pH calculation + virtual titration
CurTiPot 4.2.0 *
older ExcelTM **
in .xls format
+ first steps for
* Requirements: Microsoft ExcelTM
any version from 2007 onwards
** ExcelTM versions
8 to 11 (1997 to 2003), Windows 98 onwards;
*** Overlaid step-by-step instructions in balloons (bubble text)
A pH calculator
» "one click" fast pH calculation of any aqueous solution of acids, bases and salts, including buffers, zwitterionic amino acids, from single component to complex mixtures (30 or more species in equilibrium);
» pH , p[H] and "pH" values iteratively computed with an accurate general equation (instead of the simple Henderson-Hasselbalch equation) combined with activity coefficients estimation by the Davies equation;
» provides buffer capacity (buffer index, buffer strength), ionic strength, fractional distribution, medium charge of HiB – to find the Isoelectric Point of amino acids –, activities and apparent dissociation constants of all species at equilibrium.
Try the pH calculator now
Two Titration Data Analyzers
Treat your pH vs. volume input data – real or simulated – in the usual fashion with the Evaluation option or by an advanced Regression method;
» the Evaluation program finds the inflection point(s) (also known as end points or equivalence points) on a titration curve automatically with enhanced accuracy thanks to cubic splines smoothing and interpolation;
» the Regression spreadsheet determines concentrations of acids, salts and bases in a sample and refines pKa values by least squares nonlinear regression – essential for titrations of very diluted and/or complex samples, eg., acid rain, generating curves with undefined inflections. This advanced resource takes ionic strength effects and activity coefficients in account.
Two Virtual Titrators
» Titration module for beginners with clickable digital burette, color transition of the chosen indicator for visual endpoint detection and generation of samples with random unknown concentration;
» simulation of pH vs. volume titration curves of any aqueous solution of acids, bases and mixtures;
» simulation of "near real" data tables and plots with random errors (Gaussian distribution) in pH and/or volume, to test data analysis procedures;
» user selectable increments of pH, volume, pH or "pH" plot and titration speed;
» overlay of curves (>10) for visualization of the effect of changes in parameters;
» unlimited generation of different titration curves for drilling exercises and students' examinations.
A Distribution Diagram Generator
» distribution diagrams (alpha plots or molar fraction) and buffer capacity curves of any mono or multiprotic acid or base showing the fractional contribution of each protonated and unprotonated species in equilibrium;
» distribution curves plotted against volume of titrant, with overlaid titration curve, revealing the principal species at the inflections (endpoints) and the contribution of each species at any stage of the titration;
» protonation curves an average charge curves of acids or bases showing the average number of protons bound to the Brönsted-Lowry (or Lewis) base – and their weighted charges – as a function of pH as well as volume of titrant (with overlaid titration curve); a zero-crossing of the charge reveals an Isoelectric Point.
A pKa Database
» equilibrium constants of some 250 acids and bases (see list) are stored in a user-expandable database.
» quick load of pKa sets of seven acid-base systems into the pH_calc, Simulation and Regression modules, for simultaneous use.
CurTiPot is released as freeware for personal, educational and non-commercial use; for other applications, contact the author (copyright holder). Download the most recent release of CurTiPot, free of virus, spyware and addware, from this page <www2.iq.usp.br/docente/gutz/Curtipot_.html>.
There is no need to install (or uninstall) CurTiPot. Simply run the Microsoft ExcelTM software and open the curtipot_.xlsm file like any other spreadsheet workbook. All preprogrammed equations and Visual Basic embedded macros are self-contained and completely removed when closing CurTiPot (no functions added, no changes made to Excel).
It is necessary to enable macros in Excel to activate the buttons that run the macros for iterative computing of pH, distribution curves generation, smoothing, etc.
If, while opening CurTiPot, Excel does not display an option 'enable macros' to click you must update the configuration (only once for a computer). E.g., In Excel 2010 the simple steps are:
1. Click the File tab. The Backstage view opens.
2. Under Help, click Options; the Options dialog box appears.
3. Click Trust Center, then click Trust Center Settings.
4. In the Trust Center, click Macro Settings.
5. Select disable all macros with notification. Click OK.
6. Reload CurTiPot and enable macros.
In Excel 2007, click on: Office button (top left) and follow the above steps 2 to 6.
In older versions of Excel (97-2003), click on: Tools / Options / Security / Macro security / Security Level / Medium. Reload CurTiPot and enable macros.
All worksheets have embedded instructions and comments, editable/expandable by the user. In addition, the CurTiPot option i version contains balloons (bubble text) with a numbered sequence of first steps to be followed by beginners, like a recipe. Balloons can be deleted as they become superfluous.
The Regression module of CurTiPot uses the Excel supplement named Solver for the determination of concentrations and pKas of acids and bases from titration data by nonlinear least squares regression. If not yet visible in the Excel Data tab, Solver needs to be activated by checking the box in the Excel Supplements list.
CurTiPot adheres to the Brönsted and Lowry concept of acids and bases. Solely instantaneous protonation-deprotonation equilibria and effects of ionic strength are computed. No other type of chemical reaction or phase transition is taken in account in the calculations, although they may occur for many combinations of acids and bases (listed or not in the Database).
The pH, usually measured by potentiometry with a cell comprising a glass electrode and a reference electrode, is strictly defined as -log a[H+] (see definition of pH), where a[H+] is the activity of hydrogen ions, more precisely hydrated protons, H3O+ or hydronium (the simplest type of oxonium ion). At increasing ionic strength, I, ion-ion interactions reduce the activity coefficients (gamma) of all ions including the hydrated protons, H+. The pH Calculator, Simulation and Regression modules estimate activity coefficients with help of the Davies equation.
The Davies equation gives reasonable estimates up to I ~0.1 mol/L or so (better than the Debye Hückel equation). There are more complete equations applicable at higher I (e.g., Pitzer equation) that take in account individual hydrated ion-size parameters and ion-ion association constants, but these are available only for a limited number of acids and bases in certain electrolytes.
Besides pH, the pH Calculator also displays the p[H] and the "p[H]". Both correspond to -log [H+] with the difference that "p[H]" is computed with thermodynamic constants but ignoring the I effect (like simplistically done in high school), while the constants used in the p[H] calculation (and pH as well) are previously corrected for the I effect (ion-ion interaction) by the Davies equation.
Ion-ion iteration corrections are disregarded Titration and Distribution modules of CurTiPot; this does not affect the volume of titration end points (stoichiometric points or equivalence points).The author provides the freeware on an "as is" basis, with no warranties, expressed or implied, and reserves the right not to be responsible for the correctness, completeness, accuracy and error-free operation of CurTiPot. The author has not introduced any spyware, adware, viruses or malicious code in the program, as checked and assured by many of the distributors of the software (see list).
Bug reports and suggestions welcomed by e-mail firstname.lastname@example.org.
The all-in-one modular and interactive design of CurTiPot is user-friendly and lets you rapidly calculate the pH of any aqueous solution, from the simplest to the most complex one. The Virtual Titrator makes the simulation of the titration curve of any acid, base or mixture a breeze; flexibility in the selection of sample size, concentration of ingredients, titration range, type, size and speed of titrant addition and dispersion of the "measurements" give great realism to the process. Quick loading of dissociation constants and one-click data transfer from the Virtual Titrator to both of the data analysis modules - Evaluation and Regression - make it easy to compare a "graphical" or empirical method with the numerical one in a matter of seconds! This is great for learning and teaching as well as for the optimization of new titrations.
Introduce your experimental data pairs of volume of titrant and pH readings from de pH meter (potentiometer with a combined glass electrode or another pH sensor) directly into the spreadsheet of the Evaluation module. Visualize the curve as you enter data point by point during the titration in the laboratory, or afterwards. Select the smoothing factor of the spline that shows the most accurate interpolation of the endpoints (stoichiometric points or equivalence points) on the derivative curves. You will be pleasantly surprised with the effectiveness of spline smoothing for volumetric titration curves with clearly defined inflections and with the power of the Regression module to deal with more difficult data analysis.
Try the Regression module to obtain the best possible estimation of the concentrations (and pKas) of species involved in protonation chemical equilibria. The chemometric approach of multiparametric least-squares nonlinear regression is effective when all relevant pKas fall within (or near outside) the pH range covered by your titration data.
A background in chemometrics, statistics or numerical data analysis is valuable but not essential to profitably explore the power and recognize the limits of the Regression module, in special, for data untreatable by graphical and linearization methods (Gran plot). For example, with Regression, minute concentrations of some acidic and basic components in acid rain samples titrated with strong base can be determined individually or grouped as follows: strong acids (H2SO4 + HNO3), weak carboxylic acid (formic + acetic), bicarbonate (H2CO3/HCO3-/CO3=) and ammonium ion (NH4+/NH3) (FORNARO, A.; GUTZ, I.G.R., Wet deposition and related atmospheric chemistry in the São Paulo metropolis, Brazil. Part 3: Trends in precipitation chemistry during 1983–2003, Atmospheric Environment, 2006, 40(30), 5893-5901).
In principle, CurTiPot can simulate any titration curve in aqueous medium regardless of the number of mixed acid-base systems in equilibrium (within limitations given above). The program is frequently downloaded by users looking for the simulation and evaluation of titration curves of diprotic and triprotic amino acids. We have used CurTiPot, e.g., to simulate and feed pH vs. titrant volume values to a new method of analysis of conductometric titration data (COELHO, L.H.G. and GUTZ, I.G.R., Trace analysis of acids and bases by conductometric titration with multiparametric non-linear regression, Talanta, 2006, 69(1), 204-209).
The program is helpful also for other tasks like determining the amount of acid or base required to neutralize a sample (neutralization), to prepare or displace the pH of a buffer, to change color of a visual indicator, to find the isoelectric point of amino acids, etc. Users in one hundred and thirty countries have found the freeware valuable in their own research as well as to prepare lectures, tutorials, exercises, examination questions, lab guides and experiments, classroom simulations, presentations, papers, etc.
The user-expandable Database reproduces pKas of some 250 monoprotic, diprotic and polyprotic acids and bases selected in larger equilibrium constants databases (references given), including the essential amino acids and ending with some visual indicators: acetamide, acetic acid/acetate, acetoacetic acid, acrylic acid/acrylate, adipic acid/adipate, alanine, aminobenzene, aminobenzene sulfonic acid/sulfonate, aminophenol, ammonia, aniline, arginine, arsenic acid/arsenite, arsenous acid/arsenate, ascorbic acid/ascorbate, asparagine, aspartic acid/aspartate, barbital, barbituric acid, benzenesulfonic acid, benzoic acid/benzoate, benzylamine, benzylpyridine, betaine, boric acid/borate, butanoic acid, butenoic acid, butylamine, butylamine, carbonic acid/carbonate, catechol, chloroacetic acid/chloroacetate, chloroaniline, chlorobenzoic acid, chlorophenol, choline, chromic acid, citric acid/citrate, codeine, creatinine, cyanic acid, cysteine, decylamine, dichloroacetic acid, dichlorophenol, diethylamine, dimethylamine, dimethylglyoxime, dimethylpyridine, dinicotinic acid, diphenylamine, dipicolinic acid, dopamine, ephedrine, ethanolamine, ethylamine, ethylenediamine, ethylenediaminetetraacetic acid (EDTA), formic acid/formate, fumaric acid/fumarate, glutamic acid/glutamate, glutamine, glutathione, glyceric acid, glycerol, glycine, glycolic acid, glyoxylic acid, hexamethylenediamine, hexanoic acid, hexylamine, histamine, histidine, hydroazoic, hydrogen chloride, hydrogen chromate ion, hydrogen cyanide, hydrogen fluoride, hydrogen peroxide, hydrogen sulfide, hydrogen thiocyanate, hydroquinone, hydroxylamine, hydroxybenzoic acid, hypochlorous, imidazole, isocitric acid, isoleucine, lactic acid/lactate, ephedrine, leucine, lysine, maleic acid, malic acid/malate, malonic acid/malonato, melamine, methionine, methylamine, methylphenol, methylpyridine, morphine, morpholine, nicotine, nitrophenol, nitrobenzoic acid, nitrous acid, noradrenaline, oxalic acid, oxaloacetic acid, papaverine, pentanoic acid, perchloric acid/perchlorate, phenanthroline, phenetidine, phenol, phenylacetic acid, phenylalanine, phosphate/phosphoric acid, phthalic acid/phtalate, picolinic acid, picric acid/picrate, pilocarpine, proline, propanoic acid, propylamine, purine, pyridine, pyridinecarboxylic acid, pyrimidine, pyrocatechol, pyrophosphoric, pyrrolidine, pyruvic acid/pyruvate, quinine, quinoline, resorcinol, saccharin, salicylic acid/salicylate, serine, silicic acid, strychnine, succinic acid/succinate, sulfuric acid/sulfate, sulfurous acid/sulfite, tartaric acid/tartarate, terephthalic acid/terephtalate, thiazole, thioacetic acid, thiosulfuric acid, threonine, trichloroacetic acid, triethanolamine, triethylamine, trimethylacetic acid, trimethylamine, tris(hydroxymethyl)-aminomethane (TRIS), tryptophan, tyrosine, urea, uric acid/urate and valine. Examples of indicators: thymol blue, methyl orange, bromocresol green, methyl red, bromothymol blue, phenol red, phenolphthalein and alizarine yellow R are also included.
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