Determination of the Acid Dissociation Constant of ... - ACS Publications

Laboratory Experiment Cite This: J. Chem. Educ. 2018, 95, 310−314

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Determination of the Acid Dissociation Constant of a Phenolic Acid by High Performance Liquid Chromatography: An Experiment for the Upper Level Analytical Chemistry laboratory Ghada Rabah* Department of Chemistry, North Carolina State University, 2620 Yarbrough Drive, Raleigh, North Carolina 27695, United States

J. Chem. Educ. 2018.95:310-314. Downloaded from pubs.acs.org by UNIV OF READING on 08/13/18. For personal use only.

S Supporting Information *

ABSTRACT: A high performance liquid chromatography (HPLC) experiment for the upper level analytical chemistry laboratory is described. The students consider the effect of mobile-phase composition and pH on the retention times of ionizable compounds in order to determine the acid dissociation constant, Ka, of a phenolic acid. Results are analyzed using nonlinear regression.

KEYWORDS: Upper-Division Undergraduate, Analytical Chemistry, Inquiry-Based/Discovery Learning, Hands-On Learning/Manipulatives, Chromatography, HPLC

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INTRODUCTION High performance liquid chromatography (HPLC) is a powerful analytical tool, and several undergraduate chemistry laboratory experiments have been developed and published in this Journal to give students hands-on experience using this technique. The majority of the experiments focus on separation, identification, and quantification of compounds by linear calibration methods.1−4 The experiment reported here is adapted from the literature5−7 for the upper level analytical chemistry laboratory and expands the application of high performance liquid chromatography to the determination of an acid dissociation constant, Ka. Students use a nonlinear model that relates retention factors and activity coefficients to pH values in order to calculate the acid dissociation constant. The model considers the effect of ionic strength and the activity coefficient. This is an effect that students are often told to ignore in dilute aqueous solutions and may be considerable in hydro-organic systems such as the buffer−acetonitrile mixtures used here.8 Many samples studied in organic and biochemistry contain complex mixtures of ionizable compounds, and as such, the consideration of their acid dissociation constant and the pH of the environment in which they exist is essential in understanding their chemical reactivity and physicochemical properties. For example, determination of Ka of a drug is essential when studying its transport into cells and across membranes.9 Many experiments are reported for the undergraduate teaching laboratory that describe the use of potentiometric10 and spectrophotometric methods11−14 for the determination of the acid dissociation constant. There are limited reports using © 2018 American Chemical Society and Division of Chemical Education, Inc.

HPLC. One experiment published in this Journal by Harvey et al.15 describes the use of response surface curves to optimize the separation of several benzoic acids by reverse-phase HPLC where the Ka values of the acids are also determined. This article describes the first laboratory experiment reported in this Journal that focuses on using reversed-phase HPLC for the determination of the Ka of a weak acid using a nonlinear model that considers the effect of ionic strength and the activity coefficient. There are many advantages to the HPLC method. It is free from concerns about chemical and spectral interferences and more amenable to automation. In addition, mobile-phase systems used in reversed-phase HPLC, such as the aqueous buffer−acetonitrile mixtures employed here, are believed to simulate the environment in biological systems6 and might be preferred when determining the acid dissociation constant and the behavior of an analyte in vivo. The determination of the pKa values in hydro-organic media is indeed recommended by IUPAC for analytes found in biological systems and active pharmaceutical ingredients. In the teaching laboratory setting, the comparison of Ka values to values determined in aqueous solutions offers the opportunity to consider how electrostatic and solvation effects impact the value of the acid dissociation constant. Ferulic acid (Figure 1A) was selected as a model ionizable compound for the determination of its Ka by HPLC. It has two ionizable functional groups, a carboxylic acid (−COOH, Ka1) Received: August 26, 2017 Revised: December 18, 2017 Published: January 19, 2018 310

DOI: 10.1021/acs.jchemed.7b00647 J. Chem. Educ. 2018, 95, 310−314

Journal of Chemical Education

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Laboratory Experiment

EXPERIMENTAL SECTION

Reagents and Apparatus

Analytical reagent grade chemicals, deionized water, and HPLC grade acetonitrile were used for solution preparation. A stock solution of nominally 0.02 M ferulic acid in acetonitrile was prepared at the beginning of the lab week by the instructor and stored in 10 mL aliquots at 4 °C. Aliquots were taken out at the beginning of the laboratory period, and students used this stock solution to prepare working ferulic acid solutions diluted 100fold with the mobile phase for each injection. A 0.01% potassium bromide solution was used to measure the hold-up time (tm). Formic acid buffers (30 mM) were prepared from sodium formate and a 1 M HCl solution. The experiment was run on an Agilent 1200 chromatographic system consisting of a degasser, a binary pump, an autosampler, and a diode array detector. A 150 mm × 4.6 mm Zorbax S8-Aq C18, 3.5 μm (Agilent) column is used at ambient temperature. Students recorded the temperature reading on the day of the experiment using a stick-on digital temperature thermometer placed on the HPLC column.17 A 30% CH3CN−70% formate buffer was used as the mobile phase at pH values that range from 2.7 to 5.5. The mobile-phase pH for each run was determined from triplicate measurements of the pH of mixtures consisting of 30% acetonitrile and 70% aqueous buffer using an electrode calibrated with aqueous buffers. Ideally the pH electrode should be calibrated with reference buffers prepared in the same mixed solvent used as a mobile phase, but literature reference suggests that the system we adopted here was expected to give a good result and was simple to measure.18 The experiment can be adapted to any comparable HPLC system that might be found in other teaching laboratories; different C18 columns and mobile-phase compositions result in different retention times. The column and mobile-phase compositions selected here resulted in short run times in the range 2−5 min (based on pH) per injection making this experiment feasible for a 3 h lab period. Since Ka can vary with temperature, if HPLC column heater and pH solutions can be controlled by a thermostat then it is recommended to do so and to report the temperatures. In the absence of temperature control, students should record and report the temperature readings on the day of the lab period. Temperatures usually do not fluctuate significantly within the same lab period, but values between lab periods might vary considerably.

Figure 1. Chemical structures of (A) ferulic acid and (B) coumaric acid.

and a phenolic acid (Ph−O−H, Ka2). Only Ka1will be determined here (expressed as pKa1); the second dissociation constant cannot be determined by this method since this would require a mobile phase with a pH that is outside the range of stability of the HPLC column packing. Good chromatographic data was also observed in our laboratory for the coumaric acid (Figure 1B). A ferulic−coumaric mixture would be good to consider if an instructor wishes to expand the HPLC experiment to more than one laboratory period and cover both separation and Ka determination. The model used here16 to determine the Ka1 value by reversed-phase HPLC is based on the dependence of the chromatographic retention factor k, which is calculated by eq 1, on the pH of the mobile phase. The tr and tm in eq 1 represent the retention times of the retained and unretained components, respectively. k=

tr − tm tm

(1)

The retention factor of a ionizable compound at a given H+ activity, aH+, is a weighted average of the retention factors of the deprotonated and protonated forms, kA− and kHA, of the solute as described by eq 2 where xi represents the mole fraction of the species.

k = x HAkHA + x A−k A−

(2)

Substitution of the expressions for the mole fractions xHA and xA− in eq 2 gives eq 3. k=

[HA]kHA + [A−]k A− [HA] + [A−]

(3)

Procedure

Substitution of the acid dissociation constant, Ka, in eq 4 into eq 3 and rearranging gives eq 5 which is used in this experiment to determine the Ka of ferulic acid where γ is the calculated activity coefficient. Ka =

k=

(a A−)(a H+) [A−]γa H+ = aHA [HA]

kHA + 1+

k A−K a γa H+ Ka γa H+

For each pH considered, students performed duplicate runs injecting each time 30 μL of the working ferulic acid solution at a flow rate of 1 mL/min. Chromatograms were collected at two wavelengths, 270 nm (ferulic acid) and 230 nm (potassium bromide). Students exported their chromatograms as commaseparated values (CSV) files and performed data analysis in Excel. The retention factor, k, was calculated from eq 1 where tr represents the retention time of ferulic acid and tm the KBr hold-up time (also commonly called void time). Students estimated the ionic strength, I, of the mobile phase from the buffer solution preparation and used the Debye− Hückel constants A and a0B in 30% CH3CN from the literature.19 The experimental k values, the calculated activity coefficient values, and the pH measurements (converted to activities of H+) were then used to determine Ka1 by a nonlinear least-squares fit to eq 5 using Solver in Excel. Solver optimizes initial guessed values of Ka and the retention factors kHA and kA−

(4)

(5)

The activity coefficient is calculated using the extended Debye−Hückel equation:

−log γ =

A I 1 + a 0B I

(6) 311




to get the minimum sum of square of residuals ∑(ki,obs − ki,calc)2 where ki,obs is the observed value of the retention factor for solution, i, calculated by eq 1, and ki,calc is the corresponding retention factor calculated by eq 5.20 Students then calculated pKa1 and compared their results to the literature pKa1value of 5.33 determined in the same mobile phase.5 Sample student pKa1values are listed in Table 1. The ± values are the standard Table 1. Sample Student Values for Ferulic Acid from Chromatographic Measurements Student Group

pKa1a

kHAa

kA−a

1 2 3

5.42 ± 0.15 5.50 ± 0.27 5.32 ± 0.07

1.33 ± 0.01 1.36 ± 0.03 1.34 ± 0.01

0.23 ± 0.19 0.34 ± 0.27 0.33 ± 0.07

Figure 3. Residuals plot of ki,obs − ki,calc vs activity of H+ corresponding to student group 3 data from Table 1.

± values are the standard deviations. bThe literature value5 of pKa1 in the same percent organic mobile phase is reported to be 5.33 a

gradient methods of separation and quantification by linear calibration. This experiment has been part of the upper level analytical lab for three course offerings over the past three years, with a maximum of 32 students per semester enrolled in four lab sections. Variations on the experimental conditions were run over the last two years, and in the final version, the 30% (v/v) acetonitrile mobile phase is selected. The run times obtained with 10% and 20% acetonitrile mobile phases are too long for the scheduled teaching lab period. The experiment described here can be completed in a standard 3 h laboratory period. Column equilibration at each pH required around 20 min. Replicate injections of the sample should be run at each pH to verify that equilibration was achieved and retention time is reproducible. In order to finish the experiment during the allocated lab time, it is critical that students come to the lab prepared and ready to start the first mobile-phase equilibration immediately. They can then start preparing samples and setting up instrument methods while the column is equilibrating. Additional samples and buffer solutions can be prepared during the wait times for the subsequent column equilibrations. To ensure students are prepared to perform calculations and are considering fundamental aspects of the experiment, they are required to answer a set of prelab questions before coming to the lab. Students work in groups of 2 or 3 when performing the experiment depending on the number of students in a lab section. There are 8 students in each lab section, and experiments are run in rotation to maximize hands-on access to instruments. Students are trained on nonlinear regression and the use of Solver during a computer lab period prior to performing this experiment. The determined dissociation constant values in the mixed solvent system used as the mobile phase were consistently lower (pKa values were higher) than the reference value (pKa = 4.58) in aqueous solutions.22 This is consistent with the decrease in the polarity of the medium with increasing the organic component, given that in the dissociation of uncharged acids, as is the case of the Ka1 of phenolic acids, charges are created (HA ↔ H+ + A−) and the electrostatic interactions become important.7 Pedagogically, the goals of this experiment were the following: • to expand the application of HPLC outside the common separation and quantitative determination of an unknown

deviations. Standard deviations in the Ka1 values were determined using the SolvStat add-in in Excel, which returns regression statistics for regression coefficients obtained by using the Solver. Standard error in Ka1 obtained from SolvStat was then propagated to pKa1. Instructions for using Solver and SolvStat21 in Excel are included in the Supporting Information.

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RESULTS AND DISCUSSION Determined kHA, kA−, and pKa1 values from three student groups are reported in Table 1. Figure 2 shows plots of the chromatographic retention factor, k, of ferulic acid versus the activity of H+ of the mobile phase

Figure 2. Plot of the chromatographic retention factor, k, of ferulic acid vs the activity of H+ of the mobile phase for 30% (v/v) CH3CN. The raw data (scatter plot) correspond to student group 3 data from Table 1. The solid line indicates the retention factors predicted by eq 5.

for 30% (v/v) CH3CN. Students also check the validity of the model by calculating the residuals; Figure 3 shows the residuals plot of (ki,obs − ki,calc) versus activity of H+ corresponding to student group 3 data from Table 1 and is representative of the observed random distribution of the residuals for other groups. Students used the random distribution of the residuals as a simple diagnostic tool against outliers and lack of fit. Students performing this experiment should already be familiar with separation and retention in HPLC from previous laboratory experiments. In our program, this is the third HPLC experiment performed in the analytical laboratory series; the first two experiments are introduced in the quantitative analysis laboratory and involve the development of isocratic and 312



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• to allow students to consider factors that affect retention of ionizable species in HPLC and use the technique to determine the dissociation constant of an acid • to expand the students’ data analysis skills beyond the averaging and linear regression analysis typically performed in the quantitative analysis laboratory • to teach students to analyze data using nonlinear regression and train them to use the residuals plot as a simple but effective diagnostic tool for outliers and lack of fit Students submitted their work individually in a full laboratory report with the usual sections, Introduction, Experimental, Results, Discussion, and Conclusion. They included general considerations of the retention of ionizable compounds in reversed-phase HPLC, how the electrostatic and solvent effects impact the value of the acid dissociation constant and other fundamental aspects. Their results show that they have been successful in collecting data and performing nonlinear regression analysis to determine pKa values that are generally within the 95% confidence interval of the literature value of 5.33.

CONCLUSION This experiment expands students’ use of HPLC to the determination of the acid dissociation constant of an acid. It expands on previous experiments using HPLC for the separation and identification of small molecules and adds nonlinear regression, analysis of residuals, preparation of buffers, and considerations of electrostatic and solvent effects. Chemicals and instrumentation used are accessible to undergraduate analytical chemistry laboratories, and the experiment is relatively safe. ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.7b00647. Notes for instructors and student laboratory handout (PDF, DOCX)

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Ghada Rabah: 0000-0003-1822-1816 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The author is grateful to the many students who have participated in testing this experiment and to Dr. Jaap Folmer for his helpful discussions and suggestions along the way. This experiment was initially tested and developed on a Waters Breeze HPLC system purchased for our quantitative analysis laboratory by a generous educational enhancement grant from the North Carolina Biotechnology Center (Grant 2012-EEG6006 to G.R.). The experiment was later transferred and adapted to the Agilent 1200 system currently used by our upper level chemistry lab. 313




(21) The Solver Statistics Macro. https://www.engram9.info/excel2007-vba-methods/the-solver-statistics-macro.html (accessed Dec 15, 2017). (22) Value predicted for Ferulic acid CAS Registry Number 1135-246.

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Determination of the Acid Dissociation Constant of ... - ACS Publications

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