Article pubs.acs.org/jchemeduc
Boric Acid in Kjeldahl Analysis Gregorio Cruz* Private Laboratory, San Pedro de Alcántara, 5, 1D, Badajoz 06001, Spain S Supporting Information *
ABSTRACT: The use of boric acid in the Kjeldahl determination of nitrogen is a variant of the original method widely applied in many laboratories all over the world. Its use is recommended by control organizations such as ISO, IDF, and EPA because it yields reliable and accurate results. However, the chemical principles the method is based on are not detailed in most analytical textbooks, perhaps because the nature of boric acid is not known in depth. To introduce the reader or student to the chemistry of boric acid, this article first describes the differences in acid−base behavior of concentrated and diluted boric acid by simple calculations and experimental pH measurements. Next, polyborate structures and their respective dissociation constants are shown to explain the differences found in previous pH measurements. In the second part of the article, the determination of ammonia with HCl is made in concentrated and diluted boric acid to reproduce the final Kjeldahl titration when two different volumes of ammonia distillate are collected. From the previous information, the apparently paradoxical results of the titration curves are explained in a qualitative manner. The third part consists of a study of systematic errors produced when colored indicators are used in the final Kjeldahl titration in concentrated and diluted boric, respectively. KEYWORDS: Upper-Division Undergraduate, Analytical Chemistry, Laboratory Instruction, Inorganic Chemistry, Hands-On Learning/Manipulatives, Acids/Bases, Potentiometry, Quantitative Analysis, Titration/Volumetric Analysis
T
he Kjeldahl method1−3 is one of the most versatile methods for nitrogen determination; applications range from food and agricultural4 products to soil and wastewater5 analysis, to mention only a few examples. In spite of its versatility, no universal recipe is used for Kjeldahl determination. The great diversity of samples with different physical statessolid and liquidand chemical composition have led to the development of optimized methods for every kind of sample. Industrial and official laboratories usually follow these “normalized” proceduresISO, ASTM, or AOAC6for nitrogen analysis as they are well-tested and reliable methods. The Kjeldahl method comprises three stages: sample digestion, ammonia distillation, and final titration. In the digestion stage, the sample is treated with concentrated sulfuric acid at a high temperature so that organic nitrogen (in amino or amido form) forms ammonium sulfate. After the digestion process, NaOH is added to the sample to form an alkaline solution and the ammonia produced is distilled and collected in a vessel containing acid, HCl or H2SO4, in excess. In the final stage, the excess is titrated with sodium hydroxide, and the ammonium is calculated by difference. This technique, however, has drawbacks. In addition to the final titration, two previous titrations are needed to normalize the acid and the base. In the past century, Winkler7 modified the method using boric acid for the fixation of ammonia. The distilled ammonia reacts with boric acid to form ammonium borate. Nitrogen is © XXXX American Chemical Society and Division of Chemical Education, Inc.
determined by titration of the ammonium salt with HCl. With this modification, only a normalized HCl solution is needed. An additional advantage is that boric acid solution does not need to be very precisely prepared. A recent article has appeared in this Journal dealing with the theoretical optimization of ammonia titration in diluted boric acid.8 The present article describes the titration of ammonia in concentrated boric acid in an attempt to explain the fundamentals of a widely applied standard method and the optimization of the experimental conditions to avoid systematic errors. This study may be proposed as a classroom exercise to introduce students to the chemistry of boric acid in an inquiry− learning mode and as an initiation to bibliographic research. This multidisciplinary instruction is intended for advanced undergraduate students with previous experience in analytical techniques and at least one year of inorganic chemistry. The experimental results described in this article can also be useful for those professional chemists (academic or not) working on Kjeldahl determination. This article first describes the differences in acid−base behavior of concentrated and diluted boric acid by simple calculations and experimental pH measurements. Next, polyborate structures and their respective dissociation constants are shown to explain the differences found in previous pH
A
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measurements. In the second part of the article, the determination of ammonia with HCl is made in concentrated and diluted boric acid to reproduce the final Kjeldahl titration when two different volumes of ammonia distillate are collected. From the previous information, the apparently paradoxical results of the titration curves are explained in a qualitative manner. The third part consists of a study of systematic errors produced when colored indicators are used in the final Kjeldahl titration in concentrated and diluted boric, respectively.
Figure 1. Structures of (A) triborate, (B) tetraborate, and (C) pentaborate. The charge of the anion is given by the number of tetrahedral boron atoms.
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ACID−BASE BORIC ACID PROPERTIES Boric acid has the formula H3BO3, but it is more precisely formulated as B(OH)3.9 In aqueous solution, it behaves as a Lewis acid B(OH)3 + H 2O ⇄ B(OH)4− + H+
Global constants of dissociation, β, were calculated for triborate and pentaborate19 3B(OH)3 ⇄ B3O3(OH)4 − + H+ + 2H 2O
(1)
The equilibrium constant for solutions with concentrations less than 0.1 M is Ka =
x2 Ca − x
[B(OH)3 ]3
= 2.51 × 10−7
5B(OH)3 ⇄ B5O6 (OH)4 − + H+ + 5H 2O
[B(OH)−4 ][H+] = 5.75 × 10−10 [B(OH)3 ]
β5 =
Thus, in dilute solutions, boric acid behaves as very weak acid (pKa = 9.24).10 The pH value in these conditions can be calculated from the equilibrium constant. If we use x to refer to [B(OH4)−] and [H+] and Ca to refer to the initial boric acid concentration, Ka can be expressed as Ka =
[B3O3(OH)4 − ][H+]
β3 =
[B5O6 (OH)4 − ][H+] [B(OH)3 ]5
= 1.26 × 10−7
These dissociation constants are greater than the Ka of H3BO3 by a factor between 210 and 440. The presence of these acidic species could explain the low experimental pH values found in concentrated solutions.
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KJELDAHL APPLICATION: AMMONIA DETERMINATION WITH HCL The experiments described are designed to study the effect of the initial boric acid concentration in the Kjeldahl titration. To simulate a distillation, a fixed volume of ammonia was added to two beakers containing concentrated boric acid. In one beaker, 200 μL of ammonia solution was added to 50 mL of 0.65 M boric acid. This can be viewed as a hypothetical distillation in which all the ammonia is dissolved in the initial boric acid solution with a negligible increase in volume. The same operation was carried out in another beaker with 50 mL of 0.65 M boric acid, but an extra 100 mL of water was added to mimic a distillation in which 100 mL of distillate is collected. Then the ammonium borate solutions were titrated potentiometrically with HCl using the glass pH electrode.
(2)
Given the low dissociation of the acid, the equation can be simplified to pH = −1/2 log (KaCa). In dilute solutions (less than 0.1 M), boric acid can form buffer solutions10 in the pH range 8−10. A good estimation of the pH of these buffers can be made by applying the expression pH = pKa + log [A−]/[HA]. From these calculations, it appears that at low concentrations, boric acid behaves similarly to any other weak acid. But what happens with concentrations greater than 0.1 M? To assess this situation, we can prepare a concentrated solution of boric acid, measure the pH with a glass electrode, and compare the experimental value with the theoretical value. In many applications of the Kjeldahl method,11 boric acid is frequently added at 4%, (40 g/L) or 0.65 M, near its solubility limit12 of 47 g/L. The pH obtained with the glass electrode is 3.90, whereas the calculated value is 4.71. These differences cannot be explained only by ionic strength, water dissociation, and so forth. Therefore, we have to consult inorganic chemistry textbooks12−14 to understand the real nature of boric acid.
Material and Methods
The titrant HCl, 0.1 M, was previously calibrated with a standard solution of tris(hydroxymethyl)aminomethane. The ammonia solution was prepared by dissolving 2 mL ammonia at 25% in 3 mL of water. The solution was stored in a 5 mL flask. In the assays, 200 μL of ammonia solution was added to each boric acid solution. The titrations were made with an electronic buret (Brand Titrette). With this device, volumes as low as 0.03 mL can be delivered with great precision (see titration data in the worksheet included in Supporting Information).
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POLYBORATES Studies of concentrated boric acid solutions by potentiometric titrations of borate salts were conducted in the 1960s and1970s.15−17 After the calculations, several polymeric borates were formulated: triborate, in two forms B3O3(OH)4− and B3O3(OH)52−; tetraborate, B4O5(OH)42−; and pentaborate, B5O6(OH)4−; among others. Further studies of boric acid salts in solution were made by Raman spectroscopy and characteristic frequencies were compared to those of solid salts.18 The appearance of common bands supported the presence of triborate, tetraborate, and pentaborate anions. The structures of these polyanions are shown in Figure 1.
Titration
The titration curves for the two solutions are depicted in Figure 2. Characteristics values of the curves are summarized in Table 1. When boric acid concentration is diluted to one-third (compare Figure 2 panels A and B), the initial pH is raised 1 order of magnitude. This increment cannot be explained by dilution effects. Moreover, from the curves and derivative value in Table 1, the more diluted solution produces the sharper the B
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Figure 2. pH and derivative curves for ammonium borate titration, with (A) 50 mL of 0.65 M boric acid and (B) 150 mL of boric acid 0.22 M.
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Table 1. Characteristic Data from the Titration Curves Shown in Figure 2 [H3BO3],a M
pH initial
Veq, mL
Cxb, M
ΔpH/ΔV
pH at Veq
0.65 0.22
6.35 7.38
11.99 11.95
7.19 7.17
4.8 6.7
3.79 4.72
END POINT DETERMINATION: SYSTEMATIC ERRORS The equivalence volume is very similar for the two titrations (see Table 1). But the lower pH value at Veq for concentrated boric acid solutions affects the detection of the final point when colored indicators are used, as we will see in the following example. The mixture of methyl red and methylene blue known as Tashiro indicator is frequently used in this kind of titration; its color changes from green at pH 6.6 to blue at pH 4.4. In the curve of Figure 3, this value lies between 11.98 and 12.01 mL. Taking this last value, an error of 0.5% or less results due to excess in the equivalence volume.20
a
Initial boric acid concentration. bAmmonia concentration in the 200 μL initial sample.
end point. An inspection of the derivative curves shows the appearance of local minima before the end point. This is more apparent in the 0.65 M curve (see Figure 2 panels A and B.
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UNDERSTANDING BORIC ACID CHEMISTRY The striking results obtained in the titration curves can only be explained by presence of polyanions other than monoborate. These polyborates are more abundant in concentrated boric acid and progressively disappear as dilution and pH increases, becoming monoborate. In diluted solutions of H3BO3 the ammonia is dissolved as follows: NH3 + H 2O ⇄ NH4 + + OH− −
B(OH)3 + OH ⇄ B(OH)4
−
(3) (4)
In concentrated solutions, polymeric boric acids compete with B(OH)3 for ammonia to form polyanions (see Figure 1 panels A and C). The neutralization of these polyborate species explains the peaks found near the absolute minimum in Figure 2A and the lower pH at the equivalence point (Table 1). In the Kjeldahl analysis, the low initial pH values of these acids favor NH3 dissolution, especially at the first stages of distillation when more ammonia is released. Titration with HCl reverts the equilibrium (eq 4) to form boric acid and ammonium chloride. Because B(OH4)− is a stronger base than the other polyborate anions, an increase in monoborate concentration should give a higher pH interval with a steeper descent in the titration curves. This is observed in the curve of Figure 2B, where the higher pH interval results in a more accurate end point determination. In Kjeldahl distillations, it is a common practice to collect relatively large volumes of distillate (75 to 100 mL) to ensure that all ammonium is collected in the vessel; this dilution increases monoborate concentration and improves precision in the final titration.
Figure 3. Titration in 0.22 M boric acid. The brown line is the pH at the minimum derivative value. The dashed green line is the pH value for Tashiro indicator color change.
For an initial 0.65 M boric acid solution, a pH of 4.4 corresponds to a volume of 11.8 mL (Figure 4). Because the derivative end point is found at 11.99 mL, the change in color is produced too early and an error of 1.6% results by default, more than three times that obtained with diluted boric acid. Therefore, when colorimetric indicators are used, it is advisable to use a 3-fold or more final dilution up to an initial pH ≥ 7.4 and always to collect the same volume for repetitive results.21,22 In potentiometric titrations, accurate determination of the equivalence point can be obtained by derivative methods or Gran’s linear extrapolation (see the Supporting Information). C
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(7) Winkler, L. W. Beitrag zur titrimetrischen Bestimmung des Ammoniaks. Angew. Chem. 1913, 26, 231. (8) Michalowski, T.; Asuero, A. G.; Wybraniec, S. The Titration in the Kjeldahl Method of Nitrogen Determination: Base or Acid as Titrant? J. Chem. Educ. 2013, 90 (2), 191−197. (9) European Chemical Agency, Boric Acid. http://echa.europa.eu/ documents/10162/13638/svhc_supdoc_boric_acid_publication_en. pdf (accessed Oct 2013). (10) Kolthoff, I. M.; Sandell, E. B.; Meehan, E. J.; Bruckenstein, S. Analisis Quimico Cuantitativo, 4th ed; Nigar: Buenos Aires, 1969; p 1198 (11) Scales, F. M. Boric acid modification of the Kjeldahl method for crop and soil analysis. Ind. Eng. Chem. 1920, 12 (4), 350−352. (12) Mellor, J. W. Mellor’s Comprehensive Treatise on Inorganic & Theoretical Chemistry, Volume V Boron, Part A: Boron-Oxygen Compounds; Longman: London and New York, 1980. ́ (13) Cotton, A.; Wilkinson, G. Quimica Inorgánica Avanzada, 3rd ed.; Editorial Limusa: Mexico City, Mexico,1974; p 279. (14) Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements; Pergamon Press: Elmsford, NY, 1984; 231−233. (15) Ingri, N. Equilibrium Studies of Polyanions. On the first Equilibrium Steps in the Acidification of B(OH)4− . An Application of the Self Medium Method. Acta Chem. Scand. 1963, 17, 573−580. (16) Ingri, N. Equilibrium Studies of Polyanions Polyborates in 3.0 M Na Br, 3.0 M LiBr and 3.0 M KBr. Comparison with Data Obtained in 3.0 M NaClO4. Acta Chem. Scand. 1963, 17, 580−589. (17) Mesmer, R. E.; Baes, C. F.; Sweeton, F. H. Acidity Measurements at Elevated Temperatures. VI. Boric Acid Equilibria. Inorg. Chem. 1972, 11, 537−543. (18) Maya, L. Identification of Polyborate and Fluoropolyborate Ions in Solution by Raman Spectroscopy. Inorg. Chem. 1976, 15, 2179− 2183. (19) For tetraborate, a log(ß4) value of −14.66 was found. (20) The mixture, 0.01% methyl red, 0.02% bromothymol blue, and 0.06% bromocresol green, has a break point at pH 4.6, which is better than Tashiro indicator for diluted boric acid; see refs 21and 22. (21) Community Bureau of Reference The certif ication of the contents (mass f raction) of Nitrogen, Phosphorus, Chloride, Sodium, Potassium, Magnesium and Calcium and the Kjeldahl-nitrogen Content in a Skim Milk Powder. Commission of the European Communities, BCR No. 63. (22) International Dairy Federation IDF Standard 1982, 114, Anex A
Figure 4. Titration in 0.65 M boric acid. The brown line is the pH at minimum derivative value. The dashed green line marks the pH value for the Tashiro indicator final color.
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CONCLUSIONS This review of boric acid chemistry makes students aware of the limitations of the classical acid−base theory in concentrated solutions when association or condensation reactions may take place that produce species with different acid−base behavior, a topic rarely treated in elementary textbooks. Nitrogen determination by the Kjeldahl method using concentrated boric acid is a common practice in many laboratories. However, the chemical bases involved the process are not very well known. Understanding boric acid chemistry can aid the interpretation of titration curves and provide an explanation for the experimental conditions described in the standard methods.
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ASSOCIATED CONTENT
S Supporting Information *
Information for the instructors and students; detailed description of the calculations and Gran’s end point determination; titration data are included in an Excel file. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*G. Cruz. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Veibel, S. John Kjeldahl. J. Chem. Educ. 1949, 26 (9), 459−461. (2) Kjeldahl, J. Z. A new method for the determination of nitrogen in organic bodies. Anal. Chem. 1883, 22, 366. (3) Bradstreet, R. B. The Kjeldahl Method for Organic Nitrogen. Academic Press Incorporated: New York, 1965. (4) EN ISO 20483:2006 Cereals and pulses − Determination of the nitrogen content and calculation of the crude protein content − Kjeldahl method (5) United States Environmental Protection Agency. EPA-600/4-79020: Methods for Chemical Analysis of Water and Wastes. Environmental Protection Agency, Environmental Monitoring and Support Laboratory: Cincinnati, OH, 1979. (6) Official Methods of Analysis, 18th ed.; Association of Official Analytical Chemists, Inc.: Arlington, VA, 2007. D
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