Theory of titration curves : The locations of inflection points on acid-base and related titration curves

Consideration of the effect of dilution on the locations of the inflection points of potentiometric titration curves for titrations of monobasic acids or bases and for precipitation titrations in which the ions of the precipitate have numerically equal valences shows that;(I) In a strong acid-strong base or isovalent precipitation titration, the inflection point always precedes the equivalence point. No physically meaningful inflection point exists, regardless of the concentration of the substance titrated, if the concentration of the reagent is smaller than a certain value or if, when the concentration of reagent exceeds this limit, the concentration of the substance titrated is smaller than another limiting value.(2) In a weak acid-strong base or weak base-strong acid titration, the inflection point at which the slope is greatest also precedes the equivalence point, and vanishes under certain conditions. Earlier calculations are shown to have given incorrect information regarding the location and existence of this inflection point. The location of the inflection point at which the slope is smallest— the “point of maximum buffer capacity”—is shown to depend on the concentrations of the reagents employed.     

Logarithmic diagrams in acid-base titrations and estimation of titration errors

The use of a logarithmic diagram for the estimation of the pH-value at the equivalence point and the titration error when a solution containing one or two acids is titrated with standard alkali is described.     

On the accuracy of acid-base determinations from potentiometric titrations using only a few points from the titration curve

There are several procedures which use only a few points on the titration curve for the calculation of equivalence volumes in acid-base titrations. The accuracy of such determinations will depend on the positions of the points on the titration curve. The effects of errors in the stability constants and in the pH measurements on the accuracy of the analysis have been considered, and the results are used to establish the conditions under which these errors are minimized.     

Approximation of potentiometric titration curves by logarithmic functions: Prediction of random errors in titration parameters

Two possible types of the propagation of random errors in measurements of potential (pH) and the volume of the titrant to titration parameters determined using logarithmic functions are considered. It is demonstrated that errors in calculated values are variously related to the errors in initial data. Expressions that provide the estimation of errors in characteristics of the titration curve from known errors in measurement are obtained.     

Theory of titration curves : Points of minimum slope on potentiometric strong acid-strong base and precipitation titration curves

Strong acid-strong base and precipitation titration curves, like other kinds of potentiometric titration curves, inherently possess an inflection point where the slope is a minimum as well as one where it is a maximum. In any kind of titration the first of the inflection points can be caused to occur earlier, and can eventually be made to disappear altogether, by adopting certain expedients. For a weak acid-strong base titration, for example, these include decreasing the concentration of the acid titrated and titrating in the presence of an excess of its conjugate base. For strong acid-strong base and precipitation titrations they include decreasing the concentration of the substance titrated and increasing the concentration of the titrant. The conditions under which a physically significant inflection point of minimum slope can exist are defined, and explicit equations are given from which its position can be calculated under various experimental conditions, for strong acid-strong base and for both isovalent and heterovalent precipitation titrations.     

A note on the calculation of acid-base titration curves and their equivalence points

An equation has been developed for the calculation of the titration curve of any mixture of acids and bases, and an alternative way of defining an equivalence point, suitable for computer calculations, is presented.     

Rapid determination of the equivalence volume in potentiometric acid-base titrations to a preset pH-I Theory and applications

A new approach to shorten the time needed for an acid-base titration has been made. The method developed is based on the equation for acid-base titrations derived by Ingman and Still. The equation is transformed into such a form that only one titration point is needed to calculate the equivalence volume when the titration is carried out to a preset pH which can be chosen according to the experimental conditions. The method is used for titration of acetic acid, log K(H)(HA) = 4.65, hydroxylammonium ion, log K(H)(HA) approximately 6.2, and boric acid, log K(H)(HA) approximately 9.1, with an error of 0.1-0.5%. In titration of hydrogen ascorbate ion, log K(H)(HA) approximately 11.3, the error obtained was about 0.3-2%.     

Lewis acid-base titrations employing megacycle-frequency oscillators : Part III. Preparation,isolation and characterization of some adducts predicted from titration curves

Adducts of stannic chloride with thirteen oxygen bases, isolated as solids from benzene or heptane solution, were characterized by analysis and melting point behavior; several of these are new compounds. Diethyl ether, n-dibutyl ether and tetrahydrofuran form AB₂ adducts; p-dioxane, in conformity with its being a diacid base, forms only a 1 : 1 species. Methyl, ethyl, n-propyl and n-butyl alcohols form simple AB₂ adducts at room temperature which on recrystallization from boiling solvent give SnCl₃(OR)ROH; iso-propyl alcohol gives only the AB₂ adduct; tert.-butyl alcohol only forms SnCl₃. OC₄H₉ (steric hindrance probably prevents formation of the AB2 adduct). Water gives a AB₄ or AB₅ adduct.Adducts of aluminum chloride with three nitrogen bases were similarly prepared from acetonitrile solution. Pyridine forms a 1 : 1 species. Acetonitrile itself forms a AB₂ species. Piperidine forms a AB₃ species. The latter two adducts support the view that AlCI₃ can form other than 1 : 1 adducts with nitrogen bases.     

Four points function fitted and first derivative procedure for determining the end points in potentiometric titration curves: statistical analysis and method comparison.

A new method that belongs to the differential category for determining the end points from potentiometric titration curves is presented. It uses a preprocess to find first derivative values by fitting four data points in and around the region of inflection to a non-linear function, and then locate the end point, usually as a maximum or minimum, using an inverse parabolic interpolation procedure that has an analytical solution. The behavior and accuracy of the sigmoid and cumulative non-linear functions used are investigated against three factors. A statistical evaluation of the new method using linear least-squares method validation and multifactor data analysis are covered. The new method is generally applied to symmetrical and unsymmetrical potentiometric titration curves, and the end point is calculated using numerical procedures only. It outperforms the "parent" regular differential method in almost all factors levels and gives accurate results comparable to the true or estimated true end points. Calculated end points from selected experimental titration curves compatible with the equivalence point category of methods, such as Gran or Fortuin, are also compared with the new method.     

The use of linear potentiometric titration curves in the determination of alkalinity and acid-base properties of diluted solutions of humic substances

A critical study of the use of Gran and modified Gran functions for the determination of alkalinity and acid-base properties of diluted solutions containing humic substances is presented. These solutions were composed of 340 muM HCO3(-)(3) in 0, 10, 20.5 and 41 mg/1. of sodium humate in order to simulate natural waters with different levels of dissolved organic carbon. The results showed that the alkalinity may be determined in good agreement with the expected value using both methodologies. The modified Gran functions give information about acid-base speciation in addition to the alkalinity. The application of the modified Gran functions for determination of humic acid pK(a)s and stoichiometry was studied under conditions simulating waters rich in natural organic matter in terms of humic acid concentrations.     

Assessment of two theoretical methods to estimate potentiometric titration curves of peptides: comparison with experiment

We compared the ability of two theoretical methods of pH-dependent conformational calculations to reproduce experimental potentiometric titration curves of two models of peptides: Ac-K5-NHMe in 95% methanol (MeOH)/5% water mixture and Ac-XX(A)7OO-NH2 (XAO) (where X is diaminobutyric acid, A is alanine, and O is ornithine) in water, methanol (MeOH), and dimethyl sulfoxide (DMSO), respectively. The titration curve of the former was taken from the literature, and the curve of the latter was determined in this work. The first theoretical method involves a conformational search using the electrostatically driven Monte Carlo (EDMC) method with a low-cost energy function (ECEPP/3 plus the SRFOPT surface-solvation model, assumming that all titratable groups are uncharged) and subsequent reevaluation of the free energy at a given pH with the Poisson-Boltzmann equation, considering variable protonation states. In the second procedure, molecular dynamics (MD) simulations are run with the AMBER force field and the generalized Born model of electrostatic solvation, and the protonation states are sampled during constant-pH MD runs. In all three solvents, the first pKa of XAO is strongly downshifted compared to the value for the reference compounds (ethylamine and propylamine, respectively); the water and methanol curves have one, and the DMSO curve has two jumps characteristic of remarkable differences in the dissociation constants of acidic groups. The predicted titration curves of Ac-K5-NHMe are in good agreement with the experimental ones; better agreement is achieved with the MD-based method. The titration curves of XAO in methanol and DMSO, calculated using the MD-based approach, trace the shape of the experimental curves, reproducing the pH jump, while those calculated with the EDMC-based approach and the titration curve in water calculated using the MD-based approach have smooth shapes characteristic of the titration of weak multifunctional acids with small differences between the dissociation constants. Nevertheless, quantitative agreement between theoretically predicted and experimental titration curves is not achieved in all three solvents even with the MD-based approach, which is manifested by a smaller pH range of the calculated titration curves with respect to the experimental curves. The poorer agreement obtained for water than for the nonaqueous solvents suggests a significant role of specific solvation in water, which cannot be accounted for by the mean-field solvation models.     

Theoretical study of the acid-base properties of the montmorillonite/electrolyte interface: influence of the surface heterogeneity and ionic strength on the potentiometric titration curves

The parallel shape of the potentiometric titration curves for montmorillonite suspension is explained using the surface complexation model and taking into account the surface heterogeneity. The homogeneous models give accurate predictions only if they assume unphysically large values of the equilibrium constants for the exchange process occurring on the basal plane. However, the assumption that the basal plane is energetically heterogeneous allows to fit the experimental data (reported by Avena and De Pauli [M. Avena, C.P. De Pauli, J. Colloid Interface Sci. 202 (1998) 195-204]) for reasonable values of exchange equilibrium constant equal to 1.26 (suggested by Fletcher and Sposito [P. Fletcher, G. Sposito, Clay Miner. 24 (1989) 375-391]). Moreover, we observed the typical behavior of point of zero net proton charge (pznpc) as a function of logarithm of the electrolyte concentration (log[C]). We showed that the slope of the linear dependence, pznpc=f(log[C]), is proportional to the number of isomorphic substitutions in the crystal phase, which was also observed in the experimental studies.     

Potentiometric study of reaction between periodate and iodide as their tetrabutylammonium salts in chloroform. Application to the determination of iodide and potentiometric detection of end points in acid-base titrations in chloroform

A potentiometric method for the titration of tetrabutylammonium iodide (TBAI) in chloroform using tetrabutylammonium periodate (TBAPI) as a strong and suitable oxidizing reagent is described. The potentiometric conditions were optimized and the equilibrium constants of the reactions occurring during the titration were determined. The method was used for the determination of iodide both in chloroform and aqueous solutions after extraction into chloroform as ion-association with tetraphenylarsonium. The reaction between TBAPI and TBAI was also used as acid indicator for the potentiometric detection of end points of acid-base titrations in chloroform.     

Development of quinhydrone electrode in chloroform. Application to the determination of equilibrium constants of acid-base reactions and potentiometric titration of some amine drugs

The optimum conditions for the functioning of quinhydrone electrode as acid indicator in chloroform was determined by voltammetric and potentiometric studies. This electrode was used for the determination of equilibrium constants of acid-base reactions and the potentiometric determination of the end point of acidimetric titrations of some amine drugs such as phenothiazinic derivatives in pharmaceutical preparations, after extraction into chloroform. The relative standard deviations of 20 mg of aliphatic amines, piperidine and piperazine substituted phenothiazines were 0.5, 0.7 and 1 % respectively.     

Estimation of uncertainty in p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> values determined by potentiometric titration

A procedure is presented for estimation of uncertainty in measurement of the pK(a) of a weak acid by potentiometric titration. The procedure is based on the ISO GUM. The core of the procedure is a mathematical model that involves 40 input parameters. A novel approach is used for taking into account the purity of the acid, the impurities are not treated as inert compounds only, their possible acidic dissociation is also taken into account. Application to an example of practical pK(a) determination is presented. Altogether 67 different sources of uncertainty are identified and quantified within the example. The relative importance of different uncertainty sources is discussed. The most important source of uncertainty (with the experimental set-up of the example) is the uncertainty of pH measurement followed by the accuracy of the burette and the uncertainty of weighing. The procedure gives uncertainty separately for each point of the titration curve. The uncertainty depends on the amount of titrant added, being lowest in the central part of the titration curve. The possibilities of reducing the uncertainty and interpreting the drift of the pK(a) values obtained from the same curve are discussed.     

Rapid determination of the equivalence volume in potentiometric acid-base titrations to a preset pH-II Standardizing a solution of a strong base, graphic location of equivalence volume, determination of stability constants of acids and titration of a mixture of two weak acids

A newly proposed method of titrating weak acids with strong bases is applied to standardize a solution of a strong base, to graphic determination of equivalence volume of acetic acid with an error of 0.2%, to calculate the stability constants of hydroxylammonium ion, boric acid and hydrogen ascorbate ion and to analyse a mixture of acetic acid and ammonium ion with an error of 0.2-0.7%.     

Determination of the equivalence point in potentiometric titrations with gran's first method used to test the electrode response

Gran's first method is compared to the standard addition (subtraction) method. It is shown that Gran's first method canbe used to test the electrode response of, for example, a copper-selective electrode.     

Determination of carbonate in the presence of hydroxide: Part 2. Evidence for the existence of a novel species from first-derivative potentiometric titration curves

An additional maximum has been detected in the differential potentiometric titration of mixtures of sodium hydroxide and sodium carbonate with hydrochloric acid using pH-responsive glass electrodes. This maximum is not detected under the following conditions: if ethanol (mol fraction >0.2) or t-butanol (mol fraction >0.1) is added; when the temperature is raised above 55°C; when hydrogen gas is bubbled through the solution; if a hydrogen gas electrode is used instead of the glass electrode; when carbonic anhydrase is added. The additional feature is ascribed to a new species HCO₃·H₂CO₃^- formed in solutions by a slow reaction.