PbCl3). Once PbSO4 is formed, the presence of sulfate decreases PbSO4 solubility by shifting the equilibrium to the left (reaction R1).
(R1)
The sulfate and chloride tab in the app allows students to quantify PbSO4 solubility when sulfate ions are present in solution (ignoring other equilibria).
Chloride ions in solution complex with Pb2+ to form soluble complexes (reaction R2 to reaction R6). Chloride therefore has the opposite effect of sulfate ions and increases PbSO4 solubility.
(R2)
(R3)
(R4)
(R5)
(R6)
Thus, an increased chloride to sulfate ratio means more soluble lead chloride complexes form (increasing the solubility of sparingly soluble lead species) while also decreasing the concentration of sulfate available to form insoluble PbSO4. The α value for free Pb2+ ions (the fraction of the total lead in solution ([Pb]Total) that Pb2+ ions constitute) is found using eq 1, assuming a low pH where lead hydroxide complex formation is negligible; in the equation, βi is the equilibrium constant for the reaction between the uncomplexed Pb2+ and i chloride ions. (19) Concentrations of uncomplexed lead and lead chloride complexes were found using eqs 2 and 3, and a total Pb concentration of 1 × 10–6 M. For CSMR calculations, a sulfate concentration of 24 mg/L is used, the median concentration found in a survey of 20 states. (20) The selected CSMR value and the set sulfate concentration are used to calculate the molar chloride concentration used in eqs 1 and 3.
(1)
(2)
(3)
In question 1d,e, students use the app to check their conceptual reasoning about the effects of sulfate and chloride ions on lead solution. In the Flint example, the increased chloride to sulfate ratio with the change in water chemistry caused by using a new source water increased corrosion, and no phosphate corrosion inhibitor was added during water treatment.

Phosphate and Hydroxide Equilibrium Calculations

Questions 2–4 consider the lead phosphate system. In question 2, students calculate the solubility and Ksp of lead phosphate ignoring all other equilibria. Question 3 presents the chemical equilibria for lead(II) and hydroxide ions, and the phosphate ion, and students make qualitative predictions about the effect of pH on lead phosphate solubility. Question 4 then uses the app to check if their predictions were correct. This process allows students to gradually add complexity to their mental model of lead solubility and then test their model’s predictions without performing complex calculations themselves by hand.
Clicking on the link for the app opens a main page with multiple tabs (Figure 1). The left panel has a pH slider which allows the user to select a pH, which is indicated in the figure by a red dropline. The equilibria used to calculate lead phosphate solubility (S, (M)) are also selected here: “Lead Phosphate Ksp Only”, “Phosphate Ion”, “Hydroxide Complexation”, or “Phosphate and Hydroxide” equilibria. Once selections are made, the user clicks on the “Update” button to update the dropline position and tables of calculated data.

Figure 1

Figure 1. Screenshot of the application window.

The first tab, “Lead Phosphate Solubility”, displays a log S vs pH plot showing the various equilibria. The lead phosphate solubility (S), total soluble Pb species ([Pb]soluble), and Pb2+ concentrations in mol/L are tabulated.
When “Lead Phosphate Ksp Only” is selected, S and [Pb]soluble are calculated on the basis of the lead phosphate solubility product (reaction R7) and by ignoring the pH.
(R7)
Expressing the dissolved ion concentrations in terms of the solubility gives [Pb2+] = 3S and [PO43–] = 2S. Replacing the ion concentrations in the solubility-product constant expression (reaction R7) allows us to solve for S and [Pb2+] (eq 4).
(4)
When the options for “Phosphate Ion”, “Hydroxide Complexation”, or “Phosphate and Hydroxide” equilibria are selected, the lead phosphate solubility is modified to reflect speciation using eqs 6, 7, and 8, respectively. In these equations, the fraction of the total concentration (e.g., [PO4]Total) that the free ion of interest (e.g., PO43–) constitutes, α, is included in the calculation of S. For example, [PO43–] as a function of [PO4]Total is given by eq 5, since
and
(5)
Therefore, [PO43–] = αPO43–2S.
(6)
Here
(7)
Here
(8)
To calculate the concentration of free (uncomplexed) Pb2+ when considering hydroxide, or both phosphate and hydroxide equilibria, eq 9 is used:
(9)
since
and
At intermediate pE and/or pH values, the lead hydroxide complexes are soluble so that all of the Pb(II) is dissolved (i.e., mobile). (19)
The second and third tabs display distribution diagrams of the various species as functions of pH for the hydroxide and phosphate equilibria. Lead hydroxide complex formation was modeled treating the metal as a polyprotic acid (reactions R8R11) and using constants from Table 8.2 in Water Chemistry. (21) The α expressions as functions of pH were calculated by eq 10 (21) and values at the user-selected pH are displayed in tables. These equations and equilibrium constants are given for the deprotonated ligands in the worksheet to make the system more intuitive for students.
(R8)
(R9)
(R10)
(R11)
(10)
Here, Ka1 = 1.0. Note that the Ksp for Pb(OH)2 is 4.4 × 10–15.

Student Feedback

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Undergraduate students at Trinity College used the app in two courses, Analytical Chemistry and Environmental Chemistry, during three semesters and offered feedback. On the basis of an anonymous survey with 26 respondents, students overwhelmingly found the app easy to use (100%) and helpful in understanding the impact of Le Chatelier’s principle and ion-complex formation on solubility (88% yes, 12% maybe). When asked which elements of the exercise were most helpful, students said that the plots and data visualization were helpful. One student said, “I thought the ease of use of the app was the best for learning about complex ion formation in solution with the combination of the worksheet.” In one class (environmental chemistry), one student commented in front of the entire class that the app was “way better than doing the problems [unaided by the app].”

Summary

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The lead solubility case study coupled with the app provides an accessible way for instructors to explore more complex equilibria without getting into complex calculations. Students are able to interact with these systems without the added intimidation of solving many equations.

Supporting Information

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The Supporting Information is available at https://pubs.acs.org/doi/10.1021/acs.jchemed.1c00887.

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Author
  • Authors
    • Michelle L. Kovarik - Department of Chemistry, Trinity College, 300 Summit Street, Hartford, Connecticut 06106, United StatesOrcidhttps://orcid.org/0000-0001-8225-2487
    • Janet F. Morrison - Department of Chemistry, Trinity College, 300 Summit Street, Hartford, Connecticut 06106, United States
  • Notes
    The authors declare no competing financial interest.

    The mobile-compatible, browser-based app is freely available for use at https://bazilio.shinyapps.io/LeadSolubilityCaseStudy/. An instructor’s answer key is available from the authors upon request.

References

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This article references 21 other publications.

  1. 1
    Chang, W.; Cheng, J.; Allaire, J. J.; Sievert, C.; Schloerke, B.; Xie, Y.; Allen, J.; McPherson, J.; Dipert, A.; Borges, B. Shiny: Web Application Framework for R. R Package ; 2021.
  2. 2
    R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2021.
  3. 3
    Harvey, D. Developing and Using Digital Simulations to Engage Students Learning Analytical Chemistry. In 69th Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy ; 2018.
  4. 4
    Harvey, D. Leveraging R for the Teaching of Analytical Chemistry. In 254th National Meeting of the American Chemical Society ; 2017.
  5. 5
    Harvey, D. Shiny Apps. http://dpuadweb.depauw.edu/harvey_web/shiny.html (accessed 2021-08-12).
  6. 6
    Brunning, A. Lead in the Water─The Flint Water Crisis. Compound Interest; 2016. https://www.compoundchem.com/2016/01/25/flint-water/.
  7. 7
    Davey, M. Flint Will Return to Using Detroit’s Water After Findings of Lead in Local Supply. New York Times; October 8, 2015.
  8. 8
    U.S.EPA. Reference Guide for Public Water Systems Lead and Copper Rule Comparison; U.S. Environmental Protection Agency, 2020.
  9. 9
    Bae, Y.; Pasteris, J. D.; Giammar, D. E. Impact of Orthophosphate on Lead Release from Pipe Scale in High PH, Low Alkalinity Water. Water Res. 2020, 177, 115764,  DOI: 10.1016/j.watres.2020.115764
  10. 10
    Feierabend, T.; Eilks, I. Teaching the Societal Dimension of Chemistry Using a Socio-Critical and Problem-Oriented Lesson Plan Based on Bioethanol Usage. J. Chem. Educ. 2011, 88 (9), 12501256,  DOI: 10.1021/ed1009706
  11. 11
    Cornwell, D. A.; Brown, R. A.; Via, S. H. National Survey of Lead Service Line Occurrence. J. - Am. Water Works Assoc 2016, 108, E182E191,  DOI: 10.5942/jawwa.2016.108.0086
  12. 12
    Neu, H. M.; Lee, M.; Pritts, J. D.; Sherman, A. R.; Michel, S. L. J. Seeing the “Unseeable,” A Student-Led Activity to Identify Metals in Drinking Water. J. Chem. Educ. 2020, 97 (10), 36903696,  DOI: 10.1021/acs.jchemed.9b00553
  13. 13
    Dameris, L.; Frerker, H.; Iler, H. D. The Southern Illinois Well Water Quality Project: A Service-Learning Project in Environmental Chemistry. J. Chem. Educ. 2020, 97 (3), 668674,  DOI: 10.1021/acs.jchemed.9b00634
  14. 14
    Buckley, P.; Fahrenkrug, E. The Flint, Michigan Water Crisis as a Case Study to Introduce Concepts of Equity and Power into an Analytical Chemistry Curriculum. J. Chem. Educ. 2020, 97 (5), 13271335,  DOI: 10.1021/acs.jchemed.9b00669
  15. 15
    Lasker, G. A.; Mellor, K. E.; Mullins, M. L.; Nesmith, S. M.; Simcox, N. J. Social and Environmental Justice in the Chemistry Classroom. J. Chem. Educ. 2017, 94 (8), 983987,  DOI: 10.1021/acs.jchemed.6b00968
  16. 16
    Gerdon, A. E. Connecting Chemistry to Social Justice in a Seminar Course for Chemistry Majors. J. Chem. Educ. 2020, 97 (12), 43164320,  DOI: 10.1021/acs.jchemed.0c01043
  17. 17
    ChemMatters Teacher’s Guide. https://www.acs.org/content/acs/en/education/resources/highschool/chemmatters/teachers-guide.html (accessed 2021-07-07).
  18. 18
    Edwards, M.; Triantafyllidou, S. Chloride-to-Sulfate Mass Ratio and Lead Leaching to Water. J. - Am. Water Works Assoc. 2007, 99 (7), 96109,  DOI: 10.1002/j.1551-8833.2007.tb07984.x
  19. 19
    Pankow, J. F. Aquatic Chemistry Concepts, 2nd ed.; CRC Press, 2019.
  20. 20
    Contaminant Candidate List Preliminary Regulatory Determination Support Document for Sulfate; EPA/815/R-01/015; U.S. Environmental Protection Agency (U.S. EPA), 2001.
  21. 21
    Benjamin, M. M. Water Chemistry, 1st ed.; Waveland Press, 2010.

Cited By

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This article is cited by 1 publications.

  1. Marisa Rachek, Benjamin P. Wilson. An R Shiny Application for Visualizing the Radial Distribution Functions of Hydrogen-Like Atoms. Journal of Chemical Education 2025, 102 (2) , 857-860. https://doi.org/10.1021/acs.jchemed.4c01251

Journal of Chemical Education

Cite this: J. Chem. Educ. 2022, 99, 2, 526–530
Click to copy citationCitation copied!
https://doi.org/10.1021/acs.jchemed.1c00887
Published January 6, 2022

Copyright © Published 2022 by American Chemical Society and Division of Chemical Education, Inc. This publication is available under these Terms of Use.

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  • Abstract

    Figure 1

    Figure 1. Screenshot of the application window.

  • References


    This article references 21 other publications.

    1. 1
      Chang, W.; Cheng, J.; Allaire, J. J.; Sievert, C.; Schloerke, B.; Xie, Y.; Allen, J.; McPherson, J.; Dipert, A.; Borges, B. Shiny: Web Application Framework for R. R Package ; 2021.
    2. 2
      R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2021.
    3. 3
      Harvey, D. Developing and Using Digital Simulations to Engage Students Learning Analytical Chemistry. In 69th Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy ; 2018.
    4. 4
      Harvey, D. Leveraging R for the Teaching of Analytical Chemistry. In 254th National Meeting of the American Chemical Society ; 2017.
    5. 5
      Harvey, D. Shiny Apps. http://dpuadweb.depauw.edu/harvey_web/shiny.html (accessed 2021-08-12).
    6. 6
      Brunning, A. Lead in the Water─The Flint Water Crisis. Compound Interest; 2016. https://www.compoundchem.com/2016/01/25/flint-water/.
    7. 7
      Davey, M. Flint Will Return to Using Detroit’s Water After Findings of Lead in Local Supply. New York Times; October 8, 2015.
    8. 8
      U.S.EPA. Reference Guide for Public Water Systems Lead and Copper Rule Comparison; U.S. Environmental Protection Agency, 2020.
    9. 9
      Bae, Y.; Pasteris, J. D.; Giammar, D. E. Impact of Orthophosphate on Lead Release from Pipe Scale in High PH, Low Alkalinity Water. Water Res. 2020, 177, 115764,  DOI: 10.1016/j.watres.2020.115764
    10. 10
      Feierabend, T.; Eilks, I. Teaching the Societal Dimension of Chemistry Using a Socio-Critical and Problem-Oriented Lesson Plan Based on Bioethanol Usage. J. Chem. Educ. 2011, 88 (9), 12501256,  DOI: 10.1021/ed1009706
    11. 11
      Cornwell, D. A.; Brown, R. A.; Via, S. H. National Survey of Lead Service Line Occurrence. J. - Am. Water Works Assoc 2016, 108, E182E191,  DOI: 10.5942/jawwa.2016.108.0086
    12. 12
      Neu, H. M.; Lee, M.; Pritts, J. D.; Sherman, A. R.; Michel, S. L. J. Seeing the “Unseeable,” A Student-Led Activity to Identify Metals in Drinking Water. J. Chem. Educ. 2020, 97 (10), 36903696,  DOI: 10.1021/acs.jchemed.9b00553
    13. 13
      Dameris, L.; Frerker, H.; Iler, H. D. The Southern Illinois Well Water Quality Project: A Service-Learning Project in Environmental Chemistry. J. Chem. Educ. 2020, 97 (3), 668674,  DOI: 10.1021/acs.jchemed.9b00634
    14. 14
      Buckley, P.; Fahrenkrug, E. The Flint, Michigan Water Crisis as a Case Study to Introduce Concepts of Equity and Power into an Analytical Chemistry Curriculum. J. Chem. Educ. 2020, 97 (5), 13271335,  DOI: 10.1021/acs.jchemed.9b00669
    15. 15
      Lasker, G. A.; Mellor, K. E.; Mullins, M. L.; Nesmith, S. M.; Simcox, N. J. Social and Environmental Justice in the Chemistry Classroom. J. Chem. Educ. 2017, 94 (8), 983987,  DOI: 10.1021/acs.jchemed.6b00968
    16. 16
      Gerdon, A. E. Connecting Chemistry to Social Justice in a Seminar Course for Chemistry Majors. J. Chem. Educ. 2020, 97 (12), 43164320,  DOI: 10.1021/acs.jchemed.0c01043
    17. 17
      ChemMatters Teacher’s Guide. https://www.acs.org/content/acs/en/education/resources/highschool/chemmatters/teachers-guide.html (accessed 2021-07-07).
    18. 18
      Edwards, M.; Triantafyllidou, S. Chloride-to-Sulfate Mass Ratio and Lead Leaching to Water. J. - Am. Water Works Assoc. 2007, 99 (7), 96109,  DOI: 10.1002/j.1551-8833.2007.tb07984.x
    19. 19
      Pankow, J. F. Aquatic Chemistry Concepts, 2nd ed.; CRC Press, 2019.
    20. 20
      Contaminant Candidate List Preliminary Regulatory Determination Support Document for Sulfate; EPA/815/R-01/015; U.S. Environmental Protection Agency (U.S. EPA), 2001.
    21. 21
      Benjamin, M. M. Water Chemistry, 1st ed.; Waveland Press, 2010.
  • Supporting Information

    Supporting Information


    The Supporting Information is available at https://pubs.acs.org/doi/10.1021/acs.jchemed.1c00887.


    Terms & Conditions

    Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.