CurTiPot pH and Acid-Base Titration 3.3.2 for Excel

CurTiPotSome features and uses of CurTiPot (hover on red mark at Q2 to read about the name and origins of the program) pH calculation of aqueous solutions (>30 species in equilibrium) Simulation of simple and complex acid-base titration curves - Virtual Titrator generation of curves with equally spaced data in pH or volume simulation of experimental random errors in pH and volume overlay of multiple simulated curves for comparison Data analysis of real and simulated curves Evaluation of curves by interpolation, smoothing and automatic endpoint detection determination of concentrations and refinement pKas by non-linear regression Distribution of species and protonation of bases vs. pH and vs. volumeRead the License first (place mouse on red dot at left); if you agree with all terms, you can use CurTiPot in educational and non-commercial applicationsConfigure Microsoft Excel to medium security (Tools/Macro/Security/Security level/Medium), open the curtipot_.xls file and activate the macrosThe Regression module becomes operational after activation of the Solver supplement; you can do this laterRegularly check for updated releases at the authors site www2.iq.usp.br/docente/gutz (University of So Paulo, Brasil)Ionic strength and activity coefficient corrections available only in the pH calc moduleExperimental pH values are assumed free of calibration, junction potential and alkaline errors of the sensor (to be corrected previously for most accurate results)The author reserves the right not to be responsible for the correctness, completeness, accuracy and bug-free operation of the freeware CurTiPotPlease report errors and incompatibilities of Curtipot (developed for Excel 9 and 10) to the author;Use the e-mail:gutz@iq.usp.brClick on the pH_calc tab, at the botton of the page; If you are a high shool student and can't grasp all the stuff at once, look for the pH at the dark blue cell H21;Click on Calculate pH; clear all concentrations and check the pH of water; test various solutions with one ore more species of the preloaded acid-base systems;Read local instructions in comment boxes by placing the mouse on cells with red marks (like in Q2, Q13, Q15 and Q21 in this page);Switch to the preloaded Simulation of the titration of phosphoric acid; start clicking on the buttons at the left of the figure; change some concentrations afterwards;Find endpoints of your real or simulated curves with Evaluation. There are buttons to load the last titration curve from Simulation;Play and learn with the Distribution module; enjoy the Graphs before you advance to the less simple but more powerful Regression to fit concentrations and pKas;Save your data, settings and results in Curtipot_anyname.xls files to preserve the original software (optionally deleting unused spreadsheets, but not the this first one);Dr. Ivano Gebhardt Rolf Gutz - Full Professor (since 1992)The software CurTiPot, version 1.0 for DOS (Disk Operating System, Microsoft), was created in 1991 in Turbo Basic and launched in 1992.Instituto de Qumica - Universidade de So Paulo, So Paulo, SP, BrazilVersion 2 appeared in 1992. Besides volumetry, it accepts data from titrations with coulometric generation of reactants.Head of the Chemistry Department of IQ-USP (2004-2006; 2006-2008)Version 3.0 for Excel is an evolution of the DOS version. A new Regression module is the most significant improvement. It was released in 2006 (in Portuguese).Member of the Editorial Boards of Talanta (2005-2007) and Electrochemistry Communications (2005 -->)Version 3.1 was the first translated to English. It was launched at May 1st, 2006, at the site www2.iq.usp.br/docente/gutz/Curtipot_.html.Honored with the National Order of Scientific Merit, Brazil, 2007Version 3.2, released in December 2006, includes a separate pH_calc module with activity coefficient estimation.Fellow of International Union of Pure and Applied ChemistryVersion 3.3, from January 2008, has a frindlier interface with the Database; logarithmic distribution diagram generation overlayed on the titration curve was added.Research interests:Some 30 thousand copies of CurTiPot 3.1 and 3.2. were downloaded to over 100 countries from the author's site during the first 20 months; 200 other software sites distribute the program.CV, Publications, see: www2.iq.usp.br/docente/gutzCurTiPot was written almost during weekends and holidays, in So Paulo and, sometimes, at the beach: http://maps.google.com/maps?hl=en&ie=UTF8&om=1&z=15&ll=-23.822097,-45.464902&spn=0.020101,0.028753&t=h

Version 3.3.2 (2008) for MS-Excel 1997 - 2007ApplicationsInstallationRemarksFast StartCopyright 1992 - 2008Prof. Ivano G.R. Gutzgutz@iq.usp.brhttp://www2.iq.usp.br/docente/gutz/Curtipot_.htmlHistoryThis freeware is a courtesy ofpH and Acid-Base Titration Curves:Analysis and SimulationThe acronym CurTiPot means Potentiometric Titration Curves (in reversed order).

Originally written in Turbo Basic for DOS and first demonstrated and distributed during the 15th Annual Meeting of the Brazilian Chemical Society (1992) versions 1 and 2 (not translated do English) became widely diffused in Brazil.

The Excel version was launched in 2006 and presents extra features, like the powerful Regression module and a separated pH calculation module, that takes activity coefficients and ionic strength in account.

Sitemeter tracks over one thousand downloads of the freeware monthly to one hundred countries from my website http://www2.iq.usp.br/docente/gutz/Curtipot_.html. Many more copies of CurTiPot are downloaded from over 200 sowtware distribution sites.

Feedback by e-mail with criticism and suggestions is welcomed (and answered when I find time).

If you are really satisfied with CurTiPot, please link to http://www2.iq.usp.br/docente/gutz/Curtipot_.html from your homepage,

Ivano G. R. Gutz www2.iq.usp.br/docente/gutzEnd user license agreement

Thank you for your interest in the CurTiPot version 3 freeware, a workbook of spreadsheets for Excel (proprietary software of Microsoft), authored by Dr. Ivano G. R. Gutz, Professor of the Institute of Chemistry of the University of So Paulo, So Paulo, Brazil, now on referred as Author of CurTiPot. Please examine the License Agreement before you start using CurTiPot.

Personal or Educational Use OnlyThe Author grants you a non-exclusive and non-transferable freeware license of CurTiPot for your personal or educational use at home, in classroom or in academic laboratories. If you intend to make commercial use of CurTiPot, including but not limited to any profitable non-educational activity or selling or distributing CurTiPot for payment, you must obtain a written permission from the Author in advance.

RestrictionsYou may introduce modifications in the spreadsheets to suit your needs, but you are not allowed to remove the original notices about the intellectual property of the workbook and macros, in special but not only from the front page. You shall not distribute copies of modified versions without approval by the Author of the clearly identified changes.

DistributionYou may share unmodified copies of CurTiPot with students and colleagues that do not have access to the Internet, if they agree to be bound to these Terms and Conditions and as long as you take all reasonable precautions to avoid exposure of your copy to viruses. To minimize risks, it is highly advisable, to use only updated copies obtained from the Authors download page.

Changes to Terms and ConditionsThe author reserves the right to update CurTiPot and to modify these Terms and Conditions at its sole discretion, without notice or liability to you. You agree to be bound by these Terms and Conditions, as modified. Please download updated versions of CurTiPot from time to time and review the Terms and Conditions.

Disclaimer of WarrantiesThe Author disclaims any responsibility for any harm resulting from your use (or use by your colleagues or students) of CurTiPot and third party software used in conjunction with it. CurTiPot is provided "AS IS," with no warranties whatsoever, express, implied, and statutory, including, without limitation, the warranties of merchantability, fitness for a particular purpose, and non-infringement of proprietary rights. The author also disclaims any warranties regarding the security, reliability, accuracy, stability, convergence and performance of CurTiPot. You understand and agree that you download and/or use CurTiPot at your own discretion and risk and that you will be solely responsible for any consequences of incorrect information or results obtained with CurTiPot. This license does not entitle the Licensee to receive from the Author any extra documentation not contained in the program file, support or assistance by any means, or enhancements or updates of CurTiPot other than those made available for download at the Authors site.

Limitation of LiabilityUnder no circumstances shall the Author or his employer be liable to any user on account its use or misuse of CurTiPot.

If you accept the terms and conditions given above, you are entitled to use CurTiPot free of charge for unlimited time and number of uses. The Author will enjoy your comments, error reports and suggestions by e-mail.Gutz:Before using the Regression module, check if Solver figures under Data / Analysis / ? (Solver) in Excel 2007 or under the Tools list in former versions of Excel. If not, close CurTiPot, open a blank page and install the Solver. For Excel 2003, under Tools/Supplements/check the Solver box, find it and install. If the supplement is not pre-loaded on the HD, insert the Office installation disk and upload the file.

This installation is required only once on a PC.

Open CurTiPot again and start using the regression module.Gutz:a) Invention, development, miniaturization, automation and application of analytical devices, systems and methods, with preference for electroanalytical, electrophoretic and spectroeletroanalytical flow systems, including microfluidic ones.b) Research in environmental chemistry with emphasis on the liquid phase and related chemistry of the atmosphere in the So Paulo megacity the largest laboratory of ethanol use as fuel; development of sampling, speciation and determination methods.

pH_calc pH Calculatorread commentpKas of the acids and bases in the solutionClick on K2 to Q2; select acids/bases; click on J2; read M1Overall protonation constants = bp = SKp (calculated by the program)pKas loaded from the DatabaseSolution composition - reagents added, in mol/LFill out concentrations; Enter; Click button B18.12845173pKa(n) = -log Kd(HB-->B) = log Kp(1)Click on J2 to use these pKas in the pH calculationAcid / BaseProtonationAcetic acidAmmoniaPhosphoric acidCitric acidEDTAAlanineCarbonic acidAcid / BaseAcetic acidAmmoniaPhosphoric acidCitric acidEDTAAlanineCarbonic acidAcid / BaseAcetic acidAmmoniaPhosphoric acidCitric acidEDTAAlanineCarbonic acidAcid / BaseAcetic acidAmmoniaPhosphoric acidCitric acidEDTAAlanineCarbonic acid[B]Charge of B-10-3-3-4-1-2Charge of B-10-3-3-4-1-2Charge of B-10-3-3-4-1-2[HB]0.061pKa14.7579.2442.1483.1280.0002.3486.352bp15.715E+041.754E+092.239E+122.489E+061.479E+107.362E+092.133E+10pKa1 = logKpn4.7579.2442.1483.1280.0002.3486.352[H2B]0.039pKa27.1994.7611.5009.86710.329bp20.000E+000.000E+003.540E+191.435E+111.905E+161.641E+124.797E+16pKa2 = logKpn-10.0000.0007.1994.7611.5009.86710.329[H3B]pKa312.3506.3962.000bp30.000E+000.000E+004.977E+211.928E+149.120E+180.000E+000.000E+00pKa3 = logKpn-20.0000.00012.3506.3962.0000.0000.000[H4B]pKa42.680bp40.000E+000.000E+000.000E+000.000E+009.120E+200.000E+000.000E+00pKa4 = logKpn-30.0000.0000.0000.0002.6800.0000.000[H5B]pKa56.110bp50.000E+000.000E+000.000E+000.000E+002.884E+220.000E+000.000E+00pKa5 = logKpn-40.0000.0000.0000.0006.1100.0000.000[H6B]SSpKa610.170bp60.000E+000.000E+000.000E+000.000E+002.884E+220.000E+000.000E+00pKa6 = logKpn-50.0000.0000.0000.00010.1700.0000.000S[HiB]000.100001.000E-01ElectrolyteNa+K+Ca++Cl-NO3-ClO4--Kw1.01E-14S[H]000.13900001.390E-01Ion charge112-1-1-1SziCi00-0.1610000-0.161pKw13.997ElectrolyteNa+K+Ca++Cl-NO3-ClO4--Davies equation parametersColor codingCi (mol/L)0.161for activity coefficient estimationD o n o t c h a n g eziCi0.1610000000.161A0.509C h a n g e c r i t e r i o u s l yCharge BalanceOK0000b0.300Fill out, change or leave blankResults at chemical equilibriumCorrection of ionic strength effects'-log of ion activities'-log of ion concentrationsNo ion-ion interaction corrections (unity activity coefficients)Ionic strength0.2220g H+0.743a H+9.865E-08pH7.006pOH6.991p[H]6.877p[OH]6.862"p[H]"7.393"p[OH]"6.604Equilibrium concentration of species, in mol/LStepwise apparent constants recalculated for I =0.22200Overall apparent protonation constants recalculated for I =0.22200Acid / Base protonationAcetic acidAmmoniaPhosphoric acidCitric acidEDTAAlanineCarbonic acid[H+]Acid / BaseAcetic acidAmmoniaPhosphoric acidCitric acidEDTAAlanineCarbonic acidAcid / BaseAcetic acidAmmoniaPhosphoric acidCitric acidEDTAAlanineCarbonic acid[B]1.221E-061.79E-07Charge of B-10-3-3-4-1-2Charge of B-10-3-3-4-1-2[HB]6.100E-02pK'an = logK'p14.4999.24411.5755.6219.1379.6099.813b'p13.15E+041.75E+093.76E+114.18E+051.37E+094.06E+096.49E+09[H2B]3.900E-02[OH-]pK'an-1 = logK'p26.6834.2455.3352.3486.094b'p21.81E+187.34E+092.97E+149.05E+118.06E+15[H3B]4.018E-071.37E-07pK'an-2 = logK'p31.88982.86982.1635b'p31.40E+205.44E+124.32E+16[H4B]pK'an-3 = logK'p41.7418b'p42.39E+18[H5B]pK'an-4 = logK'p51.5000000606b'p57.54E+19[H6B]SSpK'an-5 = logK'p60.2582347081b'p61.37E+20S[HiB]0.000E+000.000E+001.000E-010.000E+000.000E+000.000E+000.000E+001.000E-01pK'w13.74K'w1.82E-14Species distribution (fractional composition, in %)at pH =7.006and p[H] =6.877Acid / Base protonationAcetic acidAmmoniaPhosphoric acidCitric acidEDTAAlanineCarbonic acid% B99.580.430.0094.730.530.190.10% HB0.4299.5761.005.2696.6999.8185.77% H2B39.000.012.780.0014.14% H3B0.000.000.00% H4B0.00% H5B0.00% H6B0.00% S[HiB]100.00100.00100.00100.00100.00100.00100.00Activity coefficient (g) of speciesat pH =7.006and I =0.2220Acid / Base protonationAcetic acidAmmoniaPhosphoric acidCitric acidEDTAAlanineCarbonic acidg B0.7431.0000.0690.0690.0090.7430.304g HB1.0000.7430.3040.3040.0691.0000.743g H2B0.7430.7430.3040.7431.000g H3B1.0001.0000.743g H4B1.000g H5B0.743g H6B0.304EletrolyteNa+K+Ca++Cl-NO3-ClO4--gi0.7430.7430.3040.7430.7430.743Average protonation (h) of (conjugated) basesat pH =7.006Acid / BaseAcetic acidAmmoniaPhosphoric acidCitric acidEDTAAlanineCarbonic acidh0.0040.9961.3900.0531.0220.9981.140

Calculate pH and related equilibrium dataGutz:Summation of the concentrations of all H+ potentially dissociable from reagents available in the solution, coined CHtotal. to be equaled with CHcalc obtained by iteractively changing fitting the pH value.Gutz:These activity coefficients were estimated with the Davies equation and their uncertainty increases with the ionic strength. More information in cells A21 e K15.Gutz: Leave blank/fill out with the concentration (mol/L) of fully deprotonated base (of a conjugated acid) added to the solution, e.g.: [Na2CO3], [Na3PO4], [NH4OH], [pyridine] or [Na4EDTA]Gutz:Leave blank/fill out with the concentration (mol/L) of monoprotonated base (or acid, HB) added to the solution, e.g.: [Acetic acid], [NH4+], [pyridonium], [NaHCO3] or [Na2HPO4]Gutz: Leave blank/fill out with the concentration (mol/L) of biprotonated base (H2B) added to the solution, e.g.: [H2CO3], [H2Na2EDTA] or [NaH2PO4]Gutz:dLeave blank/fill out with the concentration (mol/L) of triprotonated base (H3B) added to the solution, e.g.: [H3PO4]Gutz:Sum of concentrations of all forms of the base B introduced in the solution: [HB] + [H2B] + [H3B] + ...Gutz:Total concentration of each base (regardless of the protonation level of the added component) in columns B to H; grand total in column I.Gutz:Maximum H+ concentration available from the full deprotonation of all forms of HiB used in the formulation of the solution: [HB] + 2[H2B] + 3[H3B] + ...Gutz:Maximum concentration of H+ that could possibly be dissociated from all the components added to the solution.Gutz:Cizi = ion concentration times charge of the ion (e.g., 2[Ca2+]).Gutz:Summation of Cizi of all acidic and basic ingredients; if not zero, it shoud be neutralized by counterions in the electrolyte.Gutz:Fill out with the concentration of counter-ions of the salts of acids and bases, as well as other electrolytes added to the solution (e.g., to adjust ionic strength).

This data is not essential but it will reduce the uncertainty of the estimation of activity coefficients and pH.

Note: sulfate, a common divalent anion, is only fully dissociated a pH>4 because of its first protonation constant of 100 (= pKa2 2 of sulfuric acid). To deal more accurately with this acid/base system, load sulfuric acid from the Database (instead of defining it as electrolyte).Gutz:Name of the ion (strong electrolyte). To change it, write in cell K11.Gutz:Para adicionar NH4Cl 0,1 mol/L soluo, lanar 0,1 nesta linha, coluna do Cl- e 0,1 na linha 5, coluna do hidrxido de amnio.

NaCl 0,1 mol/L, lanar 0,1 em Na+ e 0,1 em Cl-.Gutz:Cizi = ion concentration times charge of the ion (e.g., 2[Ca2+]).Gutz:Summation of Cizi of all electrolytesGutz:Electroneutrality is not a must to calculate the pH (by clicking B18). However, there will be some extra uncertainty in the results due to incorrect ionic strength calculation.Gutz:Charge Balance of all Cizi of ingredients added (before equilibrium); if not zero, it shoud be neutralized by adding counterions.pH Calculator - Fast start:

This module calculates the pH of simple or complex aqueous solutions, with correction for ionic strength effect based on the Davies equation. Here are some exercises to become familiar with the main resources:

- Click on the button "Calculate pH ..." (cell B18) and check cell H21 for the solution of the default acid-base chemical equilibrium problem: a buffer mixture of NaH2PO4 and Na2HPO4.

- Change the default concentrations in cells D5 and D6; press Enter; click Calculate pH.

- Write the value of D5 in D4 and clear D5; write D6 in D7 and clear D6; click Calculate pH.

- Change pKa2 (M6), e.g. 7.2 to 9.2, Enter, Calculate pH.

If you haven't learned what acid-base dissociation constants are, or whatfor acids are titrated, perhaps you should go through a simple tutorial first, e.g., a flash animated one: http://www2.wwnorton.com/college/chemistry/gilbert/tutorials/ch16.htm

- Check the pH of water at 25 C: Delete D4 and D7, Enter, Calculate pH.

- Compare the values of pH, p[H] and "pH" in line 21; have a look at other results in lines 21 to 57 (you don't need to understand all these figures now - some are for advanced users).

- formulate multicomponent mixtures and solve them instantly.

- load other acid/base systems clicking on K2, selecting another acid and clicking on J2.

This acid-base pH calculator first appeared as a separated module in the 3.2 Excel version of CurTiPot, an evolution of the 1.0 Turbo Basic version launched in 1992.

Prof. Dr. Ivano G. R. Gutz www2.iq.usp.br/docente/gutzGutz:Name of the acid or base (of the conjugated acid).To change it, write in cell K3 or load a different system from the DatabaseGutz:Definition of pH, see:http://www.iupac.org/goldbook/P04524.pdfActivity coefficient dependence from I, see: http://www.beloit.edu/~chem/Chem220/activity/index.htmlGutz: Write the name (or formula) of ions of strong electrolytes (not involved in protonation equilibria), like counter-ions of salts of weak acids.

This is required for ionic strength calculation and activity coefficient estimation.Gutz:Fill out with the charge of the ion.Gutz:The ionic dissociation product of water changes with temperature and ionic strength, I. For pure water at 25C, the accepted value is 13.997 (or 14.00). The program corrects for I variation using the Davies eq. and displays the resulting value in K31.Gutz:

A and b are parameters of the Davies equation, used for activity coefficient estimation. They depend on temperature, dielectric constant, electrolyte, etc. The recommended values for water at 25C are: A=0.509; b=0.300.

The Davies eq. does not require the size of different hydrated ions but, to some degree, the A and b parameters may be empirically adjusted to more closely describe a given electrolyte.For example: For NaCl + HCl solutions, A=0.43 and b=0.49 conducts to gH+ values in excellent agreement with those provided (up to 0.5 mol/kg) in http://www.iupac.org/projects/2000/Aq_Solutions.zipon base of more complete equations fitted to experimental data.

For phosphate solutions, A=0.51 and b=0.20 seems appropriate at pHs above neutrality.Gutz:Read comment in cell J6 (above) and K15.Gutz:

CurTiPot recalculates apparent equilibrium constants at the ionic strength, I, of the solution from thermodynamic constants (I=0) by estimating activity coefficients with help of the Davies equation. The accuracy is good for I0.01 mol/L, where the effective hydrated ion size of the species also becomes relevant. As a general trend, the activity coefficient decreases with the increase of I (due to ion-ion interactions like the formation of ion pairs) down to a minimum in the region of I = 0.3 to 0.7 mol/L. At such high values of I, the association constants of each with all other major ions need to be feed to the equations or empirically fitted, to reduce uncertainty in estimates. The Davies equation, based on the average behavior of the ions and used here to deal with in complex mixtures for witch such constants are not readily available, renders estimates with greater uncertainty.Gutz: The pKas shown here are copied automatically from the Database by changing K2 to Q2.

See U5 to understand why pKa1 = -logKpnGutz:See R5 to understand the conversion of pKa in logKpGutz:See comment in cell M1 on how to change acids ans bases.Gutz:Selecting/editing names, charges ans pKas. Options:a) Write directly in the cells K3 to Q10 and R3 to T6; b) Click on names in line 2, slide along the list, click on another name; finally, click on J2 to load the constants from the Database.

Frequently used acids missing in the Database should be added to it.Load pKas of these HiB --->Gutz: Options:a) pKa1 , -logarithm of the dissociation constant of a monoprotic acid or first constant for a polyprotic system.b) logKpi, logarithm of the protonation constant of a (conjugated) base, with i=1 for a monoprotonable base and i= n (most deprotonated species) for polyprotic systems (more about at U5);c) pKw - pKbi, for -log of the dissociation constant of a base, with i=1 for a monoprotonable base and i= n (most deprotonated species) for polyprotonable base.

Numerically, values of a, b e c are taken as similar.Gutz: Options:a) pKa2 , -log of the 2nd dissociation constant of a biprotic or polyprotic acid; b) logKpi, log of the first protonation constant of a biprotonable (conjugated) base or i=n-1 for a system with n protonations;c) pKw - pKbi, with i=1 for a biprotonable base or i=n-1 por a base with n protonations; for a monoprotonable base, leave blank.Gutz: Charge of the most deprotonated species of an acid or base in accordance with the highest pKa for the system, e.g., 0 for NH3 or pyridine-1 for acetate/acetic acid-2 for carbonate//carbonic acid-3 for phosphate///phosphoric acid -4 for EDTAGutz:The betas are cumulative (or global) protonation constants, obtained by multiplying the protonation constants Kp from 1 to i, with i stepping up to n, the maximum number of protons accepted by a (conjugated) base (same as the maximum number os dissociable protons of an acid, but in reversed order).

Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa.

Protonation constants, Kp, and betas are preferred here in agreement with the most extensive compilations of equilibrium constants, e.g., Critical Stability Constants, Vol. 14 (complete references in the Database), and because the equations become unified with those used for metal-ligand-proton equilibria, based on formation (instead of dissociation) constants.

SimulationVirtual Titrator Simulation of curvesread instructionspKas of the acids and bases in the solutionClick on K2 to Q2; select acids/bases; click on J2; read M1Overall protonation constants = bp = SKp (calculated by the program)pKa(n) = -log Kd(HB-->B) = log Kp(1)pKas loaded from the DatabaseTitrand (sample) and titrant (standard) composition (concentrations in mol/L)58981263TitrantTitrandTitrantTitrandClick on J2 to use these pKas in the SimulationTitrandSpeciesEDTAPhosphoric acidL-Glutamic acidAcetic acidAmmoniaHClCarbonic acidAcid / BaseEDTAPhosphoric acidL-Glutamic acidAcetic acidAmmoniaHClCarbonic acidStrong ACIDStrong BASECarbonic ac.Acid / BaseEDTAPhosphoric acidL-Glutamic acidAcetic acidAmmoniaHClCarbonic acidStrong ACIDStrong BASECarbonic ac.Acid / BaseEDTAPhosphoric acidL-Glutamic acidAcetic acidAmmoniaHClCarbonic acid[B]Charge of B-4-3-1-10-1-2-1-1-2Charge of B-4-3-1-10-1-2-1-1-2Charge of B-4-3-1-10-1-2[HB]pKa10.0002.1482.2304.7579.244-7.0006.352-615.7456.352bp11.479E+102.239E+128.913E+095.715E+041.754E+091.000E-072.133E+101.000E-065.559E+152.133E+10pKa1 = logKpn0.0002.1482.2304.7579.244-7.0006.352[H2B]pKa21.5007.1994.42010.32910.329bp21.905E+163.540E+192.344E+140.000E+000.000E+000.000E+004.797E+160.000E+000.000E+004.797E+16pKa2 = logKpn-11.5007.1994.4200.0000.0000.00010.329[H3B]0.05pKa32.00012.3509.950bp39.120E+184.977E+213.981E+160.000E+000.000E+000.000E+000.000E+00pKa3 = logKpn-22.00012.3509.9500.0000.0000.0000.000[H4B]pKa42.680bp49.120E+200.000E+000.000E+000.000E+000.000E+000.000E+000.000E+00pKa4 = logKpn-32.6800.0000.0000.0000.0000.0000.000[H5B]pKa56.110bp52.884E+220.000E+000.000E+000.000E+000.000E+000.000E+000.000E+00pKa5 = logKpn-46.1100.0000.0000.0000.0000.0000.000[H6B]SSpKa610.170bp62.884E+220.000E+000.000E+000.000E+000.000E+000.000E+000.000E+00pKa6 = logKpn-510.1700.0000.0000.0000.0000.0000.000S[HiB]00.05000005.000E-02pKw13.997Kw1.007E-14S[H]00.15000001.500E-01TitrantStrong ACIDStrong BASECarbonic ac.Volumes of titrand and titrant (in mL)[B]0.1TitrandWaterSum[HB]Dispensedadded(initial vol.)Color coding[H2B]SS20020.00Dispersion simulationTitration speedD o n o t c h a n g eS[HiB]00.101.00E-01Titrant max.N of titrant additionsS pH=0.000Slower0C h a n g e c r i t e r i o u s l yS[H]0000.00E+0050.0050S Vol=0.000Fasterdelay (s)Fill out, change or leave blankinitial "pH"1.806Data ID on curvesCopying curvesResizing axisOther graphicsData analysisCurvas anteriores retidasVadd"pH"Vadd"pH"[H]CHtot =Dill. factorDill. Factorh1h2h3h4h5h6h7h1 titranth2 titranth3 titrantVolpHVolpHVolpHVolpHVolpHVolpHVolpHVolpHVolpHVolpHVolpHVolpHVolpH(mL)simulatedwith "error" (do not use)simulated with "error"CHcalcTitrand (sample)Titrant (buret)EDTAPhosphoric acidL-Glutamic acidAcetic acidAmmoniaHClCarbonic acidStrong ACIDStrong BASECarbonic ac.11223344556677889910101111121213130.0001.8061.563E-021.500E-011.000E+000.000E+002.68731.00002.1572.0209.540E-031.354E-019.026E-019.735E-022.57291.00004.0962.2355.822E-031.245E-018.300E-011.700E-012.45011.00005.7542.4493.553E-031.165E-017.766E-012.234E-012.33311.00007.0772.6642.168E-031.108E-017.386E-012.614E-012.23361.00008.0612.8781.323E-031.069E-017.127E-012.873E-012.15681.00008.7493.0938.073E-041.044E-016.957E-013.043E-012.10191.00009.2103.3074.927E-041.027E-016.847E-013.153E-012.06471.00009.5083.5223.006E-041.017E-016.778E-013.222E-012.04031.00009.6973.7361.835E-041.010E-016.735E-013.265E-012.02481.00009.8173.9511.120E-041.006E-016.708E-013.292E-012.01491.00009.8944.1656.832E-051.004E-016.690E-013.310E-012.00861.00009.9444.3804.169E-051.002E-016.679E-013.321E-012.00431.00009.9824.5942.544E-051.001E-016.671E-013.329E-012.00111.000010.0144.8091.552E-059.995E-026.664E-013.336E-011.99811.000010.0505.0239.474E-069.983E-026.656E-013.344E-011.99471.000010.0985.2385.781E-069.967E-026.645E-013.355E-011.99001.000010.1705.4523.528E-069.944E-026.629E-013.371E-011.98291.000010.2825.6672.153E-069.907E-026.605E-013.395E-011.97181.000010.4575.8811.314E-069.850E-026.567E-013.433E-011.95431.000010.7306.0968.017E-079.763E-026.508E-013.492E-011.92701.000011.1446.3104.892E-079.633E-026.422E-013.578E-011.88561.000011.7486.5252.985E-079.450E-026.300E-013.700E-011.82521.000012.5776.7391.822E-079.209E-026.139E-013.861E-011.74231.000013.6266.9541.112E-078.922E-025.948E-014.052E-011.63741.000014.8247.1686.784E-088.615E-025.743E-014.257E-011.51761.000016.0447.3834.140E-088.323E-025.549E-014.451E-011.39561.000017.1467.5982.526E-088.076E-025.384E-014.616E-011.28541.000018.0417.8121.542E-087.886E-025.258E-014.742E-011.19601.000018.7068.0279.408E-097.751E-025.167E-014.833E-011.12951.000019.1698.2415.741E-097.659E-025.106E-014.894E-011.08311.000019.4788.4563.503E-097.599E-025.066E-014.934E-011.05241.000019.6778.6702.138E-097.561E-025.041E-014.959E-011.03251.000019.8048.8851.305E-097.537E-025.025E-014.975E-011.01991.000019.8869.0997.961E-107.521E-025.014E-014.986E-011.01191.000019.9419.3144.858E-107.511E-025.007E-014.993E-011.00671.000019.9829.5282.965E-107.503E-025.002E-014.998E-011.00321.000020.0189.7431.809E-107.497E-024.998E-015.002E-011.00041.000020.0599.9571.104E-107.489E-024.993E-015.007E-010.99771.000020.11510.1726.737E-117.478E-024.986E-015.014E-010.99451.000020.20010.3864.111E-117.463E-024.975E-015.025E-010.98991.000020.33310.6012.509E-117.438E-024.959E-015.041E-010.98291.000020.54810.8151.531E-117.399E-024.932E-015.068E-010.97191.000020.89611.0309.342E-127.336E-024.890E-015.110E-010.95451.000021.45911.2445.701E-127.236E-024.824E-015.176E-010.92741.000022.36511.4593.479E-127.081E-024.721E-015.279E-010.88630.999923.81811.6732.123E-126.846E-024.564E-015.436E-010.82620.999926.15511.8881.296E-126.500E-024.333E-015.667E-010.74360.999929.98312.1027.906E-136.002E-024.001E-015.999E-010.63900.999836.64412.3174.824E-135.296E-023.531E-016.469E-010.51920.999650.00012.5312.944E-134.286E-022.857E-017.143E-010.39730.9994

Simulation

pH_simpH_sim_dispret_1ret_2ret_3ret_4ret_5ret_6ret_7ret_8ret_9ret_10ret_11ret_12ret_13Volume of titrant (mL)pHTitrations of hydrochloric, phosphoric and glutamic acids (20 mL, 0.05 mol/L, with 0.1 mol/L NaOH)

DistributionDistribution Diagrams and Protonation Curvesread commentAcid/base systemOverall protonation constantsColor coding of speciesColor coding1for the pKasbpa BD o n o t c h a n g eOptions of the A8 sliderpKa1 = logKpn4.757b15.715E+04a HBC h a n g e c r i t e r i o u s l ySimulated titration curveof the acid/base systempKa2 = logKpn-10.000b20.000E+00a H2BData ID on curvesFill out, change or leave blankTitration curve under EvaluationAcetic acidpKa3 = logKpn-20.000b30.000E+00a H3BHow to copy/paste a curveTitration curve under Regressiona) as a function of pH e b) overlayed onpKa4 = logKpn-30.000b40.000E+00a H4BHow to change the axis of a curveNo titration curve4pKa5 = logKpn-40.000b50.000E+00a H5BpKa6 = logKpn-50.000b60.000E+00a H6BMolar fraction of each species as a funciton of pHMolar fraction of each species during titrationlogarithm of molar fraction of each species as a funciton of pHlogarithm of molar fraction of each species during titrationCharge of B-1Protonations1alpha 0alpha 1alpha 2alpha 3alpha 4alpha 5alpha 6alpha 0alpha 1alpha 2alpha 3alpha 4alpha 5alpha 6scalingscalinglog alpha 0log alpha 1log alpha 2log alpha 3log alpha 4log alpha 5log alpha 6samesamelog alpha 0log alpha 1log alpha 2log alpha 3log alpha 4log alpha 5log alpha 6scalingpHhBHBH2BH3BH4BH5BH6BVolpHhBHBH2BH3BH4BH5BH6BpH/14n*pH/14[H][OH]BHBH2BH3BH4BH5BH6BVolpHBHBH2BH3BH4BH5BH6BpH (-8 a 0)0.0001.0000.0001.0000.00014.000-4.757-0.0000.2001.0000.0001.0000.20013.800-4.557-0.0000.4001.0000.0001.0000.40013.600-4.357-0.0000.6001.0000.0001.0000.60013.400-4.157-0.0000.8001.0000.0001.0000.80013.200-3.957-0.0001.0001.0000.0001.0001.00013.000-3.757-0.0001.2001.0000.0001.0001.20012.800-3.557-0.0001.4001.0000.0001.0001.40012.600-3.357-0.0001.6000.9990.0010.9991.60012.400-3.157-0.0001.8000.9990.0010.9991.80012.200-2.957-0.0002.0000.9980.0020.9982.00012.000-2.758-0.0012.2000.9970.0030.9972.20011.800-2.558-0.0012.4000.9960.0040.9962.40011.600-2.359-0.0022.6000.9930.0070.9932.60011.400-2.160-0.0032.8000.9890.0110.9892.80011.200-1.962-0.0053.0000.9830.0170.9833.00011.000-1.765-0.0083.2000.9730.0270.9733.20010.800-1.569-0.0123.4000.9580.0420.9583.40010.600-1.376-0.0193.6000.9350.0650.9353.60010.400-1.186-0.0293.8000.9010.0990.9013.80010.200-1.002-0.0454.0000.8510.1490.8514.00010.000-0.827-0.0704.2000.7830.2170.7834.2009.800-0.663-0.1064.4000.6950.3050.6954.4009.600-0.515-0.1584.6000.5890.4110.5894.6009.400-0.387-0.2304.8000.4750.5250.4754.8009.200-0.280-0.3235.0000.3640.6360.3645.0009.000-0.196-0.4395.2000.2650.7350.2655.2008.800-0.134-0.5775.4000.1850.8150.1855.4008.600-0.089-0.7325.6000.1260.8740.1265.6008.400-0.058-0.9015.8000.0830.9170.0835.8008.200-0.038-1.0816.0000.0540.9460.0546.0008.000-0.024-1.2676.2000.0350.9650.0356.2007.800-0.015-1.4586.4000.0220.9780.0226.4007.600-0.010-1.6536.6000.0140.9860.0146.6007.400-0.006-1.8496.8000.0090.9910.0096.8007.200-0.004-2.0477.0000.0060.9940.0067.0007.000-0.002-2.2457.2000.0040.9960.0047.2006.800-0.002-2.4457.4000.0020.9980.0027.4006.600-0.001-2.6447.6000.0010.9990.0017.6006.400-0.001-2.8447.8000.0010.9990.0017.8006.200-0.000-3.0438.0000.0010.9990.0018.0006.000-0.000-3.2438.2000.0001.0000.0008.2005.800-0.000-3.4438.4000.0001.0000.0008.4005.600-0.000-3.6438.6000.0001.0000.0008.6005.400-0.000-3.8438.8000.0001.0000.0008.8005.200-0.000-4.0439.0000.0001.0000.0009.0005.000-0.000-4.2439.2000.0001.0000.0009.2004.800-0.000-4.4439.4000.0001.0000.0009.4004.600-0.000-4.6439.6000.0001.0000.0009.6004.400-0.000-4.8439.8000.0001.0000.0009.8004.200-0.000-5.04310.0000.0001.0000.00010.0004.000-0.000-5.24310.2000.0001.0000.00010.2003.800-0.000-5.44310.4000.0001.0000.00010.4003.600-0.000-5.64310.6000.0001.0000.00010.6003.400-0.000-5.84310.8000.0001.0000.00010.8003.200-0.000-6.04311.0000.0001.0000.00011.0003.000-0.000-6.24311.2000.0001.0000.00011.2002.800-0.000-6.44311.4000.0001.0000.00011.4002.600-0.000-6.64311.6000.0001.0000.00011.6002.400-0.000-6.84311.8000.0001.0000.00011.8002.200-0.000-7.04312.0000.0001.0000.00012.0002.000-0.000-7.24312.2000.0001.0000.00012.2001.800-0.000-7.44312.4000.0001.0000.00012.4001.600-0.000-7.64312.6000.0001.0000.00012.6001.400-0.000-7.84312.8000.0001.0000.00012.8001.200-0.000-8.04313.0000.0001.0000.00013.0001.000-0.000-8.24313.2000.0001.0000.00013.2000.800-0.000-8.44313.4000.0001.0000.00013.4000.600-0.000-8.64313.6000.0001.0000.00013.6000.400-0.000-8.84313.8000.0001.0000.00013.8000.200-0.000-9.04314.0000.0001.0000.00014.0000.000-0.000-9.243

Titrate with constant pH incrementsCalculate initial pHTitrate with constant Volume additionsRetain curveDelete retainedGutz:Nmero mdio de prtons associados base 1 no pH dado.

Para HiB, h mdio seria o valor fracionrio de i que reflete a mdia das concentraes de H+ no dissociado em dado pH.Gutz:Simulao opcional de erros aleatrios nas medidas de pH (instabilidade da leitura) especificados como desvio padro aproximado dos resduos para a curva completa.Por exemplo, 0,03Gutz:Simulao opcional de erros aleatrios nas medidas de volume (p.ex., erro na leitura do menisco da bureta), expressos como desvio padro dos erros para a curva completaPor exemplo, 0,05Gutz:CO2 absorvido por qualquer titulante ou titulado exposto ao ar; em solues alcalinas, ocorre acumulao na forma de carbonato; da ser importante simular o efeito da sua interferncia, seja no titulante, seja no titulado, ou em ambos.Gutz:The titrand is the sample to be evaluated by titration with a strong acid or strong base.

Tipically, 5 to 25 mL of titrand (cell F16) are carefully measured and placed in a beaker, a combined glass electrode (connected to a pH meter) and a magnetic stirrer bar are introduced and water is added till the electrode is covered (cell G16).

Titration is carried out by adding small aliquots of titrant (usually with a buret or motor driven syringe) and registering the pH afterstabilization of the reading.Gutz: Leave blank/fill out with the concentration (mol/L) of fully deprotonated base (of a conjugated acid) to be considered in the simulation, e.g.: [Na2CO3], [Na3PO4], [NH4OH], [pyridine] or [Na4EDTA]Gutz:Leave blank/fill out with the concentration (mol/L) of monoprotonated base (or acid, HB) to be considered in the simulation, e.g.: [Acetic acid], [NH4+], [pyridonium], [NaHCO3] or [Na2HPO4]Gutz: Leave blank/fill out with the concentration (mol/L) of biprotonated base (H2B) to be considered in the simulation, e.g.: [H2CO3], [H2Na2EDTA] or [NaH2PO4]Gutz:dLeave blank/fill out with the concentration (mol/L) of triprotonated base (H3B) to be considered in the simulation, e.g.: [H3PO4]Gutz:Sum of concentrations of all forms of base B introduced in the titrand (e.g., [HB] + [H2B] + [H3B])Gutz:Maximum H+ concentration available from full deprotonation of all forms of HiB used in the formulation of the titrand (e.g., [HB] + 2[H2B] + 3[H3B])Gutz:Leave blank - this cell corresponds to the conjugated base of the acid, e.g., Cl- or NO3-.Gutz:Leave blank/fill with de concentration of strong monoprotonable base used as titrant e.g., NaOH, KOH (or twice the concentration of Ca(OH)2)Gutz:Leave blank/fill out with de concentration of carbonate used as titrant

To simulate the absorption of CO2 in an alkaline titrant, leave blank and fill cell D16Gutz:Leave blank/fill with de concentration of strong monoprotic acid used as titrant e.g., HCl. For weak or diprotic acids like H2SO4 change charge and pKas first, at cells R4 to R6.Gutz:Leave blank - as a rule, this cell corresponds to the protonated of OH- , H2O2, handled as solvent. However, if a different acid/base is system is specified in column S, [HB] may be required.Gutz:Leave blank/fill out with de concentration of bicarbonate, if used as titrant.

To simulate the absorption of CO2 from the air by an alkaline titrant, leave blank and fill H2CO3 (cell D16)Gutz:Leave blankFill out just in case you have replaced the base, its charge and pKas in cells S4 to S6.Gutz:Leave blank/fill out to simulate the absorption of CO2 by an alkaline titrant (effect visible on the curve for 1% or more of [H2CO3] relative to the titrant concentration)Gutz:Volume of the aliquot of titrand (with the composition given above) to be titratedGutz:Water is frequently added to the sample until the glass electrode bulb and reference electrode junction are covered by the solution. The (undesirable) effect of dillution on the simulated curve may be best appreciated by exagerating this volume, retaining the curve and repeating the titration without added water.Gutz:Total volume before titration (F16+G16)Gutz:Maximum volume of titrant to be added up to the end of the titration (may be less or equal to the capacity of the buret ).Gutz: Total number of additions of the titrant from the buret (max.: 120; typical: 30 or 50).

You can choose constant volume additions (A24) or constant pH increment (A27).Gutz:Click on button at A22 to calculate the "pH" of the starting solution, before addition of any titrant (but after dillution, if G16 not zero).

Refer to the spreadsheet pH_calc to calculate the pH (instead of "pH") of the same solution and for distiction between pH, p[H] and "pH". These values depart increasingly as the electrolyte concentration (more precisely, the ionic strenght) of a solution increases, due to ion-ion interactions.

pH = -log aH+ where aH+ is the proton activity (concentration x activity coefficient)

This Simulation module calculates p[H], when pK'as (apparent constants at the I of the solution) are provided, or "pH" when thermodynamic constants (from the Database) are used instead.

p[H] = -log [H+] , where [H+] is the hydrated proton concentration, in mol/L.Gutz:Hover the mouse on a curve and point any data point to readout its ID and coordinates.To add labels to your graphics, activate the drawing tools of Excel and insert text boxes.Gutz:To copy graphics with simulated curves and paste them into other documents (e.g.: Word or Excel without links to the original:- Fill out the header of the figure (optional)- Click in the box of the figure near the margins, to select it- Repeat the last simulation of a curve - Press Ctrl+C and wait for processing- Switch to the Word document - Select Insert/Paste Special/Picture (enhanced metafile)Gutz:Click twice on the volume or pH scale to redifine it.Use Ctrl+Z (as many times as needed) to undo scale expansionGutz:- Use the Graphics spreadsheet to plot derivatives by the DpH/DV aproximation and to overlay curves.- Use Evaluation to generate first and second derivative curves with interpolation and smoothig and to accurately locate inflection points of real and simulated titration curves.- Use Distribution to obtain de fractional composition and the mean protonation level of the bases during the titration as well as in function of pH.Gutz:- Use Evaluation to accurately evaluate well defined inflection points on real and simulated titration curves, assisted by cubic splines smoothing and interpolation- Use Regression to refine the concentrations of analytes and/or pK values of real or simulated titration curves by nonlinear multiparametric regression and to analyse complex curves, with hidden inflections (some learning required)

Data transfer from Simulation to Evaluation or Regression:- Copy data of columns A and B from line 41 on- When evaluating the effect of dispersion (simulation of experimental errors), copy columns A and D instead (select column A, press Ctrl and select column D)Gutz:Data transfer from Simulation to Evaluation or Regression:- Copy data of columns A and B from line 41 on- When evaluating the effect of dispersion (simulation of experimental errors), copy columns A and D instead (select column A, press Ctrl and select column D)- Paste data in columns A and B of the destination spreadsheetGutz:This version of the CurTiPot's Virtual Titrator calculates p[H] (=-log of the concentration of H+) instead of pH (=-log activity of H+), because it does not yet correct for the effect of ionic strength, I, on activity coefficients, taken as unity.

This does not change the volume of the inflections, nor the general shape of the curves.

Refer to the pH_Calc module to calculate the pH and activity coefficents of any solution.

The apparent pKas for a given I can be computed in pH_Calc and pasted in cells K3 to Q10 of this spreadsheet to obtain titration curves closer to pH.Gutz:Do NOT use this column for Evaluation or Regression.

Values displayed to ilustrate the simulated dispersion in the volume dispensing by the "buret".

This column will remain blank when null dispersion is choosen in J17 and J18.Gutz:These pH values with dispersion will be overlayed in the graphic

This column will remain blank when null dispersion is choosen in J17 and J18Gutz:Free hydrated proton concentration (or activity)Gutz:Total concentration of H+ required to satisfy all protonation equilibria, using the general equation, the concentration s of line 11 and the pKas given or under refinement.Gutz:Dillution factor of the titrant when added to the sample (+water). For example, when the added titrant equals the volume of sample (+water), the factor is 0.5Gutz:Dillution factor of the sample by optional addition of water (at the beginning) and addition of titrant during the experimentGutz:Leave blankFill out just in case you have replaced the base, its charge and pKas in cells S4 to S6.Gutz:Do NOT write in this cell or any other one of the same color, not to corrupt the equations.Gutz:The ionic dissociation product of water changes with temperature and ionic strength, I. For pure water at 25C, the accepted value is 13.997 (or 14.00).

Values corrected for I can be calculated with module pH_calc.Gutz:Keep delay = 0 for titration at maximum speed (dictated by the computer performance)Choose delay > 0 to pause between additions of titrant, resembling the time required to wait for pH measurements to sabilize in a real titrations.

Press Escape during a titration to ignore the delay, proceeding at max. speed.Gutz:See comment in cell M1 on how to change acids ans bases.Load pKas of these HiB -->Gutz:Selecting/editing names, charges ans pKas. Options:a) Write directly in the cells K3 to Q10 and R3 to T6; b) Click on names in line 2, slide along the list, click on another name; finally, click on J2 to load the constants from the Database.

Frequently used acids missing in the Database should be added to it.Gutz: Options:a) pKa1 , -logarithm of the dissociation constant of a monoprotic acid or first constant for a polyprotic system.b) logKpi, logarithm of the protonation constant of a (conjugated) base, with i=1 for a monoprotonable base and i= n (most deprotonated species) for polyprotic systems (more about at U5);c) pKw - pKbi, for -log of the dissociation constant of a base, with i=1 for a monoprotonable base and i= n (most deprotonated species) for polyprotonable base.

Numerically, values of a, b e c are taken as similar.Gutz: Options:a) pKa2 , -log of the 2nd dissociation constant of a biprotic or polyprotic acid; b) logKpi, log of the first protonation constant of a biprotonable (conjugated) base or i=n-1 for a system with n protonations;c) pKw - pKbi, with i=1 for a biprotonable base or i=n-1 por a base with n protonations; for a monoprotonable base, leave blank.Gutz: Charge of the most deprotonated species of an acid or base in accordance with the highest pKa for the system, e.g., 0 for NH3 or pyridine-1 for acetate/acetic acid-2 for carbonate//carbonic acid-3 for phosphate///phosphoric acid -4 for EDTAGutz: The pKas shown here are copied automatically from the Database by changing K2 to Q2.

See U5 to understand why pKa1 = -logKpnGutz:See U5 to understand why pKa1 = logKpnGutz:Total concentration of each base (regardless of the protonation level of the added component) in columns B to H; grand total in column I.Gutz:Maximum concentration of H+ that could possibly be dissociated from all the components added to the solution.Gutz:The betas are cumulative (or global) protonation constants, obtained by multiplying the protonation constants Kp from 1 to i, with i stepping up to n, the maximum number of protons accepted by a (conjugated) base (same as the maximum number os dissociable protons of an acid, but in reversed order).

Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa.

Protonation constants, Kp, and betas are preferred here in agreement with the most extensive compilations of equilibrium constants, e.g., Critical Stability Constants, Vol. 14 (complete references in the Database), and because the equations become unified with those used for metal-ligand-proton equilibria, based on formation (instead of dissociation) constants.Gutz:Strong acids like HCl ou HClO4 have negative pKas, possibly -6 or lower.

For a diprotic titrant like H2SO4, use pKa1 = -6 e pKa2 = 1,8.

Do not specify systems with more than 2 pKas here.Gutz:The accepted value of the pKa (=log Kp) of the strong base OH- is 15,745 at 25C and infinite dilution. As I increases, the activity coefficient of OH- decreases (as can be checked with module pH_calc), and more specific interaction can occur with cations, so that lower values are sometimes mentioned in the literature (see references in the Database for details).

Any other mono or biprotonable acid or base can be used instead of OH-Gutz:Aqueous solutions exposed to air or stored in (gas permeable) plastic flasks are always contaminated with CO2. Thus, it is advisable to include the carbonic acid system in simulations and regressions. But any othe mono- or biprotic system can be specified here.

The pKa1 from the Database for for H2CO3 is apparent. By considering the fraction of dissolved CO2 converted in H2CO3 (most of it remains as CO2(aq)) a "true" pKa1 of 3.58 is found.Gutz:The titrant may contain up to three diprotic reagents (other than the default ones).Names and constants must be changed manually.Gutz:Sum of concentrations of all forms of base B introduced in the titrand (e.g., [HB] + [H2B] + [H3B])Gutz:Maximum H+ concentration available from full deprotonation of all forms of HiB used in the formulation of the titrand (e.g., [HB] + 2[H2B] + 3[H3B])"Hands on" the "VIRTUAL TITRATOR":

- Click on the button "Clear ret(ained) curves" (cell A32) - all but the last simulated curve will disappear;- click on the button "Titrate with constant volume additions" (A28) - the default tiration of 20 mL of 0.07 mol/L H3PO4 with 0.1 mol/L NaOH will be generated with 50 additions of 1 ml of titrant;- click on "Titrate with constant pH increments" (A24) - notice the difference in data distribution;- click on "Retain curve" (A30);- change the H3PO4 concentration in (C7), press Enter;- titrate again and retain the curve;- change pKa2 (cell M6) from 7.2 to 9.2 (Enter) and titrate;

If you haven't learned what acid-base dissociation constants are, or whatfor acids are titrated, perhaps you should go through a simple tutorial first, e.g., a flash animated one: http://www2.wwnorton.com/college/chemistry/gilbert/tutorials/ch16.htm

- click on K2 or L2, select another acid; click on J2; ...- observe the effect of CO2 absorption by NaOH solution by writing 0.001 in D16;- add other components to the mixture and titrate;- add random experimental error to the curve fillng values in cells J17 and J18 (e.g., 0.03 and 0.1);- titrate a phosphate buffer of Na2HPO4 + NaH2PO4 with strong base, retain the curve and titrate it with strong acid;- user your creativity...

Remark: This version of the CurTiPot's Virtual Titrator calculates "pH" or p[H] (=-log of the concentration of H+) instead of pH (=-log activity of H+), because it does not (yet) correct for the effect of ionic strength, I, on activity coefficients, taken as unity (see cell A20 or the pH_calc module for more information). This does not however change the volume of titrant spent to reach the inflections, nor does it modify the general shape of the curves.

Refer to the pH_calc module to calculate the pH of any solution with estimated activity coefficents. Use the apparent pKas for a given I, computed in pH_calc pasted in cells K3 to Q10 of Simulation to obtain titration curves with pH values closer to reality.

Copyright: This acid-base titration curve simulator is an expanded Excel version of the original Turbo Basic for DOS program CURTIPOT launched by the Author in 1992.

Prof. Dr. Ivano G. R. Gutz www2.iq.usp.br/docente/gutz

Distribution

alfa 0alfa 1alfa 2alfa 3alfa 4alfa 5alfa 6pHaiDistribution of HiB species

Evaluation

n mdiopHaverage protonationAverage protonation (h) of the base B

Regression

pH

7014140alfa 0alfa 1alfa 2alfa 3alfa 4alfa 5alfa 6pH/14Volume (mL)aiDistribution of HiB species along a titration

Graphs

14pH

70h mdion*pH/14Volume (mL)average protonationAverage protonation (h) of the base along a titration

Database

Alpha BAlpha HBAlpha H2BAlpha H3BAlpha H4BAlpha H5BAlpha H6BpHlog aiDistribution of HiB species

14pH

70log alfa 1log alfa 0log alfa 2log alfa 3log alfa 4log alfa 5log alfa 6pH em escalaVolume (mL)log aiDistribution of HiB species along a titration

Evaluation of Real and Simulated Titration Data by Derivatives with InterpolationColor codingInterpolation and smoothing by cubic splinesDegree of smoothingFitting range (zoom)Inflectionauto-finderVolumedpH/dVD o n o t c h a n g e(0 to 100%)90Initial volume0.000Maximum10.0209339481.7751855212C h a n g e c r i t e r i o u s l yInterpolated points100Final volume50.000MinimumFill out, change or leave blankVolumepHInterp. Vol.Fitted pHdpH/dVd2pH/dV20.0002.2650.00002.26280.02930.00002.4992.3860.50512.27810.03210.00574.6182.6641.01012.29630.04080.01146.2782.7841.51522.32020.05520.01717.4993.0592.02022.35290.07530.02288.3553.3022.52532.39730.10110.02758.9343.4373.03032.45420.12200.01399.3183.5523.53542.51820.12920.00049.5693.8234.04042.58240.1227-0.01329.7343.8914.54552.63990.1026-0.02689.8444.3015.05052.68580.0830-0.00739.9224.1185.55562.72800.08830.01779.9844.4226.06062.77920.11880.042710.0424.8416.56572.85140.16600.037910.1085.1867.07072.94260.19040.010410.1985.1927.57583.03910.1879-0.005410.3285.3808.08083.13690.20750.044110.5255.5678.58593.25900.30240.202710.8255.7689.09093.48810.65720.519411.2786.0839.59603.98101.33380.741611.9536.22210.10104.80381.7494-0.308612.9266.44410.60615.54871.1537-0.630614.2676.61711.11115.98900.6246-0.419516.0076.82811.61626.21520.3059-0.211118.0906.99512.12126.33310.1884-0.061120.3627.22412.62636.41540.1428-0.029122.5967.53713.13136.48270.1273-0.008224.5847.63113.63646.54530.1216-0.003226.1997.78314.14146.60630.12080.001727.4187.98314.64656.66780.1221-0.001028.2888.28515.15156.72870.1183-0.006328.8858.40615.65666.78640.1093-0.011529.2848.62916.16166.83830.0955-0.013629.5478.79816.66676.88350.0844-0.008429.7209.09617.17176.92440.0785-0.003329.8369.08517.67686.96360.07780.001929.9189.40018.18187.00380.08220.006529.9839.45118.68697.04720.09000.009030.0459.81219.19197.09520.10030.011430.11610.28519.69707.14890.11300.013830.21210.29520.20207.20970.12820.016230.35410.52220.70717.27840.14240.008830.57010.62821.21217.35160.1452-0.003230.90510.91521.71727.42310.1360-0.0151Assisted calculation of concentrations (optional)How to change the axis of a curve31.42711.08522.22227.48690.1146-0.0271Vol. of titrand (sample)Concentration ofHow to copy/paste a curve32.23911.22622.72737.53690.0821-0.0324SampleWaterTotaltitrant (mol/L)Data ID on curves33.49511.38523.23237.57130.0564-0.0184200200.135.42211.67723.73747.59630.0449-0.0044Vol. Inflectionn (mols)delta n[species]38.36511.80524.24247.61910.04750.0095110.020.0010020.0010020.050142.87812.00724.74757.64660.06350.0195230.020.0030020.0020.150.00012.22425.25257.68380.08390.0210300025.75767.73170.10600.0226400026.26267.79110.12960.0242500026.76777.86290.15520.0264600027.27277.94820.18290.0285700027.77788.04850.21700.0422800028.28288.17040.26890.0606900028.78798.34430.46620.33261000029.29298.68920.95080.629429.79809.34141.62790.5750Results of the Example:30.303010.20211.5367-0.66490,0501 mol/L H3PO4 and 0,0499 mol/L NaH2PO430.808110.80200.8563-0.5952Remember: half of the determined H2PO4- comes from the H3PO431.313111.10380.3852-0.325231.818211.23450.1605-0.143132.323211.29200.0909-0.013232.828311.33630.08800.007333.333311.38430.10560.027733.838411.44540.13490.021734.343411.51750.14750.003434.848511.59130.1416-0.015035.353511.65750.1172-0.033435.858611.70800.0838-0.029536.363611.74340.0577-0.022236.868711.76750.0390-0.014837.373711.78410.0278-0.007537.878811.79690.0240-0.000138.383811.80960.02760.007038.888911.82520.03410.005839.393911.84380.03940.004739.899011.86480.04360.003640.404011.88770.04660.002440.909111.91180.04850.001341.414111.93650.04930.000241.919211.96140.0489-0.000942.424211.98580.0474-0.002142.929312.00910.0448-0.003143.434312.03090.0418-0.002843.939412.05130.0390-0.002644.444412.07040.0365-0.002444.949512.08820.0342-0.002245.454512.10490.0321-0.002045.959612.12060.0302-0.001746.464612.13550.0285-0.001546.969712.14950.0271-0.001347.474712.16290.0259-0.001147.979812.17570.0249-0.000948.484812.18810.0241-0.000748.989912.20010.0236-0.000449.494912.21190.0232-0.000250.000012.22360.0231-0.0000

Plot curvesGutz:Options for selecting pKas:a) Click on control D3, slide along the list, click on a name; the pKas will be loaded from the Database; finally, click on B3 to plot the curves;b) Write the pKas of any real or hypothetical system in line 10 of the Database (or at the end of the list); return to Distribution and proceed as before (option a).

Frequently used systems can be added definitively to the Database by saving the updated curtipot_.xls file.Gutz:Do NOT write in this cell or any other one of the same color, not to corrupt the equations.Gutz:The betas are cumulative (or global) protonation constants, obtained by multiplying the protonation constants Kp from 1 to i, with i stepping up from 1 to n (the maximum number of protons accepted by a (conjugated) base, same as the maximum number os dissociable protons of an acid, but in reversed order).

Note that pKa = logKp for a monoprotic acid (because Kp = 1/Kd or pKd = 1/logKd ) and, for multiprotic systems, the first logKp is the last pKa.Gutz:Hover the mouse on a curve and point any data point to readout its ID and coordinates.Gutz:Click twice on the volume or pH scale to redifine it.Use Ctrl+Z (as many times as needed) to undo scale expansionGutz:To copy graphics with one or more curves and paste them into other documents (e.g.: Word o Excel) without links to the original:- Fill out the header of the graphic- Click in the box of the graphic near the margins, to select it- Repeat generation of at least one curve - Press Ctrl+C and wait processing - Switch to the Word document - Select Insert/Paste Special/Picture (enhanced metafile)Gutz:Do not write here! Click on D3 to select an acid or base.To try other real or hypothetical systems, write their pKas in line 10 of the Database (or at the end of the list); return to Distribution and proceed as before.Gutz:The distribution diagrams (or alpha plots) of acids and bases reveal the molar fraction of each species in equilibrium at any pH of the solution. For example, phosphoric acid / phosphate system at pH 7.0:a0 = 0.00 or 0% and log a0 = -5.76 a1 = 0.387 or 38.7% and log a1 = -0,412 a2 = 0.613 or 61.3% and log a2 = -0,213a3 = 0.00 or 0% and log a3 = -5.07Since the index i of ai is the numbe or protons bound to the base, we have H2PO4 as dominant species, with 61.3%, followed by HPO4= with 38.7%, while only 0.0002% of phosphate and 0.0009% of H3PO4 coexist at this pH; the average number of protons bond to each phosphate is 1.61, as shown in column P (the data used to plot the figures appears at columns O to BE).

smoothed data derivatives2nd derivativeVolume (mL)dpH/dV

raw datasmoothed dataVolume (mL)pH

Titration Data Analysis - Multiple Regressionread important remarks and instructionspKas of the acids and bases in the solutionClick on K2 to Q2; select acids/bases; click on J2; other options, read M1Overall protonation constants = bp = PKp (calculated by the program)pKas loaded from the DatabaseFitted total concentrations of all forms of each base (in blue) and equilibrium conc. at the initial pH (in mol/L)628311263TitrantTitrandTitrantTitrandClick on J2 to use these pKas in the RegressionTitrand SpeciesCitric acidPhosphoric acidAscorbic acidAcetic acidAmmoniaHClCarbonic acidAcid / BaseCitric acidPhosphoric acidAscorbic acidAcetic acidAmmoniaHClCarbonic acidStrong ACIDStrong BASECarbonic ac.Acid / BaseCitric acidPhosphoric acidAscorbic acidAcetic acidAmmoniaHClCarbonic acidStrong ACIDStrong BASECarbonic ac.Acid / BaseCitric acidPhosphoric acidAscorbic acidAcetic acidAmmoniaHClCarbonic acid[B]0.0000000013000000Charge of B-3-3-2-10-1-2-1-1-2Charge of B-3-3-2-10-1-2-1-1-2Charge of B-3-3-2-10-1-2[HB]0.000016393700.0004560230000pKa13.1282.1484.1004.7579.244-7.0006.352-615.7456.352bp12.489E+062.239E+126.166E+115.715E+041.754E+091.000E-072.133E+101.000E-065.559E+152.133E+10pKa1 = logKpn3.1282.1484.1004.7579.244-7.0006.352[H2B]0.004952765300.03007173490000pKa24.7617.19911.79010.32910.329bp21.435E+113.540E+197.762E+1510E-1010E-1010E-104.797E+1610E-1010E-104.797E+16pKa2 = logKpn-14.7617.19911.7900.0000.0000.00010.329[H3B]0.0348352942000000pKa36.39612.350bp31.928E+144.977E+2110E-1010E-1010E-1010E-1010E-10pKa3 = logKpn-26.39612.3500.0000.0000.0000.0000.000[H4B]0000000pKa4pKwbp410E-1010E-1010E-1010E-1010E-1010E-1010E-10KwpKa4 = logKpn-30.0000.0000.0000.0000.0000.0000.000[H5B]0000000pKa513.9970bp510E-1010E-1010E-1010E-1010E-1010E-1010E-101.01E-14pKa5 = logKpn-40.0000.0000.0000.0000.0000.0000.000[H6B]0000000SSpKa6bp610E-1010E-1010E-1010E-1010E-1010E-1010E-10pKa6 = logKpn-50.0000.0000.0000.0000.0000.0000.000S[HiB]0.039804454400.030527757900007.033E-02SS[bases]Correction of the pH sensor calibrationS[H] bound0.114427806900.060599492800001.750E-01SS[H] bound7.0000intersection (may be fitted)max. free H0.004985556400.00045602300005.442E-03SS[H] max.free H+ (negative results are possible)1.0000slope (fittable, read comment)TitrantStrong ACIDStrong BASECarbonic ac.Vol. Tittrand (mL)5.027E-05"Extra" H+ from non-fitted HiB (e.g., a strong acid), if any.Color coding[B]0.1SampleWaterTotal[H]=10^-p[H]5.238E-032.281initial "pH"D o n o t c h a n g e[HB]20020.00[OH]=Kw/[H]1.922E-1211.716initial "pOH"C h a n g e c r i t e r i o u s l y[H2B]SSinitial CHcalc1.803E-01Fill out, change or leave blankS[HiB]00.100.1SS[HiB]CHRNL1.805E-01