Titrator 3.0 Tutorial: Calcite precipitation November 2008 Steve Cabaniss A. Introduction This brief tutorial is intended to acquaint you with some of the features of the program Titrator. It assumes that you are somewhat familiar with both Windows software and with equilibrium reactions, and that you have a copy of the Titrator program accessible on your computer. It may be useful (but not essential) to have read the Titrator User s Manual, especially the section on definitions. We will consider the equilibrium system consisting of calcium carbonate dissolved in water. The equilibrium reactions of this system are responsible for determining the ph of rainwater, the buffering capacity of natural waters, the precipitation of calcium (as calcite and related carbonate minerals) in water treatment processes and the solubility of mollusk shells in the oceans. The ph-related properties are primarily related to the acid-base equilibria of carbonic acid, bicarbonate and carbonate (H 2 CO 3, HCO 3 -, and CO 3 2- ), while the dissolution and precipitation properties are principally due to the limited solubility of CaCO 3. For this simulation, we have selected the following reactions as at least potentially important. The components selected for this system are H 2 O (always present with an activity of 1), the hydronium ion H +, the aquo calcium ion Ca 2+ and the carbonate ion CO 3 2-. It was possible to select a different set of components, but this set leads to relatively simple reactions. Note that it is not possible to select both H + and OH - as components, since in aqueous solutions their concentrations are not mutually independent. Table 1. Reaction list Log K ΔH ΔS I = 0 kj/mole J/mole K H 2 O - H + W OH - -14.00 55.8-80.7 H + 2- - + CO 3 W HCO 3 10.33-14.6 148 2 H + 2- + CO 3 W H 2 CO 3 16.68-23.76 239 Ca 2+ 2- + CO 3 0 W CaCO 3 3.22 +15 112 Ca 2+ + H + 2- + + CO 3 W CaHCO 3 11.53 +4.4 236 Ca 2+ - H + + H 2 O W CaOH + -12.7 +64.1-27.6 Ca 2+ 2- + CO 3 W CaCO 3 calcite 8.48 +10 196 Ca 2+ - 2H + + 2H 2 O W Ca(OH) 2 solid -22.71 128.6-0.4 The formation constants (K) and the thermodynamic data (ΔH and ΔS) have been taken from the NIST Standard Reference Database 46, v. 8.0. That database gives some of the reactions in the form above, while other reactions were given as the reverse (for example, calcite K sp ) and still others were not in terms of the four components used here. 1
In those cases, the formation constants were calculated by taking the negative of given log K values (for reverse reactions) or by combining log K values to obtain numbers in the table above. B. Describing the dissolved system Open Titrator by clicking on a shortcut or using the task bar. You should see a small form labeled Titrator 3.0: Define a System with two empty lists (labeled Components and Species ), three action buttons ( Solve this system, Sweep and Titrate ) and a menu bar at the top. This system definition form is used for creating, editing, and filing the information that defines our equilibrium system. Once a system has been created, we can proceed to the more complex Sweep and Titrate calculations. To enter a new component into the (now empty) data set, click on one of the white, empty cells in the component list. This will bring up the Add a new component form. Enter the information for water from Table 2 below: Table 2. Component Data Component Name H 2 O H + 2- CO 3 Ca 2+ Type of Constraint Free Total Total Total Total Molarity 55.5 0 1.00 x 10-3 1.00 x 10-3 Log Free Molarity 0-7 -6-3 Charge 0 1-2 2 Once you have entered the information for water, click the Accept button to add this component to the data set. After confirming, you will be returned to the Define a System window, which will now list water as a component. Check the water information in the component list- if it needs to be changed, click on that row of the component list to access the editor; if it does not, proceed to enter the data for the remaining components by clicking on the empty row of the component list. Note that entering 0 for the total molarity of H + does not mean the concentration of H + must be zero (that would be silly), but rather that no H + has been added to the system (which was made by dissolving CaCO 3 to a concentration of 1 mm) or that the system has no net excess of H + relative to OH -. Once you have entered all four components from Table 2 and checked the information, enter the data for the following species from Table 3 in a similar manner, first clicking on the empty row of the species list to bring up the Add New Species form. You do not need to enter thermodynamic information (ΔH and ΔS). Note that once you click on a stoichiometric coefficient cell on the Add New Species page, a second small form appears for you to change or enter the coefficients. 2
Table 3. Dissolved Species Data Species OH - - HCO 3 H 2 CO 3 CaOH + + CaHCO 3 CaCO 3 Type Diss. Diss. Diss. Diss. Diss. Diss. Log K -14.00 10.29 16.65-12.68 11.56 3.22 *********** Stoichiometric Coefficients ************** H + -1 1 2-1 1 0 2- CO 3 0 1 1 0 1 1 Ca 2+ 0 0 0 1 1 1 H 2 O 1 0 0 1 0 0 You should now have entered a functional equilibrium system. Although it is not the complete system described in Table 1 because the solid phases have not been entered, this is a good time to review the data for accuracy and then save the current system definition as a Titrator definition file (.tdf). First, give your system a title by clicking on the Title phrase near the upper left-hand corner of the System Definition form (when the program was opened, this read No Data Set ). Clicking on the Title opens the title editor form, which allows you to enter a new title and any additional text you can fit into the following three lines. This will be saved with your definition file, and might include your name, date, data source, etc. Next, use the menu command File\Save Definition to enter a standard Windows file dialog, and can save your file in any convenient directory. Test your system definition by pressing the Solve this system button. A message box should tell you that the calculation converged in 8 iterations, and the component and species lists should be updated to reflect the calculated concentrations. You may also wish to save your results in a more reader-friendly format for later examination or printing. The menu command File\Save Results allows you to save your most recent calculation results in an ASCII text file formatted for readability. 3
The component results indicate that [H + ] = 3.775 x 10-11 M (ph = -log[h + ] = 10.423), consistent with the addition of a base (CaCO 3 ) to water. The predominant uncomplexed carbonate species is [CO 3 2- ] = 3.601 x 10-4, also displayed on the component list. Calcium exists principally as the aquo ion, [Ca 2+ ] = 6.219 x 10-4 M. Scrolling to the right on this list (scroll bar at bottom) shows the mole balance errors in the converged solution- all are quite small except for water, which has a very large error (-54.5 M); this is because since the free concentration (activity) of water is known, that term was not minimized in the solution algorithm and the error merely reflects the difference between total concentration (55.5 M) and thermodynamic activity (1 by definition). The species results should show that dissolved calcium carbonate complex ([CaCO 3 0 ] = 3.716 x 10-4 M) and bicarbonate ([HCO 3 - ] = 2.652 x 10-4 M) are also major species, while the carbonic acid concentration is much lower ([H 2 CO 3 ] = 2.293 x 10-8 M). Scrolling this list to the right shows that no thermodynamic information has been entered and also displays the stoichiometry of each species. 4
C. Titrating the system Now that you have defined a system, simulate a volumetric titration by adding a strong acid titrant to a solution containing this system. Click on the Titrate button to bring up the Titrate a Solution window. This form should have a data table in the lower left and a graph in the upper right for displaying your results; these are currently blank. In the upper left part of the form, you should see two groups of data entry fields, designated Set Titrant Composition and Set Experimental Volumes. Click in the Cation drop-down box and select H +. Next, set the concentration of H + to 0.010 M. You do not need to set the anion titrant (we assume this is a strong acid with an unreactive anion like chloride). In the Volumes area, set the initial volume to 100 mls, the volume per addition to 0.50 mls, and the number of points to 61. At this point, the total volume added should now read 30 mls. Now click on the Titrate button. The data table should fill with results almost immediately, and the graph should show log[h + ] as function of volume added. (see the Figure at the top of the following page.) You can use the scroll bars to move around and inspect the data. Note that for the first point, your calculated concentrations are the same as above, while or the last point, these values have changed dramatically: [H + ] = 7.697 x 10-4 M, [CO 3 2- ] = 2.905 x 10-14 M, [Ca 2+ ] = 7.692 x 10-4 M. The titration curve on the graph has two inflection points, corresponding to the formation of HCO 3 - and H 2 CO 3 at ph ~8.1 and ph ~4.7 (the ph is simply the negative of the log concentration). Using the drop-down boxes in the lower right of the screen, select the three carbonate species CO 3 --, HCO 3 - and H 2 CO 3 to be plotted as Species 1, Species 2 and Species 3. You should be able to see how the dominant species changes from CO 3 -- to HCO 3 - to H 2 CO 3 as acid is 5
added. Next select Ca ++, CaOH + and CaCO 3 for plotting to see how calcium behaves as acid is added. Is it reasonable to neglect CaOH + and CaCO 3 in solutions with > 2 mm acid added? The graph on this form is intended for quick and dirty inspection of your results, but you can export your calculated concentrations to a spreadsheet for more extensive data analysis. Click on the File/Export menu command to open a Windows Save File dialog. Enter a useful file name (AcidCaCO3, perhaps) and save your results. You can load them into Excel or a similar program by opening the text file and checking the boxes to indicate that this file is delimited by spaces. The resulting spreadsheet should have named columns for each concentration. D. Solid precipitation Return to the System Definition screen by closing the titration window. To add potential solid phases and complete the system definition, enter the data from Table 4 into the species list. Note that designating a species as a precipitate means it is a potential precipitate- it will only form if the solubility is exceeded. Table 4. Potential Precipitating Species Data Species CaOH 2 sol CaCO 3 calcite Type. Precip. Precip. Log K -22.71 8.48 Stoichiometric Coefficients H + -2 0 2- CO 3 0 1 Ca ++ 1 1 H 2 O 2 0 Solve this new system with the possibility of solid precipitation. The algorithm solution should require 7 iterations, and the results are rather different (See the screen display on the next page). While Ca(OH) 2 has not precipitated, most of the calcium and most of the carbonate are now present as precipitated calcite (8.863 x 10-4 M). Because the solution contains less dissolved carbonate, the ph has dropped to 9.889 and free carbonate is only 3.069 x 10-5 M, a decrease of approximately tenfold. In order to have better control over the solution, click on H + in the component list and set the component type to Free and the log molarity to -12 (ph 12) and solve again. At this higher ph, calcite is even less soluble (9.306 x 10-4 M has precipitated) but the lime (Ca(OH) 2 ) is still not supersaturated. 6
Click on the Sweep button to open the Sweep a concentration window. Select H + as the component to sweep, and notice that the type of titration is now a Speciation Diagram. This is because the titrated variable (X axis on the graph) is now a log free concentration- -ph in this case. Set the increment to 0.1 and the number of points to 101 and click on the Sweep button. The calculation should take less than one second. 7
Plot the calcite concentration- At what ph does calcite become completely soluble under these conditions? Plot the three carbonate species CO 3 --, HCO 3 - and H 2 CO 3 - Over what ph range is HCO 3 - the dominant (highest concentration) species of these three? Plot all the Ca(II)-containing species, including calcite. What are the two dominant forms of Ca(II) at ph 10? At ph 7? At ph 4? Congratulations- You have now used most of the basic features of Titrator. If you wish to learn more, you may wish to read over the manual, or maybe just play around with some of the example system definition files. 8