Louis Meites

Theory of titration curves

Abstract 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.

Coulometric determination of chromium

Abstract This paper describes an accurate and precise method for the determination of chromium by coulometry at controlled potential. A solution of the sample in 6 M hydrochloric acid is electrolyzed at a large stirred mercury cathode whose potential is maintained constant at —1.10 V vs. S.C.E. ;this reduces the chromium quantitatively to the +2 state. Copper, lead, and a number of other elements are next eliminated by simply discarding the mercury and replacing it with fresh mercury ;then uranium is re-oxidized to non-interfering uranium(IV) by a second controlled-potential electrolysis at —0.80 V vs. S.C.E.; and finally the solution is electrolyzed at a working electrode potential of —0.40 V vs. S.C.E. This serves to re-oxidize the chromium quantitatively to the +3 state, and the analysis consists of measuring the quantity of electricity consumed in this oxidation. Of the elements commonly associated with chromium, only vanadium (and, when it is present in large amounts, molybdenum) interfere in this procedure.

Corrections for double-layer charging in chronopotentiometry

Summary Numerical computations of linear-diffusion chronopotentiograms distorted by double-layer charging are used to show that previously proposed corrections are erroneous in principle and to devise a simple empirical procedure for evaluating the Sand-equation transition time from a measurement of the time required for the traversal of an arbitrary range of potentials on a single chronopotentiogram. The effect of double-layer charging in current-reversal chronopotentiometry is to increase the ratio of the reverse transition time to the forward one. Double-layer charging and extraneous faradaic processes have different effects on the time-dependence of the current efficiency for the process of interest, and corrections for them must therefore be made in different ways.

The reduction and oxidation of vanadium in acidic aqueous sulfate solutions at mercury electrodes

Abstract The rates and mechanisms of electrolytic processes occurring at mercury electrodes in aqueous acidic sulfate solutions of vanadium in its various oxidation states have been. studied by polarography, absoiption spectroscopy, and controlled-potential amperometry and chronocoulometry. The complex behavior observed is interpreted in terms of polynuclear species containing vanadium and undergoing slow transformations. Both vanadium(II) and vanadium(III) exist in three forms, each of which may be reduced to give hydrogen and a deprotonated species of vanadium ; these reductions give rise .to kinetic and induced currents the behaviors of which are described in detail.

Theory of titration curves: Locations of points of maximum slope on potentiometric heterovalent (“asymmetrical”) precipitation titration curves

By a wholly rigorous general treatment of the potentiometric titration curve representing the titration of Bm+ with An- to give the precipitate BnAm, where n ≠ m, it is shown on taking into account the effect of dilution that: (1) If nm > 1, the inflection point must precede the equivalence point, but there is no inflection point if the initial concentration of the ion titrated is smaller than a certain value, which is determined by the values of m, n, and the solubility product of the precipitate. (2) If nm < 1, the inflection point may follow the equivalence point — though not by more than a certain definite amount — or may precede it or coincide with it. In every such case there is a concentration of An- that will cause the equivalence point to coincide with an inflection point; this concentration depends on the values of m, n, and the solubility product of the precipitate. (3) Unless the difference between the equivalence and inflection points is negligibly small, the traditional treatment in which dilution is neglected gives seriously erroneous estimates of the location of the inflection point.

Polarographic characteristics and controlled-potential electro-reduction of dimethylglyoxime

Abstract Acidic solutions of dimethylglyoxime produce a well-defined polarographic wave corresponding to an 8-clcctron reduction to 2,3-diaminobutane. The effects of various experimental variables on the characteristics of the wave are described, and an equation is advanced for its rate-determining step. The reduction of dimethylglyoxime at a large mercury electrode at controlled potential induces the reduction of hydrogen ion, and the mechanism of this process is discussed on the basis of coulometric evidence. Acidic solutions of dimethylglyoxime slowly decompose, by a reaction whose rate law is given, yielding what is believed to be 2,3-dinitrosobutane as the principal product.

Theory of titration curves: Locations of points at which ph=pka on potentiometric acid-base titration curves; end-point errors in titrations to predetermined ph values

Abstract For the titration of a pure solution of a weak monobasic acid with a strong base, it is shown that the fraction of the equivalent volume of base added at the point where pCH = pKα is exactly equal to 1 2 if and only if pKα = pK ω 2 , in which case it is independent of dilution. It is less than 1 2 if pKα ω 2 and is greater than 1 2 if pKα > pK ω 2 , and in either of these cases it depends on the concentrations of both acid and base. Explicit descriptions are given of the conditions under which pcH = pKα either at the start of the titration or at the equivalence point. For the titration of either a weak or a strong acid with a strong base, exact equations are given for the titration error resulting from the termination of the titration at any preselected pcH value.

Sub-microgram-scale analysis by coulometry at controlled potential

Abstract The considerations which determine the success of controlled-potential coulometric analyses on the submicrogram level are discussed, and it is shown that the ultimate sensitivity of the method is governed by the accuracy with which the requisite background corrections, especially that for the charging quantity of electricity, can be determined. A method for the coulometric determination of zinc based on these considerations is shown to contain a limiting uncertainty of ± 0.2 mμFy, so that as little as 0.07 μg of zinc can be determined within about ± 10%, while quantities of zinc exceeding about 10 μg can be determined with an accuracy and precision of ± 0.1% or better. Possible techniques for the further extension of controlled-potential coulometric analysis into the millimicrogram range are briefly discussed.

Theory of titration curves: Part VI The slopes and inflection points of potentiometric chelometric titration curves

Abstract Exact general descriptions are given of the slopes, the relative precisions, and the locations of the inflection points obtained in potentiometric titrations of a metal ion M with a chelon Y to give the soluble 1:1 chelonate MY, using an ideally cation-responsive indicator electrode. The relative precision depends on the conditional formation constant k of the chelonate, the initial concentration C M O of the metal ion, and the dilution parameter r , which is the ratio of the concentration of the chelon solution to C M O . Criteria for the existence and number of inflection points are given. When there is a point of maximum slope, it always precedes the equivalence point. If r exceeds a certain value, which depends on the value of kC M O , a point of minimum slope also appears; if kC M O is large this appears at the very start of the titration curve when r = 1 and approaches a point two-thirds of the way to the equivalence point as r increases. The exact locations of the inflection points are given under various conditions, and equations are also given that permit them to be closely approximated in titrations for which kC M O is large.

Automatic and coulometric titrations in studies of chemical kinetics: III. Evaluation of the rate constant for the disproportionation of uranium(V) by automatic amperometric titrations of uranium(VI) with chromium(II)

The rate constants for the disproportionations of uranium(V) in perchlorate solutions having hydrogen-ion concentrations between 0.01 and 1.9 M have been evaluated by adding a solution of chromium(II) at a constant rate to one of uranium (VI), employing a vibrating dropping mercury electrode to follow the variation of the concentration of either uranium(VI) or uranium(V). The resulting values are in acceptable agreement with those obtained by other techniques.