1. Introduction

The National Bureau of Standards conducts a great deal of research towards establishment of absolute standards in all areas of the measurement field. One area which enables analytical quantification of chemical property on the absolute basis is coulometry. For this reason, over a number of years, an intense effort has been made to develop methods for precise analysis and to test the accuracy of these methods [1-5].1 This paper is one of a series of articles on the development of precise coulometric methods and their application to characterization of high purity standard reference materials (SRMs).

The expanding use of boron and its compounds in nuclear technology and the NBS program concerned with the issuance of an SRM for neutron flux monitoring necessitated the development of a method for the precise and accurate determination of this element. The most widely used method for the determination of milligram amounts of boron involves titration of boric acid in the presence of a polyol [6], usually mannitol. However, this method is somewhat empirical in nature, particularly with respect to the amount of polyol required for titration and moreover, is generally precise to only a few parts per thousand. Le Duigou and Lauer recently reported a procedure for the coulometric determination of boron [7]. Their precision for 150-mg samples of boric acid was on the order of 0.02 percent. Thus, the method appeared promising from the standpoint of precision, but the disturbing fact is that these authors found a discrepancy of 0.1 percent between the coulometric value and the value obtained by conventional acidimetric titration. Referring to the coulo

'Present address: Methods Research and Technical Service Division, Eastman Kodak, Rochester, New York 14603.

Figures in brackets indicate literature references at the end of this paper.

metric method, these authors concluded that further studies are necessary to improve its accuracy. This conclusion alone was sufficient to arouse our interest in the coulometric behavior of the system, particularly from the standpoint of possible sources of error which apparently have not been ruled out in the coulometric investigations of Le Duigou and Lauer.

We therefore undertook investigation of the effects of various titration parameters on the coulometric analysis of boric acid complexed with mannitol.

2. General Considerations

SRM #951. The analysis of this material by emission The principal material investigated was boric acid, spectroscopy indicated that total metallic impurities did not exceed a few parts per million.

Reagent grades of KCl and mannitol were used for the preparation of the supporting electrolyte. Titrations of small amounts of HCl (20-30 μeq) showed that the neutrality point of 1M KCl containing mannitol is at pH 6.98. Consequently, in all experiments, small amounts of HCl were added to the electrolyte to facilitate removal of CO2 by nitrogen purging, and the electrolyte was pretitrated to neutrality before the addition of the investigated boric acid sample.

3. Apparatus and Procedure

3.1. Apparatus

The instrumentation, apparatus, and acidimetric procedure used in our laboratory have been described previously [8]. The coulometric cell used in these analyses is shown in figure 1. The constant-current and timing facility enables measurement of charge passed through the cell with an accuracy of a few parts in

FIGURE 1. Coulometric titration cell for boric acid analysis. 106. The mass of samples is measured with an accuracy of 0.003 mg by substitution weighing on a 20-g capacity microbalance. The end point of titration is determined potentiometrically using a pH meter and a glass-calomel combination electrode. The readability of the pH meter is 0.001 pH unit. Although the accuracy of the pH measurement is not very significant since a differential procedure is used and the inflection point is taken as the equivalence point, the pH meter was regularly standardized against NBS pH 6.865 phosphate buffer (SRM #1861c and SRM #1861Ib).

3.2. Procedure

In our previous procedures, the acid was titrated at high current (100 mA) for a precalculated period of time to bring the system very near to the end point, followed by the passage of small charge increments at lower current. After passage of each charge increment, pH was measured and the inflection point on the potentiometric curve was established graphically using a ApH/AC versus C plot. In such a procedure, one titrates significantly beyond the inflection point. The final pH change, due to rinsing of cell walls, cell cover and intermediate compartments, takes place on that portion of the potentiometric curve, the slope of which is significantly lower than (ApH/AC) max. Thus, the estimate of the correction due to final rinsing is not as accurate as it could be if it were measured in the region

close to (ApH/AC) max. However, in such a procedure. one cannot stop the titration in the immediate vicinity of the inflection point without jeopardizing the accuracy of the evaluation of (ApH/AC) max. To satisfy both of these conditions, the titration procedure was modified.

It was found in a few preliminary experiments that the boric acid used was very close to stoichiometric H3BO3. Consequently 100.00 percent of the precalculated number of coulombs, necessary to reduce all of the hydrogen ion which is delivered into the cell with the boric acid sample, was passed through the cell. The cell walls, top and intermediate compartments were rinsed until no significant change in pH (within 0.003 pH units) was observed, and the final pH of the solution was recorded. Since the acid was close to stoichiometric H3BO3, this pH measurement was made in the (ApH/AC) max region and thus in the region of maximum sensitivity. To determine the difference (in coulombs) between the pH at this final rinse point and the pH at (ApH/AC) max, a small amount of hydrochloric acid (10-20 μeq) was added to the cell and the regenerated boric acid was retitrated differentially to establish pH at (ApH/AC) max. This process can be repeated several times to improve the evaluation of the inflection point (9). In practice, then, a correction of a few thousandths of a percent is applied at the end of the titration for the difference between the final pH and the pH at the inflection point.

The procedure can be clarified by considering a specific example. A sample of boric acid, contained in a polyethylene boat and weighing 0.599207 g (vacuum corrected weight), was delivered into the cathode compartment of the coulometric cell containing 100 ml of iM KC1-0.75M mannitol supporting electrolyte which had been previously pretitrated to neutrality point.

After passage of the precalculated charge of 935.204 C at 101.7840 mA, the current was interrupted, the intermediate cell compartments were rinsed, and a final pH reading of 8.234 was observed. A few drops of 0.1N HCl were added to the cathode compartment whereupon the pH of solution dropped to 7.567. Equal charge increments (0.100 C) were passed through the cell at 10.178 mA and the pH was measured following passage of each increment. The data obtained are shown in table 1 and figure 2.

The inflection point occurred at pH=8.095 (point A on the graph). The pH at the completion of the passage of charge through the cell at high current was 8.234 (point B on the graph), corresponding to an overtitration of 0.178 C. Thus, it is necessary to correct the total charge by -0.178 C, and the number of coulombs equivalent to the delivered sample of boric acid is 935.026 C. By Faraday's law this corresponds to 9.69069 meq of acid or the weight of boric acid of 0.599205 g. Since 0.599207 g of the acid was weighed out, the assay of the material found in this titration is 99.9997 weight percent H3BO3.

In an earlier communication the error which resulted from the difference between the inflection point and the equivalence point in coulometric titration of boric acid was evaluated [9]. It was found that when cK is 10-9, the error is 0.003 percent, and for larger cK, it is

correspondingly smaller, as predicted by the Roller equation [10]. All of the subsequent work was conducted under the condition when cKa⇒ 10-9 and thus the error due to this source is negligible.

4. Experimental Variables

It was pointed out above that the investigation of Le Duigou and Lauer [7] raised the question as to the accuracy of coulometric titration of boric acid. There are two ways of examining this problem. First, and the simplest, would be to titrate boric acid of known stoichiometry. Unfortunately materials of stoichiometry known to a thousandth of a percent are not available. The second method would be an indirect one, involving a study of all known sources of possible systematic error. Of necessity, the second path was followed.

To determine the nature of the effect of various titration parameters, each of them was varied over the desired range and the observed effects are reported in the following discussion.

The accuracy of coulometric acidimetry conducted in IM KCl medium has been treated earlier [1, 8, 11]. In titrations of boric acid, however, the supporting electrolyte, in addition to potassium chloride, must also contain mannitol. It was therefore necessary to determine if the mannitol has any effect on the electrochemical reaction at the platinum cathode. To investigate the possible interference of mannitol in the coulometric reaction, HCl solution, single crystal oxalic acid dihydrate, and acid potassium phthalate, respectively, were analyzed coulometrically in IM KCl both with and without mannitol. This choice of acids was made to cover a range of pKa values which would include the pKa of mannitoboric acid (in 0.75M mannitol, the apparent K of boric acid is 4.17 × 10−5).

Hydrochloric acid solution was made by dilution of reagent grade concentrated acid in a one-liter volumetric flask to approximately 1M concentration. The flask was stoppered with serum rubber septum and kept between uses in a 100 percent relative humidity atmosphere. Samples of this solution were aliquoted for analysis by weight using the disposable syringe and platinum hypodermic needle as weight buret. The rubber septum, covering the HCl solution, was pierced by the hypodermic needle and the required volume of solution was withdrawn by the earlier described procedure [12].

Oxalic acid dihydrate was single crystal material, grown in a mixed acetone-water bath by the temperature dropping technique [13]. It is the same material which was used in the determination of the electrochemical equivalent and the faraday [8].

Potassium hydrogen phthalate was NBS SRM #84h. It was assayed coulometrically in 1M KCl by Paabo [14]. The data obtained by Paabo is compared with our data obtained in mannitol containing electrolyte. The results of the analyses of these acids are summarized in table 2, and will be discussed in the appropriate section of this paper.

The effect of mannitol on the strength of boric acid has been investigated quite extensively [15–22]. Much of this work can be summarized from the analytical standpoint as follows: (a) boric acid becomes stronger as the mannitol concentration increases; (b) in concentrated solutions, anomalous conductance values indicate association; (c) electrolytes in solution affect the boric acid hydrolytic equilibrium. Thus, as the concentration of mannitol increases, the end point pH of boric acid titration decreases, and the slope of the titration curve increases. However, it has not been established whether or not this has an influence on the stoichiometry of acidimetric reaction and consequently on the titration results.

Accordingly, a number of samples of boric acid were analyzed in the following electrolytes: IM KC1-0.25M mannitol; IM KC1-0.75M mannitol; 1M KC1-1.05M mannitol (saturated). The data are shown in figure 3.

In the investigation of the mannitol effect, the boric acid sample size was also varied as shown in the same figure.

Most of the analyses of boric acid were performed in IM KC1-0.75M mannitol electrolyte, and consequently much more extensive data were obtained on sample

size dependence of the assay in this medium. The data are summarized in table 3.

Study of the behavior of the SRM boric acid whi was used throughout this work indicates that th material is somewhat deficient in water. It was 4.parently prepared under conditions which resulted: the formation of small amounts of B2O3. This conc.. sion is supported by the following evidence. Samp weighed directly from the original boric acid containers! and permitted to sit in the room at 28 percent relati humidity for 30 minutes gained weight, as illustrate: in table 4. The mean value of the percentage weig gains for six samples, in the indicated period of time. was found to be 0.008 percent. Analysis of the materi after 30-min exposure to 28 percent relative humidi resulted in an assay of 100.005 percent, indicating the this treatment is still not quite sufficient to produce stoichiometric H3BO3.

Additional information on the effect of the relative humidity of the environment on the stoichiometry B2O3-H2O system at 25 °C was obtained in controled humidity experiments. Boric acid was initially exposed to room atmosphere (approx. 34% RH) for several hours, in the course of which the material absorbed water and approached stoichiometric composition. S. sequently, boric acid was placed in controlled humic environments. After at least a four-day exposure to controlled atmosphere with an occasional mixing of the crystals, samples were weighed out for analysis. T results of these analyses are shown in figure 4. It be seen that in the 0 to 60 percent relative humid range, the assay of boric acid remains constant & close to stoichiometric H3BO3. Beyond 60 percent re 2 tive humidity, additional water is sorbed by boric ac reaching a value of 0.02 percent (referred to the we.." of stoichiometric boric acid) at 90 percent rela:: humidity.

It is thus concluded that exposure of this lot of bon acid to humid atmosphere is beneficial, in fact ne sary if one wishes to insure that stoichiometric H E composition was achieved. Subsequently, the mater is stable and can be stored at any humidity below -n percent. Considering even drastic environmental con. tions, such as variation of humidity between 0 and

percent, the material changes its stoichiometry by only 0.020 percent. This probably occurs due to adsorption of water on polycrystalline boric acid.

In view of initial decrease of assay of this material when it was exposed to moderate humidity environment, its stability up to ca. 60 percent R.H., and further decrease beyond this humidity, we conclude that the material equilibrated at 35 percent relative humidity is very close to stoichiometric H3BO3 composition so far as H2O-B2O3 equilibrium is concerned.

Though accurate acidimetric assay value has been btained for the investigated H3BO3, in many instances

the element of interest is boron. Since acidimetry is only an indirect method of assaying this material for boron, one must in fact prove the correspondence between the titratable H+ and B.

The presence of strong acids or metal borates could not be detected titrimetrically below a few hundredths