Investigación

 

Potentiometric Analysis of a Reaction System of Organic Acids

 

Agustín Jaime Castro-Montoya,* Manuel Herrera-Solano, Pedro Alberto Quintana-Hernández, and Medardo Serna-González

 

Facultad de Ingeniería Química, Universidad Michoacana de San Nicolás de Hidalgo, Edif. "M", Ciudad Universitaria, Morelia, Michoacán, México. Tel: 01 (443) 327-3584. E-mail: ajcastro@zeus.umich.mx

 

Recibido el 6 de noviembre del 2002
Aceptado el 14 de abril del 2003

 

Abstract

A new potentiometric titration method for the quantitative analysis of a reaction system of diprotonic organic acids is presented. The method uses the individual potentiometric titration data for calculating the dissociation constants. With this information a set of "n − 1" linear equations and "n − 1" unknowns is solved; "n" is the number of organic acids present in the reaction mixture. This method was applied to tartaric acid process production from maleic acid. In this process two successive reactions take place: firstly the maleic acid epoxydizes to epoxysuccinic acid and secondly the epoxysuccinic acid hydrolyzes to tartaric acid, leaving three organic acids present in the reaction system. It is necessary to quantify the concentration of all three acids in order to determine the progress of the reaction. This paper describes a fast, economical and easy to carry out analytical method for determining the concentration of all three acids simultaneously by potentiometric titration.

Keywords: Acid-Base Chemistry, Quantitative Analysis, Potentiometric Titration.

 

Resumen

Se presenta un nuevo método de titulación potenciométrica para el análisis cuantitativo de un sistema de reacción de ácidos orgánicos diprotónicos. El método parte de los datos de la titulación potenciométrica para cada uno de los ácidos de manera individual para determinar sus respectivas constantes de disociación. Se plantea un sistema de "n" ecuaciones lineales con "n" incógnitas, donde "n" es el número de ácidos presentes en el sistema de reacción. Este método fue aplicado en el proceso de producción de ácido tartárico a partir del ácido maleico. En este proceso suceden dos reacciones sucesivas: el ácido maleico se convierte en ácido epoxisuccínico para posteriormente este último hidrolizarse a ácido tartárico, por lo que se forma una mezcla en la que están presentes los tres ácidos. Para determinar el grado de avance de la reacción se requiere cuantificar la concentración de los tres ácidos. El artículo describe un método analítico rápido, económico y fácil de implementar para determinar simultáneamente la concentración de los tres ácidos por titulación potenciométrica.

Palabras clave: Titulación potenciométrica, análisis cuantitativo, química ácido-base.

 

Introduction

Acid-base potentiometric titration is the most common analytical technique for determining the concentration of one acid in solution. Dashek and Micales [1] presented a summary of procedures employed for the detection and quantification of organic acids. They reported ten methods (Capillary electrophoresis, colorimetry, conductimetric titration, differential pulse polarography, enzymatic method, gas chromatography, high-pressure liquid chromatography, ion exchange chromatography, photometric determination and silica gel chromatography with gradient elution), but did not consider a potentiometric titration. A generalization of this technique for a mixture of acids is very important. Kankare [2] proposed a simple linear relationship between the deprotonation degree of the mixture and the mole fraction of the acids. He concluded that it is possible to determine by a potentiometric titration the concentration of weak acids in a mixture. Betti et al. [3] carried out a potentiometric titration of mixtures of two weak monoprotic acids. They found that the method precision was a function of the dissociation constants and the ratio of the acid concentrations. Gordus [4] carried out similar experiments but using polyprotic acids. He concluded that it is impossible to determine, by a potentiometric titration, the concentration of the individual acids in a mixture. Papanastasiou y col. [5] presented an iterative method for a potentiometric titration of a mixture of monoprotic weak acids and found that it is possible to obtain accurate results even for acids with similar dissociation constants. De Levie [6] developed a single equation describing the entire progress of the titration, but did not calculate the concentration of acids in the mixture. This work describes the potentiometric method developed by Castro [7] for calculating the concentration of three organic acids present in the catalytic peroxidation of maleic acid. This method can be extended to systems without reaction.

 

Fundamentals

When the maleic acid reacts, it produces epoxysuccinic acid and tartaric acid. The concentration of hydrogen ions present in the reaction system changes due to the different ionization constants of the three organic acids. Fig. 1 shows the titration curves for the three 0.1 N organic acids when titrated with 0.1 N sodium hydroxide. Potentiometric titrations are easy, fast and reliable techniques when the added volume and pH can be measured with high precision and the system is well stirred. The dissociation expressions for the reaction system are:

Where:

Applying the electroneutrality principle to equations 1-7 gives:

Formulating the mass balance relations that include the dilution of the sample as result of the addition of titrant and the degree of advance of two successive reactions, we get:

where:

The species acid fractions (α_HiA) and K_i values are identical to De Levi [6] expressions:

with i = 1 2, ... n, and

Combining the charge balance relation (Eq. 8), with the species acid fractions (Eq. 13) and mass balance relations (Eqs. 9-12), and considering that initially epoxysuccinic acid and tartaric acid are zero, we obtain:

where: X and Y are the conversion of maleic acid to epoxisuccinic acid and the conversion of epoxysuccinic acid to tartaric acid respectively. By definition X and Y are:

Combining the conversion definitions (Eqs. 16-17) with Eq. 15, we obtain:

where:

 

Experimental

All measurements were done with a MSE Spectro-Plus, model 41113-2244 with multiple options. The temperature was controlled by a Cole-Parmer High-Performance Utility Baths and was maintained at 25 ± 0.15 °C. The reagents used were analytical grade (Aldrich, 99 %). The procedure included titrations of each pure acid (for the dissociation constants determination) and titrations of the mixture of all three acids. An aliquot of the sample, V_m, was taken from the reactor at different times (from t = 0 until the reaction system became stabilized), diluted to 100 mL with distilled water, and titrated with a 0.1 N sodium hydroxide solution. Figs. 2 and 3 show the titration curves for the reaction system samples at different times. Fifty values of volume of NaOH added and pH were registered. Titrations of the samples were done twice.

 

Calculations

The dissociation constants (K_i) of pure acid were determined by non linear multiple regression from the titration data at 25 °C of the pure acids (Fig. 1). Table 1 shows the dissociation constants for all three acids in the reaction system found by a non linear regression algorithm.

Calculating F_ai (Eq. 19) for two pH levels in the titration curves of the mixture of acids and substituting the others variables (V_b, V_a, C_mi [H₊], C_b) with [OH⁻] = 1e-14 / [H⁺] in eq. 18, we generated a set of two linear equations and two unknowns (C_M and C_T). We can use any pair of pH values, but it es recommended to select them in a range where the slope of the titration curve is small. For example for reaction time of 1.0 hour and pH values of 3.6 and 4.2 the equations are:

The concentration for the epoxysuccinic acid (C_E) is found by subtraction using equation (22).

 

Results

We validated the developed method by analysis of the pure acids as well as the by mixture of all of them. Tables 2, 3 and 4 show the known and calculated concentrations (Eq. 18) for each acid when they were titrated separately. Table 5 shows the known and calculated concentration for different mixtures of the three acids.

In the example, solving the set of two linear equations and two unknowns (eqs. 20-21) and applying eq. 22, we obtain: C_M = 2.2619 × 10⁻² mol L⁻¹, C_T = 0.4951 × 10⁻² mol L⁻¹ and C_E = 0.1480 × 10⁻² mol L⁻¹. The Fig. 4 shows the concentration profiles for the reaction system, calculated by this method.

 

Discussion

Test of hypotheses on the equality of the calculated and known concentration for each pure acid means were done. It was assumed that both variables were normally distributed with variances unknown. The process for the statistical analysis is described by Montgomery [8]. The null hypothesis was: "there is no statistical difference between the theoretical and experimental mean values".

The test is based on the t-test:

Where S_p is a single estimate of the common variance, and are the means of calculated and known concentration, n₁ and n₂ are the the samples sizes. The null hypothesis is accepted if: |t_o| > t _{α / 2,} n1+n2-2, where t_α/2, n1+n2-2 is the t-student distribution at the a significant level and n₁ + n₂-2 degrees of freedom. Table 6 shows the results when Montgomery's method was applied.

For α = 0.05 and n₁ = n₂ = 4 the t-value is equal to 2.447. For all cases the null hypothesis was accepted. There is no difference between the calculated and the known means. Therefore, the method proposed in this work is suitable to be used successfully. Of course, the ionic strength affect the dissociation constants determination, but when the sample concentration is too small, the activity coefficient are almost unity, so the measured (or apparent) dissociation constants are very close to obtained to zero ionic strength [9]. Additionallly, Albert and Serjeant [10] recommended that the ionic strength corrections be applied when an instrument calibrated in 0.005 pH units or less has been used.

 

Conclusions

This work presents a fast, economical and easy to carry out potentiometric method for the quantitative analysis of a mixture of organic acids. The results indicate that it can be used in chemical or physical systems for simultaneous determination of the concentrations of all acids present in a ternary mixture and can compete with others methods as gas chromatography.

 

References

1. Dashek, W.V.; Micales, J.A.; Methods in Plant Biochemistry and Molecular Biology, CRC Press; Boca Raton, FL; 1997, p. 107-113.         [ Links ]

2. Kankare, J.J. Anal. Chem. 1973, 45, 1877-1880.         [ Links ]

3. Betti, M; Papoff, P; Meites, L. Anal. Chim. Acta 1986, 182, 133-145.         [ Links ]

4 . Gordus, A.A. J. Chem. Educ. 1991, 7, 566-568.         [ Links ]

5. Papanastasiou, G.; Ziogas, Y.; Kokkinidis, G.; Anal. Chim. Acta, 1993, 277, 119-135.         [ Links ]

6. De Levie, R. Anal. Chem., 1996, 68, 585-590.         [ Links ]

7. Castro-Montoya, A. J. Ph. D. Thesis, Instituto Tecnológico de Celaya, México, 1994.         [ Links ]

8. Montgomery, D.C.; Design and Analysis of Experiments, John Wiley and Sons, USA, 1984.         [ Links ]

9. Clay, J. T.; Walters, E. A.; Brabson, G. D. J. Chem. Educ. 1995, 72, 665-667.         [ Links ]

10. Albert, A; Serjeant, E. P., in: The Determinations of Ionization Constants, Ed. Chapman and Hall, New York, 1984.         [ Links ]