Axel Johansson

Acid-base titrations by stepwise additions of equal volumes of titrant with special reference to automatic titrations—I: Theory, discussion of the gran functions, the hofstee method and two proposed methods for calculating equivalence volumes

The range of acid stability constants over which the Gran functions are applicable in evaluating acid-base titrations at normal concentrations is studied and found to be quite narrow. Alternatively, the titrations can be evaluated by using non-approximative methods based upon an equation that is derived without making the simplifying assumptions leading to the Gran functions. One such method, introduced by Hofstee, is discussed and the results of a study of the effects of a systematic error in the pH-determinations upon the determination of the equivalence volume are given. Two other non-approximative methods for evaluating acid-base titrations that are particularly suitable for use in automatic titrations of many similar samples are also described. These methods yield correct values of the equivalence volume regardless of a possible systematic error in the pH-values and are particularly useful for titrations of moderately strong and very weak acids (stability constants up to 10(10)-10(11) at 0.01M concentration) where the Gran functions cannot be used.

Automatic titration by stepwise addition of equal volumes of titrant. Part I. Basic principles

A method of titration has been developed, in which titrations are carried out by adding titrant stepwise in equal volumes to the sample, with measurement of potential after each addition. This method is well suited for automatic titrations, for example, in biochemical and process control analysis.

Simultaneous multielement analysis using sequentially excited atomic fluorescence radiation

Abstract Atomic fluorescence radiation has properties which simplify instrumentation problems for simultaneous multielement analysis. An instrument for simultaneous analysis, containing a rotating filter wheel and a single photomultiplier-amplifier system, and using pulse modulated hollow cathode lamps is briefly described. The instrument has been used for the simultaneous determination of Ag, Cu, Fe and Mg with an air-hydrogen flame.

Titration of mixtures of acids of nearly equal strengths

Abstract Accurate and precise experimental methods that were developed for the purpose of determining stability constants in aqueous solutions are employed in titrations of acids which have nearly equal strengths. A computer program capable of handling five acids simultaneously has been designed to evaluate the titration data. The results show that it is possible to determine two acids which have stability constants differing by only about one logarithmic unit with an accuracy better than 1%. If the conditions are favourable, it is even possible to analyse a mixture of two acids with about 2% accuracy when the constants differ by as little as 0.2 logarithmic units.

The complexometric analysis of pyro- and triphosphates—I: Stability constants of the proton and metal complexes of the acids

Abstract The stability constants of the proton and some metal complexes formed by pyro- and triphosphoric acids at 25° have been evaluated from potentiometric titration measurements.

Simultaneous multielement analysis using sequentially excited atomic fluorescence radiation—II: An improved instrument for simultaneous analysis

Abstract An improved instrument for simultaneous multielement analysis is described. The instrument has been used for the simultaneous determination of Ag, Cu, Fe and Mg with an air-acetylene flame.

Automatic titration by stepwise addition of equal volumes of titrant. Part II. An automatic titration system

A fully automatic titration system is described. The system carries out transfer of the sample by pipette, and dilution, titration and washing of electrodes and titration vessels. Titrations are performed by adding titrant stepwise in equal volumes to the sample, with recording of potential after each addition. These results are used to calculate equivalence points. The system has a loading capacity of 200 samples, and an analysis rate of up to 30 samples per hour.

Automatic titration by stepwise addition of equal volumes of titrant. Part VII. Potentiometric precipitation titrations

The method used throughout this series to add the titrant stepwise with equal volumes each time is well suited to precipitation titrations. The advantage that one has to wait for equilibrium to be reached at only a few points is of special importance.Two methods for calculation of the equivalence volume in precipitation titrations have been evaluated. One is based on the solution of a set of linear equations and the other is an extended version of the Gran I method. The methods are characterised by the following facts: (1) side-reactions can be accounted for; (2) the values of the solubility product and the stability constants of complexes may be unknown; (3) the solutions may be so dilute that a complete precipitation is not obtained; and (4) no accurate calibration of the electrode couple is required.The calculation methods have been tested on the determination of chloride by titration with silver nitrate solution. The two methods agree closely and the errors in the calculations are negligible. The over-all errors in the determinations are 0.1–0.2% at chloride concentrations down to 10–4M. At lower concentrations the relative errors are greater.The methods have also been tested on the determination of sodium fluoride with lanthanum nitrate in (a) neutral and unbuffered solution, (b) acidic solution, (c) solution buffered with acetic acid-acetate and (d) solution buffered with formic acid-formate. The calculations were performed on experimental curves according to Lingane. For (a) and (b) good agreement between calculated and expected values were obtained. In the acetate-buffered solution too high a value was obtained in spite of the fact that acetate and mixed acetate-fluoride complexes were considered. For (d) the buffer capacity was too small to give satisfactory results.

Automatic titration by stepwise addition of equal volumes of titrant. Part III. Use of linear equations to calculate equivalence volumes in acid-base titrations

Potentiometric titrations in which the titration curve is plotted or the titration is interrupted at a pre-set end-point have important disadvantages. The following conditions must be met to obtain satisfactory results: (1) reaction between titrant and titrand must be rapid; (2) the response time of the indicator electrode must be short; and (3) electrode potentials near the equivalence point must be stable and reproducible.These disadvantages can be avoided by using the method of stepwise addition of titrant. In this method, equivalence volumes cannot be read directly and must be calculated. A computational procedure allowing the calculation of equivalence volumes for the titration of monoprotic acids, bases and ampholytes with log K values up to 11 is described. The procedure is based on the solution of a set of linear equations and requires only a few sets of measurements of e.m.f. versus volume of titrant plus initial volume and titrant concentration. Log K values are not required and e.m.f. measurements may have a constant systematic error up to ±6 mV, corresponding to ±0.1 pH unit. Only concentrations and concentration constants are used. No estimated values of equivalence volumes or stability constants are necessary.

Choice of chemical conditions in order to obtain linear titration curves in potentiometry.

In the titration of an acid HA with a strong base, [HA] diminishes, on the whole, in proportion to the addition of titrant. However, [HA] = K(HA)[H] [A], and if [A] is kept constant [HA] will be proportional to [H]. Therefore if [H] instead of [HA] is plotted against ml of titrant added, one obtains a linear titration curve. [A] is kept constant by addition of NaA before titration in such high concentration that the formation of A can be neglected during the titration. When an acid stronger than acetic acid is titrated, sodium acetate can be used as the added salt. Even mixtures of adds, mono- or polybasic, then yieldstraight titration curves since one is in fact titrating acetic acid in the presence of excess of acetate. For weaker acids sodium sulphite is used. In the oxidation-reduction titration of, for example, ferrous iron with permanganate, the potential measured is dependent on the ratio [Fe(2+)]/[Fe(3+)]. If [Fe(3+)] is kept constant by the addition of ferric chloride before the titration, the potential win be dependent only on [Fe(2+)]. Since this diminishes in proportion to the added volume of titrant, straight titration curves can be obtained in this case also. No correction for dilution should be made.