In the Laboratory
Drug Distribution: A Guided-Inquiry Laboratory Experiment in Coupled Homogeneous and Heterogeneous Equilibria
W
John Hein and Michael Jeannot* Department of Chemistry, St. Cloud State University, St. Cloud, MN 56301-4498; *
[email protected] One of the most difficult concepts for students in quantitative analysis is simultaneous equilibria. Students have difficulty understanding that there can be only one concentration of a particular chemical species, even if it is involved in more than one equilibrium simultaneously. The purpose of this guided-inquiry experiment is to provide the students with a relatively simple drug distribution system for which they must derive algebraic relationships between the concentrations of various species (mass balance, charge balance, and equilibrium constant expressions). They must decide which quantities are known values, which ones can be easily measured, and which ones must be calculated using their algebraic expressions. In doing so, the students come to realize that there can only be one concentration of each species in solution, and all concentrations and equilibrium constants can be determined using the results from a single extraction. Previous experiments related to coupled equilibria that have appeared in this Journal (1–3) all rely on multiple extractions under different conditions to determine various concentrations and equilibrium constants. Furthermore, these experiments do not require the students to work directly with the simultaneous algebraic relationships of mass balance, charge balance, and equilibrium constant expressions. The laboratory experiment reported here represents a singleextraction equilibrium system from which all concentrations and equilibrium constants can be obtained by consideration of the appropriate simultaneous algebraic expressions and two measured concentrations, with no approximations. The drug whose distribution is studied, diphenhydramine, is a commonly used antihistamine, and the equilibria that are studied represent a greatly simplified model for drug distribution in the human body. An additional benefit of this experiment is that students gain experience in both quantitative gas chromatography and the use of glass electrodes for pH measurement. The relevant equilibria for the basic drug diphenhydramine are shown in Scheme I. H 2O Kw BH+
Ka
H+
+
B
+
κ
OH᎑
Scheme I
B0
BH+ and B represent the protonated and deprotonated forms of diphenhydramine, respectively. Ka and Kw represent the acid dissociation constant of diphenhydramine and the 224
autoprotolysis constant of water, respectively. The free base dissolved in the organic phase is given the symbol Bo. The aqueous-organic distribution coefficient for the free base, B, is represented by κ. It is assumed that BH+ remains in the aqueous phase exclusively. Also, since all solutions are dilute, concentrations will be used rather than activities in all cases. The chemical structures of BH+ and B are shown below. Diphenhydramine was chosen for this study because it is readily available, it can be directly analyzed by gas chromatography (GC) without derivatization, and it is relatively nonpolar in the basic form and hence has a relatively large distribution coefficient, κ. NH+
O
N H+
+
BH+
O
B
Experimental Procedures Diphenhydramine hydrochloride (BH+Cl᎑) is inexpensive and commercially available from Sigma. The instructor can prepare the free base (required for GC calibration) by dissolving the hydrochloride salt in water and adding an excess of NaOH. The free base (an oily liquid) can be collected, washed with water, and dried with anhydrous Na2SO4. Since the GC is used to determine the concentration of B in the organic phase (n-octane), it must first be calibrated with standard solutions of B in n-octane with a fixed concentration of an internal standard, such as hexadecane. The analytical signal is taken as the ratio of the peak areas of diphenhydramine (B) to internal standard. The same internal standard– n-octane solution is then used as the organic phase for the diphenhydramine distribution experiment. The apparatus used for the equilibrium system is a simple 1-L volumetric flask. The students must accurately measure about 2 × 10᎑4 mol of BH+Cl᎑ and 1 × 10᎑4 mol of NaOH and dissolve in 1.000 L of water to produce roughly equal amounts of BH+ and B. The NaOH is most easily obtained by adding a known volume of a standardized solution. For the most accurate results, the students should use CO2-free water, purge the headspace in the flask with N2 or He gas, and thermostat the apparatus at 25 °C. Exactly 1.00 mL of n-octane–internal standard solution is then placed on top of the aqueous phase in the neck of the flask. A schematic diagram of the system is shown in Figure 1. The solution is then stirred vigorously with a magnetic stir bar until equilibrium is attained (less than 15 min). After phase coalescence (a few
Journal of Chemical Education • Vol. 78 No. 2 February 2001 • JChemEd.chem.wisc.edu
In the Laboratory
Figure 1. Schematic representation of the drug distribution system in a 1-L volumetric flask. The volume of the organic phase is small in order to only partially perturb the aqueous-phase equilibrium.
B
Organic phase (1mL)
Aqueous phase (1L) +
BH , B
Stir bar
Table 1. Student Data and Calculations for 1.96 ⴛ 10 – 4 M BH+ and 1.00 ⴛ 10 – 4 M NaOH K w / Vo/ Vaq / [Cl᎑]/ [Na+]/ [H+]/ [Bo]/ [OH᎑]/ [BH+]/ [B]/ µM µM µM µM 10᎑14 mL mL nM mM a µM 1.0 1.00 1000. 196 aAverage
100.
1.95 32.5
5.13
101
κ
Ka/ 10᎑9
62.6 519 1.21
of three samplings/injections.
minutes), 1 µL of the organic phase is sampled with a microsyringe and injected into the GC in order to determine the concentration of B in the organic phase. This sampling and injection can be repeated to obtain statistical data. Finally, the students may be instructed to measure the pH of a portion of the aqueous phase using a glass electrode and standard buffers, ideally all at 25 °C.
the NaOH that was added to convert some of the BH+ into B initially. It is prudent to guide the students in deriving these equations, particularly the mass balance and charge balance, and to make sure they have the right equations before proceeding to solve them. The instructor can then ask the students which values in eqs 1–5 are known quantities (Kw, Vo, Vaq, [Cl᎑], and [Na+]). The measured values are [H+] and [Bo]. This leaves a system of 5 equations and 5 unknowns ([OH᎑], [BH+], [B], κ , and Ka). Equations 1, 5, 4, 3, and 2 may be solved sequentially to determine [OH᎑], [BH+], [B], κ , and K a respectively. This process should be “discovered” by the students. A sample of student data is shown in Table 1. The student had prepared a 1.000-L aqueous solution of 1.96 × 10᎑4 M diphenhydramine hydrochloride (BH+), with the addition of 1.00 × 10᎑4 moles of NaOH. The calculated pK a is 8.92. Literature values for the pK a of diphenhydramine hydrochloride range from 8.4 to 9.12 (4–7 ). Discussion This experiment is a very powerful tool for facilitating the comprehension of simultaneous equilibria by students in an introductory analytical chemistry course. Although the experimental procedure is given directly to the students, the guided-inquiry approach to interpreting the data requires the students to think carefully about what is happening in the system, and gives them a very practical application of mass balance and charge balance relationships, concepts that are often difficult for beginning students in analytical chemistry. As an additional challenge, students may be asked to estimate the uncertainty in the calculated pK a value via propagation of errors.
Hazards There are no significant hazards associated with this experiment. Interpretation of Results At the completion of the experimental procedure, the students are not told exactly what to do with the data. They may simply be instructed to determine the concentrations of all chemical species with the measurements they have made and with the correct equilibrium constant, mass balance, and charge balance expressions, using the scheme shown in Scheme I. The relevant relationships that the students may be expected to derive are shown below: K w = [H+][OH ᎑ ] K a = [H+][B]/[BH+] κ = [Bo]/[B]
Autoprotolysis Acid dissociation constant Distribution coefficient [BH+] + [B] + [Bo]Vo /Vaq = [Cl ᎑ ] Mass balance [BH+] + [H+] + [Na+] = [Cl ᎑ ] + [OH ᎑ ] Charge balance
(1) (2) (3) (4) (5)
In eq 4, Vo and Vaq are the volumes of the organic and aqueous phases, respectively. Alternatively, eq 4 could be multiplied through by Vaq to write the mass balance in terms of moles. The formal concentration of diphenhydramine is simply [Cl᎑], as shown in eq 4, since the drug is initially dissolved as BH+Cl᎑. The sodium ion concentration in eq 5 comes from
Acknowledgment M.J. wishes to acknowledge St. Cloud State University for financial support in the form of a Faculty Research Grant. W
Supplemental Material
A list of chemicals and supplies, additional tips for the instructor, and a student handout including detailed experimental procedures and questions for interpreting results are available in this issue of JCE Online. Literature Cited 1. Cwikel, D.; Gutman, G.; Kodnir, G.; Rothman, A. J. Chem. Educ. 1986, 63, 905–906. 2. Adamson, R.; Parks, P. C. J. Chem. Educ. 1971, 48, 120–121. 3. Ellison, H. R. J. Chem. Educ. 1971, 48, 124–125. 4. Holcomb, I. J.; Fusari, S. A. In Analytical Profiles of Drug Substances, Vol. 3; Florey, K., Ed.; American Pharmaceutical Association: New York, 1974; pp 173–232. 5. Andrews, A. C.; Lyons, T. D.; O’Brien, T. D. J. Chem. Soc. 1962, 1776–1780. 6. Lordi, N. G.; Christian, J. E. J. Am. Pharm. Assoc., Sci. Ed. 1956, 45, 300–305. 7. deRoos, A. M.; Rekker, R. F.; Nauta, W. T. Arzneim. Forsch. 1970, 20, 1763–1765.
JChemEd.chem.wisc.edu • Vol. 78 No. 2 February 2001 • Journal of Chemical Education
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