The Acid–Base Titration of a Very Weak Acid: Boric ... - ACS Publications

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The Acid−Base Titration of a Very Weak Acid: Boric Acid M. Celeste C. Azevedo and Ana M. V. Cavaleiro* Department of Chemistry and CICECO, University of Aveiro, 3810-193 Aveiro, Portugal S Supporting Information *

ABSTRACT: A laboratory experiment based on the titration of boric acid with strong base in the presence of D-mannitol is described. Boric acid is a very weak acid and direct titration with NaOH is not possible. An auxiliary reagent that contributes to the release of protons in a known stoichiometry facilitates the acid−base titration. Students obtain the potentiometric titration curves of boric acid with standard NaOH in the absence and in the presence of different quantities of mannitol. The results are used for the determination of boric acid concentration and for the discussion of the possibility of performing the titration with a visual end-point determination, including the influence of the quantity of mannitol in solution. The experiment was developed for an introductory analytical chemistry course, but may be extended to an advanced analytical course with the inclusion of a more detailed theoretical treatment. The experiment may be adapted to general chemistry course as an example of a nontrivial titration. KEYWORDS: Second-Year Undergraduate, Upper-Division Undergraduate, Analytical Chemistry, Laboratory Instruction, Hands-On Learning/Manipulatives, Acids/Bases, Potentiometry, Titration/Volumetric Analysis

M

Several approaches may be envisaged for the use of this titration in teaching laboratories. Students in introductory laboratories may be introduced to the simple titration with a visual acid−base indicator and to the principle of the use of the auxiliary reagent to make a titration feasible. In more advanced analytical courses, they may perform potentiometric titrations and compare the titration curves obtained for the very weak acid in the presence or absence of the auxiliary reagent, as described in this article. Depending on the students’ preparation and learning objectives, the instructor may introduce the notions of conditional and composite acid ionization constants and other theoretical aspects, including calculations and curve interpretation.

uch has been published on the subject of acid−base titrations and their educational use. In the past decade, specifically, several articles and letters were published in this Journal.1−12 From an analytical point of view, a titration is a counting of the average number of analyte particles in solution through the reaction with a known number of standard particles.13 To be used in titrimetry, an acid−base reaction must come close to completion and textbooks usually emphasized that the technique cannot be applied to the accurate determination of the concentration of very weak acids using conventional equivalence point detection. The use of an auxiliary reagent to make a titration feasible is not usually discussed. In this article, we propose laboratory experiments based on the titration of a very weak acid (boric acid) with strong base, performed with the help of an auxiliary reagent (D-mannitol, Figure 1A, hereinafter referred to as mannitol) that contributes to the release of protons in a known stoichiometric proportion.

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BACKGROUND

Boric Acid Behavior

Boric acid, H3BO3, is a white solid moderately soluble in water. It is considered a very weak acid, with a tabulated ionization constant around pKa = 9.2.14 Yet, boric acid does not react in aqueous solution as a Bronsted acid, but instead, it behaves as a Lewis acid, with formation of the tetrahedral B(OH)4− anion (eq 1): B(OH)3 + H2O ⇌ B(OH)4− + H+

(1)

In dilute aqueous solutions, the monomeric B(OH)3 and B(OH)4− species are almost exclusively found, whereas polymeric species may form in more concentrated solutions.15 It is usually stated that boric acid can be transformed into a relatively strong acid by the addition of organic compounds

Figure 1. Structures of (A) D-mannitol and (B) boron complexes with polyalcohols. © 2012 American Chemical Society and Division of Chemical Education, Inc.

Ka

Published: March 28, 2012 767

dx.doi.org/10.1021/ed200180j | J. Chem. Educ. 2012, 89, 767−770

Journal of Chemical Education

Laboratory Experiment

[BL 2−]/[B−]T = (β2[H2L]2 )/(1 + β1[H2L]

with at least two hydroxyl groups, such as mannitol, sorbitol, glycerol, and others. In fact, boric acid reacts with diols and other polyalcohols originating mainly anionic boron complexes with polyol/boron molar ratio of 1 and 2 (eqs 2 and 3): −

+

B(OH)3 + H2L ⇌ B(OH)2 L + H2O + H −

+ β2[H2L]2 )

The relation between Ka* and Ka (eq 18) results from combining eqs 13 and 15:

(2)

+

B(OH)3 + 2H2L ⇌ BL 2 + 3H2O + H

Ka* = Ka(1 + β1[H2L] + β2[H2L]2 )

(3)

Ka* = Ka(1 + β1CL + β2CL 2)

β1

β2

(18a)

is applicable when a large excess of polyol is present in solution. The value of pKa* of boric acid in the presence of excess mannitol, using pKa = 9.20,14 log β1 = 3, and log β2 = 5,16,17 falls in the range of 4 to 5 in an available range of mannitol concentrations. Titration of Boric Acid

Considering the titration of boric acid with NaOH, in the presence of mannitol, the system is defined by a total of eight equations. These are eqs 6−11 plus the charge balance 19, and a new mass balance (CNa = [Na+], where CNa is the analytical concentration of NaOH).

(4)

B(OH)4− + 2H2L ⇌ BL 2− + 4H2O

(18)

It can be seen that Ka* varies with the concentration of uncombined polyol in solution. If the molar ratio CL/CB is large, the mass balance (eq 11) simplifies to CL ≅ [H2L]. Thus

where H2L is a diol or polyol. The corresponding structures are presented in Figure 1B. Many researchers considered the borate anion as the reactive species, as represented in eqs 4 and 5, for which equilibrium constants β1 and β2 are available.16,17 Formally, the formation of these species may be considered a complexation where OH− groups coordinated to B are substituted by the bidentate ligand L2‑. It can be seen that eq 2 is the sum of eqs 1 and 4, whereas eq 3 equals eq 1 plus eq 5. B(OH)4− + H2L ⇌ B(OH)2 L− + 2H2O

(17)

(5) −

In the subsequent discussion, B(OH)3, B(OH)4 , and B(OH)2L− are replaced by HB, B−, and BL− respectively. A set of seven independent equations (and seven unknowns) define the system formed by boric acid and a polyol in aqueous solutions, assuming that only monomeric species are formed. These comprise the expressions of the equilibrium constants Ka, β1, β2, and Kw (eqs 6−9), boron and polyol mass balances (eqs 10 and 11, respectively, where CB and CL are the respective analytical concentrations), and the charge balance.12

[H+] + [Na+] = [OH−] + [B−] + [BL−] + [BL 2−] (19) −

Taking in account the definition of [B ]T (eq 14), the mass balance of boric acid (eq 10) and the charge balance (eq 19) in solutions of boric acid, mannitol, and NaOH transform into eqs 20 and 21, respectively.

Ka = ([B−][H+])/[HB]

(6)

CB = [HB] + [B−]T

(20)

β1 = [BL−]/([B−][H2L])

(7)

[H+] + [Na+] = [OH−] + [B−]T

(21)

β2 = [BL 2−]/([B−][H2L]2 )

(8)

K w = [H+][OH−]

(9)

CB = [HB] + [B−] + [BL−] + [BL 2−]

(10)

CL = [H2L] + [BL−]+ 2[BL 2−]

(11)

[H+] = [OH−] + [B−] + [BL−] + [BL 2−]

(12)

The set of eqs 9, 13, 20, and 21, corresponding to the system boric acid/NaOH/mannitol in aqueous solution, is identical to that used for the study of the titration with NaOH of any weak acid.18−20 The titration of boric acid with strong base in the presence of mannitol usually takes place with CL/CB = 10−15.21 The pKa* may vary slightly along the titration, depending on the extent of the complexation. This does not prevent the feasibility of the titration, which has been repeatedly demonstrated,21−25 but has consequences if the calculation of the titration curve is attempted. It is possible to deal with this variation using an iterative calculation procedure, schematically presented in Figure 2. For a given point of the titration curve, the calculation starts with the choice of a value for [H2L]0, usually [H2L]0 = CL, which allows the determination of Ka* (eq 18a). Considering the set of eqs 9, 13, 20, and 21, [B−]T, [HB], and pH are calculated as usually done for a weak acid−strong base titration, following the procedure described in many textbooks.18−20 [B−], [BL−], and [BL2−] are obtained from [B−]T and eqs 15−17. Now, eq 11 is used to determine a value for [H2L] that is compared with that assumed initially. If the values are similar, the initial assumption is taken as correct. If not, the obtained [H2L] is used to start a new iterative cycle. The procedure may be easily performed with the help of an Excel spreadsheet. The comparison between a value obtained for [H2L] (e.g., [H2L]n) with that assumed to initiate the iterative cycle ([H2L]n−1) may

For the subsequent discussion, it is convenient to define a composite acid ionization constant for boric acid, Ka* (eq 13), where [B−]T is the total concentration of negatively charged borate species, as defined in eq 14. Fractions relating the concentration of each charged boron species to [B−]T may be calculated using eqs 15−17. Ka* = ([B−]T [H+])/[HB]

(13)

[B−]T = [B−] + [BL−] + [BL 2−]

(14)

[B−]/[B−]T = 1/(1 + β1[H2L] + β2[H2L]2 )

(15)

[BL−]/[B−]T = (β1[H2L])/(1 + β1[H2L] + β2[H2L]2 ) (16) 768

dx.doi.org/10.1021/ed200180j | J. Chem. Educ. 2012, 89, 767−770

Journal of Chemical Education

Laboratory Experiment

Figure 3. Variation of pKa* during the titration of boric acid (CB = 0.05 M) in the presence of mannitol, CL, (X = CL/CB) calculated with the help of the iterative procedure represented in Figure 2 and pKa = 9.20,14 log β1 = 2.98, and log β2 = 4.98.17 CNa = concentration of NaOH in solution. Dilutions were neglected in these calculations.

stock solution of boric acid is used by all groups. Solid mannitol is dissolved in a 25 mL aliquot of the boric acid solution for the preparation of the solution with the required CL/CB to be titrated. Each pair of students obtains the experimental potentiometric curve and determines the analyte concentration. The procedure used may depend on the laboratory resources and previous knowledge of the students and is not detailed here. Also, students discuss the results obtained and assess the possibility of performing the titration with a visual end-point determination. The experiment is intended for a laboratory period of 3 h. A typical distribution of time is (i) 1 h for experimental work; (ii) 1 h for tracing of the curves, the determination of the end point, and other calculations; and (iii) about 30−45 min for the discussion.

Figure 2. Iterative procedure to determine pH and the concentration of the species in a solution of boric acid and mannitol in a titration with strong base.

be done by visual inspection, but, in this case, the number of iterations may increase as CL/CB diminishes and the method was not applicable for C L/CB ≤ 1, because negative concentration values appeared. A better option is the use of the Excel Solver tool. In this approach, the assumed [H2L] concentration is introduced. The spreadsheet is prepared for the calculation of concentration of the species. The Solver is asked to zero the function F = [H2L]n − [H2L]n−1. No iterations are needed in most cases. More information is presented in the Supporting Information. The method just described was used to determine titration curves and the value of pKa* along the titration of a 0.05 M boric acid solution. Dilutions were neglected in these calculations. Figure 3 represents the variation of pKa* during the titration of boric acid in the presence of mannitol for different X = CL/CB. It can be seen that, for CL/CB ≥, 10 the variation of pKa* during the course of titration is not very pronounced and that the average value of pKa* is lower than 5. Thus, this condition seems acceptable for the feasibility of a titration, but the solubility of mannitol26 may limit the range of useful boron concentrations. The results of these calculations also showed that [HB] and/or [BL2−] were the predominant species during the titration of solutions with CL/CB ≥ 5. In contrast, [B−] was always very small.

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HAZARDS

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RESULTS

Caution is needed in handling the strong basic NaOH solutions, and students should be aware of the necessary precautions and safety instructions. Boric acid is hazardous in case of skin or eye contact, of ingestion and of inhalation, and presents reproductive toxicity.27 Students should avoid exposure. In case of contact, immediately flush skin with plenty of water. Mannitol is not considered dangerous.

Examples of potentiometric curves obtained in the experimental conditions used are presented in Figure 4. Students are asked to calculate the concentration of boric acid in the solution provided. The volume of NaOH used to reach the equivalence may be determined either visually or from the first derivative curve.28 In the absence of mannitol (CL = 0; X = 0), the variation of pH around the equivalence point is small, in accordance with the small ionization constant of boric acid, precluding the use of any visual indicator for this purpose. In contrast, curves obtained with CL/CB = 10 (X = 10) or higher are typical of acids that may be titrated with the help of visual indicators,

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EXPERIMENTAL PROCEDURE The work proposed to the students consists in the potentiometric titration of boric acid (∼0.05 M) with standard NaOH 0.1 M (both prepared prior to the laboratory period) in the absence and in the presence of different amounts of mannitol (with CL/CB between 2 and 20). The students work in pairs and, at the end, the results are pooled and discussed. Each pair of students uses only one CL/CB ratio. The same 769

dx.doi.org/10.1021/ed200180j | J. Chem. Educ. 2012, 89, 767−770

Journal of Chemical Education

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Laboratory Experiment

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors wish to thank one of the reviewers, who suggested the use of the Solver tool of the Excel worksheet.

Figure 4. Experimental potentiometric curves in the titration of boric acid (CB = 0.051 M, 25 mL,) with NaOH 0.100 M in the presence of mannitol (different CL concentrations, X = CL/CB).

presenting a variation of at least 4 pH units near the equivalence point. It is easily deduced that at midtitration, when the volume of NaOH used is half that of the equivalence point, [HB] = [B−]T and pH = pKa*. Students may thus determine the value of pKa* at midtitration, obtaining values between 4 and 5 for CL/CB ≥ 10. Students should be aware that pKa* may only be taken as approximately constant during the titration when CL/CB is large, specifically when CL ≅ [H2L] and Ka* = Ka (1 + β1CL + β2CL2). Nevertheless, pooling of the results will show the decrease of pKa* at midtitration with the increase of CL.

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CONCLUSIONS Acid−base titration in the presence of mannitol is a standard method of analysis of boric acid in different media. The work here described was developed with the aim of presenting the students with a case study in which an acid−base titration is made feasible by the use of an auxiliary reagent. The determination of the potentiometric curves for different CL/ CB molar ratios shows the influence of this parameter in the devising of the experimental procedure and, thus, leads to a deeper understanding of titration methods referred in the literature. The potentiometric titration curves have been published and the students may compare their results with those previously described in similar (or related) conditions.22−24 It is also possible to calculate pKa* at midtitration and observe its decrease with the increasing amount of mannitol used. The calculation of titration curves, however, is not recommended at most levels. The simple approach is presented here for the sake of interested instructors. This work may be used in analytical laboratories as it allows the discussion of a nontrivial acid−base system and of the possibility of using an auxiliary reagent to perform an uncommon titration. Nevertheless, it may be adapted to general chemistry laboratories and used namely to teach potentiometric titrations

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REFERENCES

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ASSOCIATED CONTENT

* Supporting Information S

Documentation containing the experimental procedure for the students and instructor notes. This material is available via the Internet at http://pubs.acs.org. 770

dx.doi.org/10.1021/ed200180j | J. Chem. Educ. 2012, 89, 767−770