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AnEasy andFastExperiment for theDetermination Wof the Equilibrium Constants of an AcidBase Pair,Free and Complexed with a Molecular Receptor

Elena Junqueraand Emilio Aicart*

Departamento de Qumica Fisica I, Facultad de Ciencias Qumicas, Universidad Complutense de Madrid, 28040-Madrid, Spain; *aicart@eucmax.sim.ucm.es

Molecular complexation with artificial receptors is aninteresting tool widely used in the interpretation of biologicalmechanisms based on molecular recognition processes (1, 2),where competition between equilibria plays a relevant role.A proper and accurate determination of the correspondingequilibrium constants is a necessary but not always easy task,since several processes may be involved in the interaction,and any of the properties analyzed is an overall result of thiscompetition. This is very important because in such a case thereis more than one association equilibrium, and more than one

supramolecular entity is formed. The importance and risinginterest of supramolecular systems validates their introductionto chemistry students; the picture presented to them, however,is often quite obscure. This paper shows, through easy pHexperiments, how to determine the equilibrium constants oftwo molecular receptorsubstrate systems involved in acompetitive process. The experiment is appropriate for studentsin the second semester of a junior-level physical chemistry class.

Equilibrium Constant Determination

When there is only one substrate species in solution thatcan associate with the receptor, the determination of the bind-ing constant is normally achieved by relating the percentage of

complex formed with any easily measurable physicochemicalproperty, such as conductivity, absorbance of light, fluorescence,or 1H NMR chemical shifts (3). However, in many cases thesubstrate is an ionizable weak acid; both the acid (HA) and itsconjugated base (A) are present in solution, and both are ableto associate with the receptor (R), a situation that complicatesthe usual procedure. Scheme I shows the set of equilibria thatoccur on the formation of RHA and RA complexes, assum-ing a usual 1:1 stoichiometry.

Ka

Ka'

KRHA KRA

H+

+ A

RA

+ H+

RHA

+R

+R

HA

Scheme I

The equilibrium constants are related to the activitiesof the species through these expressions:

Ka= (aH+aA)/aHA (1)

KRHA = aRHA/(aRaHA) (2)

KRA = aRA/(aRaA) (3)

Ka = (aRAaH+)/aRHA= KaKRA/KRHA (4)

where onlyKa, KRHA, and KRA are independent, since Kais related to them as eq 4 shows.

There are two possibilities for studying these associationequilibria. One is to buffer the pH of the medium so thatonly one of the two substrate species, HA or A, is in solution,and determine KRHAand KRA independently from the varia-tion of a physicochemical property as a function of total [R]at constant total [substrate] (4). It is important to ensure thatnone of the buffer species is capable of being complexed byR, because this could interfere in the final results. The other

possibility is to determine the Ka of the substrate and theassociation constants KRHA and KRA simultaneously, byfollowing the variation of the pH of an unbuffered aqueoussolution of the substrate as long as the receptor is added. SinceH+ is one of the species involved in Scheme I, this variationis a faithful indication of the shifting of these equilibria aslong as the two complexes RHA and RAare formed. Thismethod has clear advantages over the first one, since no buffersolutions are needed and all the equilibrium constants ofScheme I are obtained with only one titration, reducing thenumber of experiments and the amount of substrate andreceptorwhich is of great importance when they are veryexpensive or even not commercially available.

This paper describes an experimental setup and a math-ematical model, easily affordable in the laboratory, for thesimultaneous determination of all the equilibrium constantsof Scheme I through easy pH measurements. Several equa-tions must be considered for such a purpose: eqs 13, andthe charge and mass balances for the receptor and substrate,given by the following expressions:

[H+] = [A] + [RA] + [OH] (5)

[HA]total = [HA] + [A] + [RHA] + [RA] (6)

[R]total = [R] + [RHA] + [RA] (7)

The activities in eqs 13 are related to the concentrationsshown in eqs 57 through the activity coefficients, assumed

to be unity for the neutral species and determined with theextended DebyeHckel theory for the charged species.

Thus eqs 17 allow the simultaneous determination ofKa,KRHA, and KRA as coefficients of the nonlinear regressionof the experimental pH values (= logaH+) as a function oftotal receptor concentration. The program to carry out thenumerical analysis is a conventional nonlinear fitting proce-dure based on NewtonRaphson and Marquardt algorithms.

Equipment

Figure 1 shows a block diagram of specific apparatus for apotentiometric technique.1 A pHion meter together with acombined glass electrode was used for the pH measurements.

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The aqueous unbuffered solution of the substrate is placedin a measuring cell, with a cover to prevent evaporation of the

solution. A digital buret is filled with the receptor solution,which will be added to the cell in successive additions. Apolypropylene stirrer, activated by an external motor thatrotates at constant velocity, guarantees thorough mixing. Themeasuring cell and buret cylinder are thermostatted withrecirculating water from a thermostatted bath. The combinedglass electrode was calibrated with three buffer solutions ofpH 4, 7, and 9.

Experimental Procedure

In the experiment shown as an example, the receptor isthe -cyclodextrin (-CD) and the substrate is the salicylicacid. -CD is a torus-shaped oligosaccharide built up with 7

(1

4) linked

-D

-glucopyranose units. Its hydrophobiccavity allows for the encapsulation of an apolar substrate ofsuitable medium size, with the formation of an inclusioncomplex characterized by the stoichiometry and the associationconstant. This capability has made -CD one of the mostimportant and widely used drug carriers (5). Salicylic acid is awell-known hydroxybenzoic acid with various pharmaceuticalapplications. As a weak acid, it is dissociated in aqueoussolution and its aromatic ring is of appropriate size to fitinside the -CD cavity. Thus, salicylic acid and -CD areexamples of an acidbase pair and a molecular receptor, re-spectively, and have been chosen to show the suggested model.

pH measurements were performed on aqueous unbufferedsolutions2,3 of salicylic acid at a constant concentration of around4 mM, as a function of-CD concentration, at 25 C (Fig. 2).From these pH values, the dissociation constant of the acid(Ka) and the association constants of the complexes formedby the cyclodextrin and the ionized (KRA) and un-ionized(KRHA) forms of the substrate were determined.4 The values,reported in the third line of Table 1, lead to some conclusionsthat can be discussed by the teacher and the students: (i) thevalue of Ka is in excellent agreement with literature (8),corroborating the efficacy of the model; (ii) since the statisticsof the fits are fairly good, 1:1 stoichiometries are confirmedfor the inclusion complexes RHA and RA, as initially assumedin the model; (iii) the acid species of the substrate, salicylicacid, binds the -CD much more favorably than its ionic

Figure 3. pH values of aqueous solutions of salicylic acid at aconstant concentration of ca. 4 mM as a function of-CD con-

centration at different temperatures.

0.000 0.002 0.004 0.006 0.008

2.75

2.80

2.85

2.90

2.95

3.00

3.05 T= 15 C

T= 20 C

T= 25 C

T= 30 C

T= 40 C

[-CD] / M

pH

IemehcSnistnatsnoCmuirbiliuqEfoseulaV.1elbaTehtrof metsySretaWdicAcilycilaSnirtxedolcyC-

/]etartsbuS[Mm

T/ C 01 3 Ka

KAHR

M/ 1 KAR

M/ 1

50.4 51 2.1 1.0 0611 . 021 021 . 02

00.4 02 2.1 1.0 049 . 09 011 . 02

40.4 52 3.1 1.0 087 . 08 09 . 02

69.3 03 2.1 1.0 036 . 06 07 . 51

29.3 04 4.1 1.0 054 . 04 54 . 01

Figure 1. Block diagram of the potentiometric technique. (1)Metrohm 713 pH-Ion meter; (2) and (3) combined glass electrode;(4) measurement cell; (5) cover; (6) polypropylene stirrer; (7)Metrohm 665 Dosimat digital buret; (8) thermostatted bath.

Figure 2. pH values of aqueous solutions of salicylic acid at aconstant concentration of 4.04 mM as a function of-CD con-centration, at 25 C.

3.00

2.95

2.90

2.85

2.80

0.000 0.002 0.004 0.006 0.008

2.75

[-CD] / M

pH

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counterpart, salicylate. This can be analyzed in terms of themolecular factors affecting the inclusion process in each casesolvent reorganization, electrostatic interactions, etc., although

more energetic information is required for such discussion.

vant Hoff Analysis

The study can be completed with an analysis of the changesin the enthalpy (H), and entropy (S) of the associationprocesses, which can be estimated through the dependenceof the binding constants on temperature, following the well-known vant Hoff equation:

RlnK=

H

T+ S (8)

which assumes that Cp 0 in the temperature range studied.Figure 3 shows the pH values of the -CDsalicylic acid

water system as a function of [-CD] at five temperatures.5Table 1 reports the equilibrium constants at these temperaturesobtained as previously explained. Figure 4 shows the plots ofthe Rln Kvs 1/Tfor the two complexes formed. The Hand S values, determined from the slopes and intercepts ofthe linear fits of these data and reported on Table 2, reveal thatboth salicylic acid and salicylate species bind -CD with favor-able enthalpic terms (H < 0) dominant over unfavorableentropic terms (S < 0). Thus, the encapsulation processesare exothermic and enthalpy driven (|H| > T|S|). Thisthermodynamic pattern and its comparison with a typicalhydrophobically driven process (|H| 0, |S| < 0, andT|S| > |H|) (9) can be discussed by the teacher and

Figure 4. vant Hoff plots for RHA and RA

complexes.

R

lnK/(Jmol-1K

-1)

T-1 / (10-3 K-1)

RHA

RA60

45

30

3.2 3.3 3.4 3.5

15

(yplahtnE.2elbaT H (yportnEdna) S segnahC))8qEmorf(gnidniBnopu

etartsbuSrotpeceR .H lomJk/ 1 .S lomJ/ 1 K 1

dicacilycilasDC- 92 1 24 4

noinaetalycilasDC- 92 8 36 02

students. It is usually attributed to the contribution of a clearhydrophobic effect, van der Waals contacts between the hostand the guest, and the solvent reorganization, as noncovalentintermolecular forces responsible for the overall stability ofthe complexes (2, 5). Notice in Table 2 that it is the entropicterm that makes the CDsalicylic acid complex more stablethan the CDsalicylate, because the entropy change is moreunfavorable for the anion while the enthalpy change is equally

favorable for both the anion and acid.

Acknowledgment

We thank the DGES (M.E.C. of Spain), project No.PB95-0356, for supporting this work.

WSupplemental Material

Supplemental material for this article, including notesfor the instructor and the nonlinear regression method todetermine the equilibrium constant, is available in this issueofJCE Online.

Notes

1. An estimated price for the experimental equipment wouldbe around $4000.

2. Solutions must be freshly prepared with distilled, deionizedwater, preferably from a Millipore Super-Q System. It is advisableto sonicate initial solutions for 15 minutes in an ultrasonic bath toguarantee their homogeneity.

3. A procedure for the preparation of solutions, which guar-antees the constancy of the substrate concentration during the ti-tration, is as follows: (i) 50 mL of aqueous solution of salicylic acid4 mM is prepared; (ii) 20 mL of this substrate solution is placedinto the cell; (iii) the other 30 mL is used to prepare the -CD

solution, at a concentration of 15 mM; (iv) this CDsubstratewater solution is placed into the buret.

4. The constantsA and Band the ion size parameters for H+

and OH on the extended DebyeHckel equation are taken fromthe literature (6, 7). These parameters for salicylate species, free(A) and complexed (RA), have been estimated as 6 and 16 ,respectively, in terms of their geometry and size.

5. The vant Hoff analysis can be done by several pairs of stu-dents, each pair working at one temperature. A minimum of fourtemperatures is recommended to obtain reliable energetic parameters.

Literature Cited

1. Fersht, A. Structure and Mechanism; Freeman: New York, 1985.

2. Attwood, J. L.; Davies, J. E. D.; MacNicol, D. D.; Vgtle, F.Comprehensive Supramolecular Chemistry; Elsevier: Oxford, 1996.

3. Connors, K. A. Binding Constants: The Measurement of Molecular Complex Stability; Wiley: New York, 1987.

4. Junquera, E.; Aicart, E.J. Inclusion Phenom.1997,29, 119.5. DSouza, V. T.; Lipkowitz K. B. Chem. Rev. 1998,98, 1741.6. Kielland, J.J. Am. Chem. Soc. 1937,59, 1675.7. Robinson, R. A.; Stokes, R. H. Electrolyte Solutions;

Butterworths: London, 1965.8. CRC Handbook of Chemistry and Physics, 67th ed.; Weast, R. C.,

Ed.; CRC Press: Boca Raton, FL, 1986; p D-162.9. Tanford, C. The Hydrophobic Effect. Formation of Micelles and

Biological Membranes; Wiley: New York, 1980.

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