The Titration in the Kjeldahl Method of Nitrogen ... - ACS Publications

Article pubs.acs.org/jchemeduc

The Titration in the Kjeldahl Method of Nitrogen Determination: Base or Acid as Titrant? Tadeusz Michałowski,*,† Agustin G. Asuero,‡ and Sławomir Wybraniec† †

Faculty of Engineering and Chemical Technology, Technical University of Cracow, 31-155 Cracow, Poland Department of Analytical Chemistry, The University of Seville, 41012 Seville, Spain

‡

S Supporting Information *

ABSTRACT: The final step of the Kjeldahl method of nitrogen determination in biological and other samples faces a dilemma: which titrant, whether acid or base, should be used for the titration of ammonia? To solve this problem, a simple calculation procedure, illustrating the manner of ammonia determination in this method, enables one to resolve this dilemma with the use of theory based on acid−base titration curves. It refers, in particular, to the choice of a strong acid (HCl, H2SO4) solution as a titrant for titration of the solution with H3BO3 applied in a receiver flask following the distillation (NH3) step. The paper presents a clear illustration of the statement that “a good theory is the best practical tool”. KEYWORDS: Upper-Division Undergraduate, Analytical Chemistry, Computer-Based Learning, Problem Solving/Decision Making, Acids/Bases, Aqueous Solution Chemistry, Potentiometry, Titration/Volumetric Analysis

T

he Kjeldahl method1 is widely applied to the measurement of nitrogen content in foods, beverages (originally it was designed for the brewing industry2), meat, agricultural products, feed, waste, environmental waters, soil, biological materials, dairy products, vinegar, pharmaceutical products, and many other samples. It has been the subject of a great number of scientific studies and some review papers were devoted to this method.2−7 The Kjeldahl method consists of three steps:8

K1N

NH4 + HooI H+ + NH3 [NH3] = 10 pH − pK1N [NH+4 ]

where pK1N = −logK1N; pK1N = 9.35 at 20 °C. Among several alternatives applied for estimation of ammonia in the digest,6 the steam-distillation followed by titration is the most popular method.2 The distillation is sped up by the use of the semiautomated systems.9,10 After collection in an acid solution, ammonia is titrated with strong base or strong acid, depending on whether strong acid (HCl or H2SO4) or boric acid (H3BO3) is applied in the distillation receiver; H3BO3 is commonly used to trap ammonia.11−13 Optionally, a titration with sulfamic acid (as primary standard) solution was also suggested.14 Another titrimetric approach, the so-named “formol” titration, with formaldehyde, was also applied for this purpose.15,16 Titration of ammonia absorbed in H3BO3 solution offers an advantage that only one standardized solution (e.g., HCl or H2SO4) is needed (as titrant) and the results of titrations are obtained directly. When a strong acid (HCl or H2SO4) is applied in the receiver (i.e., in the titrand), two standard solutions are needed: (i) titrant (NaOH solution) and (ii) the strong acid in the receiver; in (ii), the results are obtained in an indirect manner. There were some proposals involved with a choice of a proper indicator or mixtures of indicators applied in these (visual) titrations. For example, mixture of methyl red and

(1) acidic (conc. H2SO4) digestion (mineralization) of nitrogencontaining sample (in presence of a catalyst and a salt promoting the ebullioscopic effect) causing its conversion into NH4+ ions; (2) transformation of NH4+ ions into NH3, distillation of NH3 with water steam and collection of NH3 in the acidic distillation receiver; (3) titration of the solution from the distillation receiver. In the Kjeldahl’s original method of nitrogen analysis, sulfuric acid alone was used as a digestion medium; the digestion in boiling H2SO4 converts organic nitrogen into NH4+. To shorten the time needed for the digestion made in a Kjeldahl flask, a selenium reagent mixture (Na2SO4, Hg2SO4, CuSO4, Se) is usually applied; Na2SO4 increases the boiling point of H2SO4, and the other components act as catalysts. Digestion in the temperature range of 360−410 °C6 is completed when the digesting liquor clarifies with the release of fumes. Transformation of NH4+ into NH3, caused by addition of NaOH (pH growth) in Parnas−Wagner apparatus, is shown as © 2012 American Chemical Society and Division of Chemical Education, Inc.

(1)

Published: December 7, 2012 191

dx.doi.org/10.1021/ed200863p | J. Chem. Educ. 2013, 90, 191−197

Journal of Chemical Education

Article

Table 1. Equations for Titration Curves Related to Different Titrand and Titrant (D + T) Systemsa System

Titrand (D)

V = V(pH)a

Titrant (T)

a

HCl (C0) + NH3 (C0N)

NaOH (C)

V = V0·

C0 − ηN̅ ·C0N − α C+α

b

H2SO4 (C0) + NH3 (C0N)

NaOH (C)

V = V0·

(2 − ηS̅ )·C0 − ηN̅ ·C0N − α C+α

c

H3BO3 (C0) + NH3 (C0N)

HCl (C)

V = V0·

ηN̅ ·C0N − (3 − ηB̅ )·C0 + α C−α

d

H3BO3 (C0) + NH3 (C0N)

H2SO4 (C)

η ̅ ·C0N − (3 − ηB̅ )·C0 + α V = V0· N (2 − ηS̅ )·C − α

e

H3BO3 (C0) + NH3 (C0N)

NaOH (C)

V = V0·

(3 − ηB̅ )·C0 − ηN̅ ·C0N − α C+α

a

The notation of the equations agrees with the notation of the plot series in Figure 1: V0 is the volume of titrand (D); V is the volume of titrant (T) added up to a given point of titration; C0, C0N, and C are the concentrations of the species indicated.

methylene blue (2:1) known later as Tashiro indicator changing its color from green to violet at about pH 5.2 was suggested.17 Knowing the number of milliliters of the volume of the standardized acid used in the titration, the amount of ammonia neutralized with boric acid can be calculated. All considerations involved with these titrations and practiced hitherto were based only on stoichiometries of the reactions involved,18,19 which do not provide a quantitative insight into the matter in question. None of the approaches presented hitherto were based on theoretical approaches, with equations for titration curves involved. The present paper is a valuable and understandable approach for students of chemical and other faculties where the Kjeldahl method is applied. The Excel file in the Supporting Information20 enables one to do some calculations related to different trapping acids and titrants (acids or bases) and helps the students to better understand the information gained experimentally. The Excel files were successfully applied during computer trainings done with students of Chemistry at Technical University of Cracow. This way, the calculations followed the experimental laboratory trainings involved with Kjeldahl method for the determination of nitrogen in meat. To find quantitative relationships between the reagents participating in the titration and check the proper pH value for the end point, the approach based on acid−base titration curves can be applied.21−23 The considerations based on formulation of “stoichiometric reactions” involved with hydrolytic effects and presumable formation of some “salts” in the system in question are thus not needed for this purpose.

ηS̅ =

ηB̅ =

[HSO4 ] + [SO4 ]

=

10 pK2S− pH 10 pK2S− pH + 1

(pK 2S = 1.8)

3[H3BO3] + 2[H 2BO3−] + [HBO32 −] [H3BO3] + [H 2BO3−] + [HBO32 −] + [BO33 −]

(pK1B = 9.24; pK 2B = 12.74; pK3B = 13.80) (5)

C ·V [NH+4 ] + [NH3] = 0N 0 V0 + V

(6)

where K2S is the second dissociation constant for sulfuric acid; one can assume [H2SO4] = 0; KiB, i = 1, 2, 3, is the acid dissociation constant for boric acid, C0N is the concentration (mol/L) of NH3 in the titrand (D), V0 is the volume (mL) of titrand, and V is the volume (mL) of titrant (T). The symbols η̅N, ηS̅ , and ηB̅ in eqs 2−5 express the mean numbers of protons attached to the corresponding, basic forms: NH3, SO42‑, and BO33‑, respectively. The values of the equilibrium constants that apply to eqs 2−5 can be found in the literature.24,25 Some of the equations presented in Table 1 are derived in the Appendix (see the Supporting Information). In these equations, the indicators are not involved. However, the indicators themselves have acid−base properties and, formally, should be included in equation for titration curve.21,22 For example, assuming that D referred to system d in Table 1 and contains a mixture of two indicators: MkiHmi−kil(i) at concentrai (j = 1, ..., qi) are the tion C0l(i) (for i = 1, 2), then HjI+j−m (i) protonated species formed by i-th indicator, M+ = Na+, K+, i I−m (i) basic (the least protonated) form of the i-th indicator, qi i is the maximum number of protons attached to I−m (i) , and we get the relation 2

V = V0

ηN̅ ·C0N + (3 − ηB,in ̅ )·C0 + ∑i = 1 (ki − mi + ηI̅ )·C0I(i) + α (i)

C(2 − ηS̅ ) − α

(pK w = 14.0)

(7)

(2)

[NH4 +] 10 pK1N − pH = pK − pH + [NH4 ] + [NH3] 10 1N +1

2−

3·10 pK1B+ pK2B+ pK3B− 3pH + 2·10 pK2B+ pK3B− 2pH + 10 pK3B− pH 10 pK1B+ pK2B+ pK3B− 3pH + 10 pK2B+ pK3B− 2pH + 10 pK3B− pH + 1

=

THEORETICAL APPROACH To check a priori the validity of a titrimetric procedure, it is advisable to gain prior knowledge based on a mathematical approach with equations for the titration curves involved. The formulas for acid−base titrations can be represented in a simple functional form, V = V(pH), where pH = −log[H+]. The formulas refer to acid−base titrations of the solution containing an acid (HCl, H2SO4, or H3BO3) and NH3 in the titrand D, titrated with strong base (NaOH) or strong acid (HCl or H2SO4) as titrant T, are specified in Table 1, where

ηN̅ =

−

(4)

■

α = [H+] − [OH−] = 10−pH − 10 pH − pK w

[HSO4−]

where q

(pK1N = 9.35)

ηI̅ = (i)

(3) 192

∑ j =i 0 j ·[HjI(+i)j − mi] q

∑ j =i 0 [HjI+j −(im) i]

(i = 1, 2)

(8)



Article

Figure 1. Series of titration curves plotted for eqs a−d in Table 1, at V0 = 10 mL, C0 = 0.05 mol/L, C = 0.1 mol/L, and C0N values indicated at the right.

Figure 2. The dpH/dV versus pH relationships plotted for different (indicated) C0N values and other data taken from caption for Figure 1.

At the equivalence (eq) point, pH = pHeq ≈ pHinf is practically independent of the C0N value when ammonia is trapped in H3BO3 solution (Figure 2). The slopes at the equivalence points are more than 2 times greater in Figure 2 panels a and d than in panels b and c. The plots in Figure 4, from system e in Table 1, do not appear to have the properties applicable for quantitative determination of NH3. In this pH range, the buffer capacity of the solution is high. The pK1N and pK1B values are similar (9.35 and 9.24, respectively) and the curves do not show differentiated jumps at different C0N values (compare with Figure 1). The curves converge near more distinct jump, as in Figure 1a,b.

The titration curves in Figure 1c,d have distinctly marked inflection (inf) points that occurred at pH ca. 5.2−5.3 (see Figure 2), where the (theoretical) relative error in NH3 determination is closest to zero value (Figure 3). The relative error is calculated as 100(Ve − Veq)/Veq (%) where Ve is the volume of the titrant at the end (e) point and Veq is the equivalence (eq) volume. The Vinf (volume of the titrant at inflection point) values corresponding to these points decrease (Figure 1a,b) or grow (Figure 1c,d) linearly with the concentration C0N of NH3 in the titrand. Then, the number of millimoles of NH3 equals (i) C·Vinf for the titration of this base with C mol/L HCl or (ii) 2·C·Vinf for titration with C mol/ L H2SO4. 193



Article

Figure 3. The relative error, δ (= 100%·(Ve − Veq)/Veq) for different C0N values (indicated) at different pH = pHe values for the systems a−d in Table 1 and Figure 1; Ve = V(pHe), pHe − pH-value, where the titration is terminated.

Figure 5. The log y versus pH = pHe relationships plotted for (1) y = 1 − η̅N, (2) y = 3 − η̅B, and (3) y = η̅S.

Figure 4. The titration curves plotted for the equation in the system e (Table 1); V0 = 10 mL, C0 = 0.05 mol/L H3BO3, C = 0.1 mol/L HCl, and C0N values indicated at the right.

Figure 5 within the pH interval 5 to 6 lead to the following approximate relationships when V = Ve is not far from equivalence volume (Veq):

Referring to results of pH titrations, one can state that ph = −log h, not pH = −log[H+] values, are measured, where h = γ·[H+] is the activity and γ the activity coefficient of H+ ions; then, ph − pH = −log γ. The values for mean activity coefficients for 0.1 mol/L solutions are 0.796 for HCl, 0.764 for NaOH, 0.770 for NH4Cl, and 0.778 for NaCl.26 Thus, −log 0.796 = 0.099 and −log 0.764 = 0.117 and the difference between pH (calculated) and ph (measured) is ca. 0.1 at ionic strength I = 0.1 mol/L, which means a shift, for example, from 5.2 to ca. 5.3 along the pH axis in Figure 3. This shift does not cause a significant change in δ value. At lower ionic strength values, this shift is smaller. It should also be noted that the ionic strength varies during the titration. Addition of a basal electrolyte into D and T to keep the ionic strength approximately constant and rather high is not usually practiced in the titrations involved with Kjeldahl method. Referring again to Table 1 and assuming C = 0.1 mol/L, C0 = 0.01 mol/L, one can state that at the end (e) point, pH = pHe ≈ 5.0−5.5, we have α = αe values that are small compared with other terms in numerator and denominator in the expressions for V in systems a, b, c, and d. Further simplifications made in the related formulas in Table 1 on the basis of

(a) C·Ve ≅ C0·V0 − C0N·V0 ,

that is,

C0N·V0 ≅ C0·V0 − C·Ve (b) C·Ve ≅ 2 ·C0·V0 − C0N·V0 , C0N·V0 ≅ 2·C0·V0 − C·Ve

(9)

that is, (10)

(c) C0N·V0 ≅ C·Ve

(11)

(d) C0N·V0 ≅ 2·C·Ve

(12)

For example, eq 9 is obtained from transformation of the approximate function referred to Table 1, system a, Ve ≅ V0

C0 − 1·C0N − 0 C+0

(13)

At the equivalence (eq) volumes, the equalities (a) C·Veq = C0·V0 − C0N·V0, (b) C·Veq = 2·C0·V0 − C0N·V0, (c) C0N·V0 = C·Veq, and (d) C0N·V0 = 2·C·Veq are valid (compare with approximate eqs 9−12). The errors involved with rounding of η̅N, ηB̅ , and ηS̅ values to 1, 3, and 0, respectively, within the pH interval 5 to 6, do not exceed ca. 0.1% (see Figure 5); the plot 194



Article

of log α (see eq 2) versus pH relationship falls here below the pH axis (beyond the figure). The approximations assumed in eqs 9−12 are comparable with an indicator error.22

When titration is terminated at Ve < Veq (DV < 0 → δ < 0), then we have: nN(e) − nN(eq) > 0, that is, nN(e) > nN(eq) for systems a and b, and nN(e) < nN(eq) for systems c and d. Reverse relations occur at Ve > Veq. Then, negative or positive error of titration is involved with positive or negative error of the ammonia determination in systems a and b, and negative or positive error of titration is involved with negative or positive error of the ammonia determination in systems c and d. Low buffer capacity, β = |dc/dpH|, where c = CV/(V0 + V),22,23 at the end (e) point of titration, in the vicinity of inflection (inf) point on the curves in Figure 1, secures good precision of results obtained in visual or pH titrations. The pH values, corresponding to maximal buffer capacities, agree very well with pH = pHe values assumed in the literature at the end points of the related titrations. It results from the relation

■

DISCUSSION The curves plotted in Figure 1a correspond to equal concentration C0 = 0.05 mol/L HCl and different concentrations C0N mol/L of NH3 in the titrand, D. The abscissas (Vinf) at the jump on the corresponding curves shift toward lower V values with growth of C0N, in accordance with eq 9. The general course of the plots in Figure 1b, referred to C0 = 0.05 mol/L H2SO4 and C0N mol/L NH3 in D, is very similar to one related to D with C0 = 0.10 mol/L HCl and C0N mol/L NH3; this system is in accordance with eq 10. The systems represented by Figure 1a,b are titrated with C = 0.10 mol/L NaOH. The buffering action at the start for titrations in the systems a and b is secured by HCl and H2SO4, respectively. In the systems c and d, with C0 = 0.05 mol/L H3BO3 and C0N mol/L NH3 in D, the buffering action of D is secured, in comparable degree, by H3BO3 and NH3; NH3 is the only component titrated with C = 0.1 mol/L solution of HCl or H2SO4, in accordance with eqs 11 and 12. In the systems a and b, the titration starts from lower pH values, ca. 1.5−2 (Figure 1a,b) at pHj+1 > pHj, whereas in systems c and d, it starts from higher pH values, ca. 8.5−9.5 (Figure 1c,d) at pHj+1 < pHj, for successive [jth and (j + 1)th] points of titration. As a consequence, • for the systems a, b: Ve < Veq at pHe < pHeq and Ve > Veq at pHe > pHeq (see Figure 1a,b); • for the systems c, d: Ve < Veq at pHe > pHeq and Ve > Veq at pHe < pHeq (see Figure 1c,d). Taking DV = Ve − Veq

CV0 dc dc dV dV = · = · 2 dpH dV dpH (V0 + V ) dpH CV0 1 = · (V0 + V )2 dpH

β=

dV

The number of millimoles of ammonia, nN = C0N·V0, is equal to the number of millimoles of the nitrogen (as an element) involved in it. Mass (g) of the nitrogen determined at the end point of titration in systems a−d equals ca. 0.01401·(C0·V0 − C·V e ), 0.01401·(2·C 0 ·V 0 − C·V e ), 0.01401·C·V e , and 0.02802·C·Ve, respectively. The percent contents of nitrogen in m grams of the sample tested equals 1.401·nN/m (%), provided that all the nitrogen involved in a sample placed in the Kjeldahl flask is captured in the Parnas−Wagner apparatus during the distillation with water vapor after addition of an excess of NaOH to the solution. When C0 is unknown, it must be determined in the titration made with use of a standardized base NaOH (C, mol/L), for example, the same as one used for titration of a sample taken from receiving flask. For titration of C0V0 mmol of H2SO4 with V mL of C mol/L NaOH, we get the relation

(14)

as the degree of misfit between the end and equivalence volumes, we get δ = DV/Veq = Ve/Veq − 1

(16)

(15)

(see Figure 3). Denoting by nN(e) = (C0NV0)e and nN(eq) = (C0NV0)eq the numbers of millimoles of ammonia calculated at Ve and Veq, respectively, for (a) we have:

V = V0·

(2 − ηS̅ ) ·C0 − α C+α

(17)

and then for V = Ve,s (i.e., the end volume for standardized solution), we get 2·C0·V0 ≅ C·Ve,s, C0N·V0 ≅ C·(Ve,s − Ve). The knowledge of exact H3BO3 concentration is not required. A comment should also be referred to pH titrations, where ph = −log h not pH = −log[H+] values are measured; h = γ·[H+] is the activity, and γ is the activity coefficient of H+ ions. However, the titrations are made at (rather) low ionic strength values and the related effects were omitted, that is, γ = 1 was assumed for simplicity of considerations. In pH titrations, indicators are not involved (see Table 1). In visual titrations, the concentration(s) of indicator(s) is (are) small and then can be omitted in the related functions V = V(pH). The NH3 trapping in the systems a and b (with HCl or H2SO4) results exclusively from low pH value and high buffer capacities of the trapping acids; in these cases, NH3 is transformed quantitatively into NH4+. In the systems c and d, buffer capacity of H3BO3 solution is low andon the trapping steppH grows rapidly to the values in the vicinity of pK1N = 9.35, where [NH3] is comparable with [NH4+]. Evolution of NH3 from the systems c and d is hampered by high solubility of NH3 in such media.

CVe = C0V0 − nN(e), CVeq = C0V0 − nN(eq) → nN(e) − nN(e) = −C·DV

Analogously, for (b): CVe = 2C0V0 − nN(e), CVeq = 2C0V0 − nN(eq) → nN(e) − nN(eq) = −C·DV

for (c): CVe = nN(e), CVeq = nN(eq) → nN(e) − nN(eq) = C·DV

for (d): 2CVe = nN(e), 2CVeq = nN(eq) → nN(e) − nN(eq) = 2C·DV 195



■

Article

confirmation of the statement (ascribed to J. C. Maxwell) that “a good theory is the best practical tool”.34

FINAL COMMENTS In spite of the fact that Kjeldahl’s nitrogen determination method was developed nearly 130 years ago, it is still widely used in nitrogen analysis. However, it is advisable to know adequately its theoretical basis, in order to be applied in a right way. The results obtained from simulated titrimetric procedure, based on prior physicochemical knowledge (equilibrium constants) and equilibrium analysis, with use of functions obtained on the basis of charge and concentration balances, confirm the proper choice of pHe values chosen by experimentalists through trial and error method (as a rule), that needs to be acknowledged. Four options, represented by the systems a, b, c, and d specified in Table 1, were discussed in detail. Comparison of the plots in Figures 1 and 4 enables to answer the question presented in the title of the paper. Namely, ammonia trapped in HCl or H2SO4 solution should be titrated with NaOH (back-titration), whereas ammonia trapped in H3BO3 should be titrated with HCl or H2SO4 solution. Two standardized (trapping and titrant) solutions are required in a and b, whereas in c and d, only one standard solution (titrant) is used. NH4Cl or ammonium sulfates are less volatile than NH3; consequently, NH4+ is less volatile than NH3. When NH3 is trapped in HCl or H2SO4 solution, the pH of the resulting solutions are low, provided that HCl or H2SO4 are in stoichiometric excess against NH3. This way, NH3 is better “preserved” in HCl or H2SO4 solution before titration with NaOH. When the related solution is titrated with NaOH, the titration is finished at pH ca. 5 to 6, that is, at the pH region where [NH4+]/[NH3] ≫ 1. It means that the risk of dissipation of NH3 on both stages, preservation and titration, is low. For comparison, the (starting) pH of H3BO3 solution is ca. 5−5.5, that is, close to the pH at the end point of titration of an excess of HCl or H2SO4 with NaOH. At this pH value, distant from pK1 = 9.24 for H3BO3, buffer capacity of the solution is low and first portions of trapped ammonia make a significant pH shift toward pK1 = 9.35, where comparable quantities of NH3 and NH4+ exist in the solution. This also means that some potential risk of evaporation of NH3 from this solution exists. According to the literature,27−29 this risk is apparent, however. The possibility to use the nonstandardized trapping acid (H3BO3) is thus a significant advantage in comparison with the alternative option; it saves the time and standards needed for standardization of the trapping solution. In addition, a carefully standardized acid solution is less than a standard alkali solution subjected to a change during storage.30 Micro-Kjeldahl nitrogen determination testifies also in favor of the method in which the ammonia is trapped in a boric acid−indicator solution and titrated with a standardized mineral acid, HCl or H2SO4.17,31−33 However, in spite of particular advantages, all the options considered from theoretical viewpoint provide good results of analyses if the pHe value close to 5.2 is assumed (Figure 3). Further quantitative information can be obtained by applying new data (C0, C0N, C, V0) in the Excel file. It enables one to evaluate the errors related to the analyses made under different conditions applied for this purpose. These calculations demonstrate the value of using theoretical models for optimizing conditions prior to experimental work. All the calculations presented in this paper are based on charge and concentration balances, and expressions for equilibrium constants related to acid−base equilibria. This approach can be perceived as the clear

■

ASSOCIATED CONTENT

S Supporting Information *

Appendix; Excel file. This material is available via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Kjeldahl, J. Z. Anal. Chem. 1883, 22, 366. (2) Bradstreet, R. B. Chem. Rev. 1940, 27, 331. (3) Dyer, B. J. Chem. Soc. Trans. 1895, 67, 811. (4) Oesper, R. E. J. Chem. Educ. 1934, 11, 457. (5) Veibel, S. J. Chem. Educ. 1949, 26, 459. (6) Fleck, A.; Mundro, H. N. Clin. Chim. Acta 1965, 11, 2. (7) Conklin-Brittain, N. L.; Dierenfeld, E. S.; Wrangham, R. W.; Norconk, M.; Silver, S. C. J. Chem. Ecol. 1999, 25, 2601. (8) McKenzie, H. A. Trends Anal. Chem. 1994, 13, 138. (9) Barlow, S. M.; Bimbo, A.; Jensen, O. B.; Smith, G. L. J. Sci. Food Agric. 1981, 32, 732. (10) Watson, M. E.; Galliher, T. L. Commun. Soil Sci. Plant Anal. 2001, 32, 2007. (11) Winkler, J. W. Z. Angew. Chem. 1913, 26, 231. (12) Beljkaš, B.; Matić, Á .J.; Milovanović, I.; Jovanov, P.; Mišan, A.; Šarić, L. Accredit. Qual. Assur. 2010, 15, 555. (13) Takatsu, A.; Eyama, S.; Saeki, M. Accredit. Qual. Assur. 2008, 13, 409. (14) Milner, O. I.; Zahner, R. J. Anal. Chem. 1960, 32, 294. (15) Sörensen, S. Biochem. Zeitschr. 1907, 7, 45. (16) Shaw, W. S. Analyst 1924, 49, 558. (17) Ma, T. S.; Zuazaga, G. Ind. Eng. Chem., Anal. Ed. 1942, 14, 280. (18) A guide to Kjeldahl nitrogen determination. Methods; Labconco, An Industry Service Publication, http://www.expotechusa. com/catalogs/labconco/pdf/KJELDAHLguide.PDF (accessed Nov 2012) (19) Kjeldahl Method for Determining Nitrogen, Cole-Palmer resource web page http://www.coleparmer.ca/TechLibraryArticle/ 384 (accessed Nov 2012), http://www.coleparmer.ca/techinfo/ techinfo.asp?htmlfile=KjeldahlBasics.htm&ID=384 (accessed Nov 2012). (20) The Excel file available in the Supporting Information enables one to check the calculation procedure applied for drawing the figures presented in this paper. The calculations can also be made for other concentrations (C0, C0N, C) and volume (V0), involved in the formulas presented in Table 1. The notation of the systems (a, ..., e) presented in Table 1 is in accordance with denotation of sheets designed for preparation of Figures 1−4. The last sheet was designed for preparation of Figure 5. In each sheet of this file, the points for the curves of pH vs V (Figures 1, 4), dpH/dV or −dpH/dV vs pH (Figure 2), and relative error vs pH (Figure 3) were calculated. All operations done in there are presented in understandable manner. (21) Michałowski, T. Chem. Anal. 1981, 26, 799. (22) Michałowski, T. Calculations in Analytical Chemistry with Elements of Computer Programming (in Polish); PK: Cracow, Poland, 2001; http://www.biblos.pk.edu.pl/bcr&id=1762&ps=-12&dir=MD. MichalowskiT.ObliczeniaChemii.html (accessed Nov 2012). (23) Asuero, A. G.; Michałowski, T. Crit. Rev. Anal. Chem. 2011, 41, 151. (24) Inczèdy, J. Analytical Applications of Complex Equilibria; Horwood: Chichester, 1976. 196



Article

(25) Guide-Book for Chemists (in Russian). Nikolsky, B. P., Ed.; Khimia: Moscow, 1964; Vol. 3, p 78. (26) Meites, L., Ed. Handbook of Analytical Chemistry; McGraw-Hill Company: New York, 1963. (27) Kolthoff, I. M.; Sandel, E. B.; Meehan, E. J.; Bruckenstein, S. Quantitative Chemical Analysis, 4th ed.; The Macmillan Company: New York, 1969; p 790. (28) Laitinen, H. A.; Harris, W. E. Chemical Analysis: an Advanced Text and Reference, 2nd ed.; McGraw-Hill: New York, 1975; p 115. (29) Thiex, N. J.; Manson, H.; Anderson, S.; Persson, J. A. J. Assoc. Official Anal. Chem. 2002, 85, 309. (30) Stover, N. M.; Sandin, R. B. Ind. Eng. Chem., Anal. Ed. 1931, 3, 240. (31) Sher, I. H. Anal. Chem. 1931, 3, 240. (32) Wagner, E. C. Ind. Eng. Chem., Anal. Ed. 1940, 12, 771. (33) Yuen, S. H.; Pollard, A. G. J. Sci. Food Agric. 1953, 4, 490. (34) Kantowitz, B. H.; Roediger, H., III; Elmes, D. G. Experimental Psychology, 9th ed.; Wadsworth: Belmont, CA, 2009.

■

NOTE ADDED AFTER ASAP PUBLICATION An minor typographical error was found in the text above eq 7 in the version published on December 7, 2012. This was corrected in the version published to the Web on December 17, 2012.

197


The Titration in the Kjeldahl Method of Nitrogen ... - ACS Publications

Recommend Documents