A Simplified Undergraduate Laboratory Experiment To Evaluate the

Laboratory Experiment pubs.acs.org/jchemeduc

A Simplified Undergraduate Laboratory Experiment To Evaluate the Effect of the Ionic Strength on the Equilibrium Concentration Quotient of the Bromcresol Green Dye Hernán B. Rodríguez†,# and Martín Mirenda*,†,‡ †

Departamento de Química Inorgánica, Analítica y Química Física, #INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. II, C1428EHA, Buenos Aires, Argentina ‡ Gerencia de Química, Centro Atómico Constituyentes, Comisión Nacional de Energía Atómica, Av. Gral. Paz 1499, 1650, San Martín, Pcia. de Buenos Aires, Argentina S Supporting Information *

ABSTRACT: A modified laboratory experiment for undergraduate students is presented to evaluate the effects of the ionic strength, I, on the equilibrium concentration quotient, Kc, of the acid−base indicator bromcresol green (BCG). The two-step deprotonation of the acidic form of the dye (sultone form), as it is dissolved in water, yields suitable hydronium concentration in the solution to carry out the experiment successfully and avoids the use of any buffer solution to fix the hydronium concentration of the media. The 95% confidence interval for the slope parameter (−2.08 ± 0.13), obtained from the linear fit of pKc versus √I/ (1 + 2.30·√I) plot, contains the theoretical value of −2.04 predicted by the Debye− Hückel extended law. From the intercept, a value for the equilibrium dissociation constant of BCG, pK = (4.91 ± 0.02), is obtained, showing a reasonable agreement with literature data. The simplification makes it possible for students to complete the experiment in the course of an ordinary 3-h laboratory session. KEYWORDS: Upper-Division Undergraduate, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Acids/Bases, Aqueous Solution Chemistry, Dyes/Pigments, Equilibrium, Thermodynamics, UV−Vis Spectroscopy

T

he fact that the activities of the species involved in a chemical equilibrium, at a fixed temperature, must be quantitatively related through a mathematical constant is one of the most fundamental concepts used in chemistry. Generally, this statement does not hold for the equilibrium concentration quotient (Kc)the relation between analytical concentrations of reagents and productsbecause this relation changes, for example, with the total concentration of the species present in the system. There are several examples in the literature related to the experimental determination of Kc of aqueous electrolytes and its dependence with the total ion concentration. For instance, at the beginning of the last century, Harned and collaborators reported a series of electrochemical foundational works1 in which they quantified the effects of the electrolyte concentration on the dissociation of hydrochloric2 and acetic3 acids. Unfortunately, there are multiple factors that must be carefully controlled in these classical experiments in order to be implemented in teaching laboratories. The list includes the proper cleaning, construction, and maintenance of the electrodes; the purity of the reagents; safety issues related to hydrogen handling; and extended temporal intervals to reach adequate thermal equilibrium, to cite a few relevant examples. Several experiments adapted for undergraduate-level labo-

iron(III)−thiocyanate equilibrium5,6 was proposed; unfortunately, this experience is restricted to a narrow gap of high ionic strengths due to the experimental conditions in which it takes place. In a different context, experiments based on volumetric titration7 or spectrophotometric quantification8 of the ions in equilibrium with a solid have also been proposed. However, in these cases, the success of the experimental procedure requires the total absence of solid in the supernatant solution, an experimental condition that is not always easy to satisfy in an ordinary laboratory class. Finally, many experiments have been proposed9,10 in which the students must assume ad hoc the validity of the Debye−Hückel theory, without evaluating its applicability in the particular experimental conditions of the experiences. In 1963, Richard W. Ramette reported an interesting teaching laboratory experiment for the determination of Kc of an acid−base indicator, the bromcresol green dye (BCG), as a function of the ionic strength,11 probably inspired in techniques used in the past for the determination of Kc of common acid− base indicators.12,13 Ramette’s experiment requires the use of acetic/acetate buffer solutions to fix the proton concentration and literature data of Kc of the acetic acid at different ionic strengths14 to calculate the proton concentration in the media.

ratory have been reported in this Journal. Fourteen years ago the evaluation of the effect of the ionic strength4 on the classical

Published: June 15, 2012

© 2012 American Chemical Society and Division of Chemical Education, Inc.

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dx.doi.org/10.1021/ed200733k | J. Chem. Educ. 2012, 89, 1201−1204

Journal of Chemical Education

Laboratory Experiment

pressure is negligible in condensed phase). When temperature is constant, a change in the ionic strength will affect the activity coefficients and will modify the activity coefficient quotient, Kγ, and the equilibrium concentration quotient, Kc. However, the changes are such that the product between both quantities should remain constant.

Moreover, the protocol involves several lengthy procedures that would make the whole experiment unsuitable to be carried out out by a single student in a 3-h laboratory class. In the experience, students need extended periods of time for the spectroscopic determination of Kc at each ionic strength from titration of BCG solutions with acetic acid. We present a simplified experiment for the evaluation of the effects of the ionic strength on the Kc of BCG, in which the use of buffer solutions can be safely avoided. The main goal of our approach is to use the free-acid form of the dye (sultone form), which shows a two-step dissociation process as it is dissolved in water. The first dissociation is strong, as is expected for a sulfonic acid group, and is responsible for the dissolution of the free-acid form of the dye in water, rendering the monoanionic form in solution. The second dissociation is weak and represents the main equilibrium subject to analysis in the experiment. The two-step dissociation process of the BCG dye is shown in Scheme 1.

Determination of Kc of BCG from Spectrophotometric Measurements

To determine Kc at different salt concentrations, the analytical concentration of reagents and products can be determined from charge and mass balances as (see the Supporting Information for details):

Scheme 1. Two-Step Dissociation Process of Bromcresol Green Dye in Water Solution

[B2 −] = X B2−·c T

(2)

[H3O+] = (1 + X B2−) ·c T

(3)

[HB−] = (1 − X B2−)·c T

(4)

where cT is the total analytical concentration of the dye in the solution and XB2− is the fraction of the dye in the dianionic form, calculated as15

X B2− =

A 616nm 2−

B A 616nm

(5) 2−

where A616nm and AB 616nm are the absorbance of the sample at a given ionic strength and the absorbance of the pure alkaline form of the dye, respectively, measured at 616 nm by using the same total dye concentration. The expression is valid on the basis that the absorbance of the monoanionic form of the dye is negligible at 616 nm. More sophisticated methods that consider the entire absorption spectra16,17 can be used in order to obtain XB2−. However, excellent results were obtained by considering only the absorbance at 616 nm. Placing eqs 2−5 into eq 1 leads to an expression to calculate Kc:

The experiment requires the recording of BCG absorption spectra at different ionic strengths and the subsequent comparison with the spectra of the pure acidic and basic forms of the dye. As such, Kc is obtained for every salt concentration by computing the calculated proton concentration, obtained from charge and mass balances, and the fraction of the dye in acidic and basic forms, obtained from spectral analysis. With this procedure, Kc can be evaluated exclusively from experimental data recorded along the experience.

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⎛ ⎞ A ⎜1 + 616nm ⎟ B2 − ⎝ A 616nm ⎠ Kc = c B2 − ⎛ A616nm ⎞ T − 1⎟ ⎜A ⎝ 616nm ⎠

THEORETICAL APPROACH

Analysis of the Dependence of Kc with the Ionic Strength Using Debye−Hü ckel Theory

Thermodynamics of Acid−Base BCG Equilibrium

The studied equilibrium can be expressed as −

2−

(6)

Two different expressions within the framework of the Debye− Hückel theory were used to analyze the dependence of pKc with the ionic strength for aqueous solutions at 25 °C (see the Supporting Information for details): (i) the limiting law, valid for very low ionic concentrations,

+

HB (aq) + H 2O(aq) ⇄ B (aq) + H3O (aq)

where HB− and B2− represent the monoanionic and dianionic forms of the dye, respectively. Because water activity is almost constant under the experimental conditions, the thermodynamic equilibrium constant, K, can be expressed as a B2−a H3O+ [B2 −]·[H3O+] γB2−·γH3O+ K= = · = KcK γ a HB− [HB−]·c0 γHB− (1)

pKc = pK − 2.04· I

(7)

and (ii) the extended law, valid from low to moderate ionic concentrations, ⎞ ⎛ I pKc = pK − 2.04·⎜ ⎟ ⎝ 1 + 2.30· I ⎠

where the symbol a represents the activities of each species involved in the equilibrium, the brackets denote the analytical molar concentrations, γ represents the corresponding activity coefficients and c0 the standard concentration (1 mol L−1). The expression of K depends only on temperature (the effect of

(8)

In the last expressions, I is the ionic strength expressed in mol L−1. 1202



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EXPERIMENTAL DETAILS

An enhancement in the absorbance of the maximum at 616 nm is clearly observed as the salt concentration increases. This change can also be visually observed in the solution color (Figure 2) and is consistent with the displacement of the

Materials and Methods

BCG (Aldrich, sultone form, dye purity ∼90%) was used as received. NaCl (Baker analyzed reagent, 99.9% purity) was used as support electrolyte. Solutions were prepared using freshly deionized water (18 MΩ cm) previously filtered in a commercial Millipore Milli-Q system equipped with a filter of 0.22 μm pore size (MQ water). Solutions with the same dye analytical concentration (2.03 × 10−5 mol L−1) and different salt concentrations (from 0.002 to 0.2 mol L−1) were prepared, including two samples without salt but acidified with HCl and alkalinized with NaOH, to record the spectra of the pure acidic and basic forms of the dye at the working concentration. Aqueous solutions were prepared 24 h before the students conduct the laboratory experiments. The solids were dissolved in hot, freshly deionized water (∼60 °C) and quickly transferred to bottles with caps to prevent the incorporation of CO2 to the solutions. Dissolution of the dye is kinetically slow and requires sonication. Students must record the absorption spectra of the solutions and then calculate Kc for the different salt concentrations as described in the theoretical approach section. A complete and detailed description of the experimental procedures is available in the Supporting Information.

Figure 2. Changes in color of BCG water solutions (dye concentration is 1.67 × 10−5 mol L−1): (a) acidic solution, [NaCl] = 0; (b) dye solution, [NaCl] = 0; (c) [NaCl] = 0.39 × 10−2 mol L−1; (d) [NaCl] = 1.06 × 10−2 mol L−1; (e) [NaCl] = 7.74 × 10−2 mol L−1; (f) [NaCl] = 20.32 × 10−2 mol L−1; (g) basic solution, [NaCl] = 0.

equilibrium position toward the product. As such, the shift in Kc with the ionic strength denotes the diminishing of the activity coefficients (eq 1), in particular the one corresponding to the dianionic form of the dye. Numerical data reflecting these changes are listed in Table 1.

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Table 1. Total NaCl Concentration, Fraction of the Dye in the Dianionic Form, Calculated Hydronium Ion Concentration, and pKc Values of BCG

HAZARDS Some care must be taken to prepare solutions of BCG from the solid reagent, as it can cause irritation in eyes and skin. Hydrochloric acid is corrosive and causes burns to all body tissue. Sodium hydroxide is caustic; it causes burns to any area of contact. No other significant hazards are foreseen.

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RESULTS AND DISCUSSION Absorption spectra of the dye at different ionic strengths, obtained by students in a standard laboratory session in a physical chemistry course, are shown in Figure 1. The spectra

[NaCl]/(10−2 mol L−1)

XB2−

[H3O+]/(10−5 mol L−1)

pKc

0 0.19 0.39 0.58 0.77 0.96 2.88 4.76 7.79 9.68 19.35

0.32 0.36 0.36 0.37 0.38 0.39 0.44 0.45 0.48 0.50 0.53

2.68 2.76 2.76 2.78 2.80 2.82 2.92 2.94 3.00 3.05 3.11

4.90 4.81 4.81 4.79 4.77 4.74 4.64 4.62 4.56 4.52 4.46

As it can be seen in Figure 3, the experimental pKc values plotted versus √I/(1 + 2.30·√I) show a linear behavior up to ionic strengths of the order of ∼0.20 mol L−1, with a correlation coefficient, R2 = 0.9921. The 95% confidence interval for the slope parameter (−2.08 ± 0.13) contains the theoretical value of −2.04 predicted by the extended law of Debye−Hückel (eq 8). From the intercept, a thermodynamic equilibrium constant, pK = (4.91 ± 0.02), is obtained. This result agrees reasonably well with those found in literature (4.9285 ± 0.0030)18 In Figure 4, pKc experimental values are plotted as a function of I1/2 together with those computed with the limiting and extended laws of Debye−Hückel (eqs 7 and 8), using the pK value obtained before. From these plots, the students can easily assess the quality of the predictions of the two laws. Identical results were obtained using KCl instead of NaCl to adjust the ionic strength (data not shown). For electrolyte concentrations greater than 0.20 mol L−1, there are deviations from the extended Debye−Hückel law that depend on the type of electrolyte used to regulate the ionic strength. Some time ago, Robinson and Biggs19 reported values for the ionization constant of p-nitrophenol, obtained from spectrophotometric measurements in four different buffer mixtures. They showed

Figure 1. Absorption spectra of BCG aqueous solutions at increasing salt concentration (thin lines) and at acidic, HB−, and basic, B2‑, conditions (thick lines). The trend of increasing ionic strength among the curves is indicated by color.

of the acidic and basic forms of BCG are included in the same figure, showing absorption maxima at 444 and 616 nm, respectively. A clean isosbestic point at 507 nm is observed, suggesting that the recorded spectra are linear combinations of the ones corresponding to the acidic and basic forms of the dye, stoichiometrically related through the studied equilibrium. 1203




only based on three fundamental concepts: mass and charge conservation and Beer−Lambert law. Another appealing feature of the experiment concerns the possibility of working in a concentration regime well below the threshold value above which the Debye−Hückel limiting law ceases to be valid. Other experiments that rely on the use of buffer solutions to fix the hydronium concentration cannot be carried out at such low ionic strengths because the ionic strength of the buffer alone imposes a minimum height.

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ASSOCIATED CONTENT

S Supporting Information *

Theoretical approach for instructors and students; instructor notes (including CAS number of BCG and safety warnings); written directions for students. This material is available via the Internet at http://pubs.acs.org.

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Figure 3. Experimental pKc as a function of [I1/2/(1 + 2.30I1/2)] (open circles). The solid line corresponds to the linear fit of experimental data up to ∼0.20 mol L−1 of ionic strength.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS H.B.R. and M.M. have a post-doctoral fellowship from CONICET. Discussions with Daniel Laria,́ Maria Laura Japas, and Roberto Fernandez Prini are greatly acknowledged.

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REFERENCES

(1) Harned, H. S. J. Am. Chem. Soc. 1920, 42, 1808−1832. (2) Harned, H. S.; Brumbaugh, N. J. J. Am. Chem. Soc. 1922, 44, 2729−2748. (3) Harned, H. S.; Ehlers, R. W. J. Am. Chem. Soc. 1933, 55, 652− 656. (4) Cobb, C. L.; Love, G. A. J. Chem. Educ. 1998, 75, 90−92. (5) Stolzberg, R. J. J. Chem. Educ. 1999, 76, 640−641. (6) Ramette, R. J. Chem. Educ. 1963, 40, 71−72. (7) Corsaro, G. J. Chem. Educ. 1962, 39, 622−626. (8) Green, D. B.; Rechtsteiner, G.; Honodel, A. J. Chem. Educ. 1996, 73, 789−792. (9) Tackett, S. L. J. Chem. Educ. 1969, 46, 857−858. (10) Lamb, R. E.; Natusch, D. F. S.; Ó Reilly, J. E.; Watkins, N. J. Chem. Educ. 1973, 50, 432−434. (11) Ramette, R. J. Chem. Educ. 1963, 40, 252−255. (12) Kolthoff, I. M. J. Phys. Chem. 1930, 34, 1466−1483. (13) Biggs, A. I. Trans. Faraday Soc. 1954, 50, 800−802. (14) Harned, H.; Hickey, F. C. J. Am. Chem. Soc. 1937, 59, 2303− 2304. (15) Patterson, G. S. J. Chem. Educ. 1999, 76, 395−398. (16) Yamaoka, K.; Takatsuki, M. Bull. Chem. Soc. Jpn. 1978, 51, 3182−3192. (17) San Román, E.; González, M. C. J. Phys. Chem. 1989, 93, 3532− 3536. (18) Yamazaki, H.; Sperline, R. P.; Freiser, H. Anal. Chem. 1992, 64, 2720−2725. (19) Robinson, R. A.; Biggs, A. I. Trans. Faraday Soc. 1955, 51, 901− 903.

Figure 4. Experimental pKc values (open circles) and limiting (dashed line) and extended (solid line) Debye−Hückel laws predictions, as a function of the root square of the ionic strength.

that, for ionic strengths higher than 0.12, the values of the ionization constant depend not only on the type of buffer used to adjust the pH of the solution, but also on the amount of acid and conjugate base present in each buffer solution. The analysis of more sophisticated theoretical models describing the behavior of ions in highly concentrated salt solutions are well beyond the scope of this teaching laboratory experiment, so we will restrict the present analysis to solutions with ionic strengths lower than 0.20 mol L−1.

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CONCLUSION A modified laboratory experiment for undergraduate students is presented including a simplified procedure to evaluate effects of the ionic strength on the equilibrium concentration quotient of an acid−base indicator, the bromcresol green dye. The simplification involves the absence of buffer solutions to fix the hydronium concentration of the media. Compared with those experiments that rely on the use of buffer solutions, the present one has two important advantages: (i) the simplification of the operational maneuvers that have to be performed by the students, allowing an individual work that can be carried out in the course of a typical laboratory class (∼3 h) and (ii) a simplification of the didactic approach, as the experimental determination of Kc at different ionic strengths is 1204


A Simplified Undergraduate Laboratory Experiment To Evaluate the

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