Determination of acid dissociation constants of some ... - NOPR [PDF]

Indian Journal of Chemistry Vol. 46A, August 2007, pp. 1263-1265

Determination of acid dissociation constants of some monobasic organic acids in acetonitrile from molar conductance Samik Nag & Dipankar Datta* Department of Inorganic Chemistry, Indian Association for the Cultivation of Science, Kolkata 700 032, India Email: [email protected] Received 21 April 2007; revised 5 July 2007 The pKa values of some 14 monobasic organic acids like carboxylates, phenols, etc. are determined in acetonitrile from conductivity measurements. These pKa values are found to be higher than those reported in the aqueous medium on the average by 2.8 (± 1.1) pKa unit. A thermodynamic rationalisation of this observation is provided. It emerges that an acid should be more acidic in water than in acetonitrile as water being more polar than acetonitrile brings about greater ionisation of an acid.

Interactions between any two chemical species can be described as acid-base interactions. Consequently knowledge of acidity/basicity of a chemical species is of fundamental importance in chemical sciences. Here, we are concerned with monobasic organic Brønsted acids of the type AH where H is a dissociable proton. The concentration of the proton released in solution is related to the acid strength of an AH molecule, as given by: Ka AH

A- + H+

… (1)

The acid dissociation constant pKa indicates the extent of ionization of an AH molecule at different pH values. The pKa of organic reagents plays a vital role in many analytical procedures such as acid-base titration, solvent extraction, complex formation and ion transport. It has been shown that acid-base properties affect the toxicity, chromatographic retention behaviour and pharmaceutical properties of organic acids and bases1. Organic acids present milder reaction conditions that make them advantageous on certain synthetic occasions. Conventionally, pKa values are measured in aqueous medium. But such data are needed in nonaqueous medium also, especially in acetonitrile2-5. Usually, pKa values are determined spectrophotometrically or potentiometrically1-4. NMR methods are also

applied6. Not all organic acids are amenable to such measurements. For example, many organic acids are colourless impairing spectrophotometric measurements. We have developed a simple method of determining the pKa values of AH molecules in acetonitrile from solution conductance, which is described here. We also indicate how such values compare with those in the aqueous medium, a clear cut idea of which is still lacking in literature. Experimental All organic acids used in the present study were purchased from Aldrich and were used without further purifications. Acetonitrile used for conducitivity measurements was prepared from the commercial solvent by CaH2 and P4O10 treatment. Conductivity measurements were made on a Systronics (India) conductivity meter (model 304) under ambient conditions. For the purpose of the determination of the pKa value of a particular AH molecule, conductances in acetonitrile were measured for at least five different concentrations in the range 10-3 to 10-4 mol dm-3. The pKa value reported here for an AH is the average of all such determinations. Results and discussion Our method is a modification of the approach of Kolthoff and Chantooni7. The molar conductance of an AH molecule in acetonitrile is found to have a definite value (Λobs) which means that in solution the equilibrium (1) is operative. Since the molar conductance of undissociated AH should be zero, we can write Eq. (2) where x is the molar fraction of dissociated AH and 140 mho cm2 mol-1 is the average value of the molar conductance of a 1:1 electrolyte in acetonitrile as specified by Greary8. 140x = Λobs

… (2)

Thus, for a solute concentration of C mol dm-3, the equilibrium concentrations of A- and H+ are Cx mol dm-3 while that of undissociated AH C(1-x) mol dm-3. Consequently, acid dissociation constant, Ka, takes the form of Eq. (3): Ka = Cx2/(1-x)

… (3)

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We have determined the pKa values of some 14 AH molecules by using Eqs (2) and (3) varying the concentration of AH in the range 10-3 to 10-4 mol dm-3. Results of our measurements for m-methoxy benzoic acid are shown in Table 1 as an example. The pKa values obtained for various monobasic organic acids, studied here, are given in Table 2. For comparison, we have given the corresponding pKa values in water9 also in Table 2. A general observation is that the pKa vaues in acetonitrile are consistently higher than those in water. On the average, the acid dissociation constant determined in acetonitrile is higher than that in water by 2.8 (±1.1) pKa unit, i.e. an acid is more acidic in water than in acetonitrile. If ∆G0w is the free energy change for reaction (1) in water and ∆G0s that in acetonitrile, then: ∆G0w = −RT ln Kw = −2.303 RT log Kw = 2.303 RT (pKw) … (4)

∆G0s = −RT ln Ks = −2.303 RT log Ks = 2.303 RT (pKs) … (5) Consequently, ∆pK = pKs – pKw = (∆G0s − ∆G0w) / 2.303 RT … (6) As ∆G0 = ∆H0 − T∆S0, we can say that ∆pK = Esols(A-) + Esols(H+) − Esolw(A-) − Esolw(H+) + S − Esols(AH) + Esolw(AH) … (7) where Esol is the enthalpy of solvation and the term S includes the terms due to differences in entropy changes for reaction (1) in the two solvents water (w) and acetonitrile (s). Recently, we have shown10 that the enthalpy of hydration of the cations can be reproduced in excellent manner by an equation like that of Born solvation (Eq. 8) where N is Avogadro’s number, Z charge on the cation, e charge of an

Table 1Conductivity data and determination of pKa for m-methoxybenzoic acid in acetonitrile at room temperature Λobs c

[AH]d

[A-]d

[H+]d

pKae

2.826 2.75 0.845 1.413 2.01 1.175 0.707 1.45 1.557 0.353 1.20 2.406 0.177 1.01 3.737 a Various concentrations are given in mmol dm-3. b In µmho. c Molar conductance in mho cm2 mol-1. d Equilibrium concentration. e Average value is 7.0.

2.809 1.401 0.699 0.347 0.172

0.017 0.012 0.008 0.006 0.005

0.017 0.012 0.008 0.006 0.005

7.0 7.0 7.1 7.0 6.9

Solute concentrationa

Solution conductanceb

Table 2pKa values of some monobasic organic acids as determined in acetonitrile and those in watera AH

pKa (water)

pKa (acetonitrile)

∆pK

Acetic acid 4.8 7.1 2.3 Chloroacetic acid 2.9 6.0 3.1 Dichloroacetic acid 1.3 5.7 4.4 Trichloroacetic acid 0.7 5.9 5.2 Iodoacetic acid 3.2 6.4 3.2 Cyclohexane carboxylic acid 4.9 7.6 2.7 Benzoic acid 4.2 6.5 2.3 m-Methoxybenzoic acid 4.1 7.0 2.9 p-Methoxybenzoic acid 4.5 6.9 2.4 1-Naphthoic acid 3.7 6.4 2.7 Phenol 9.9 10.9 1.0 Thiophenol 6.6 8.9 2.3 Nitroethane 8.5 10.1 1.6 Nitrobenzene 4.0 7.5 3.5 a At room temperature. The pKa (water) values are taken from Ref. 9. ∆pK = pKa (acetonitrile) − pKa (water). Average value of ∆pK is 2.8 with a standard deviation of 1.1.

NOTES

electron, ε0 the permittivity of vacuum, ε the relative permittivity of the medium and r Shannon's crystal ionic radii (the factor of 1012 is introduced so that r is expressed in pm). E sol =

1012.N ( Ze)2  1   − 1 8πεo(r + 53)  ε 

… (8)

For anions, Born equation works quite well with van der Waals radii10. In terms of Born solvation, dissolution of neutral species is accompanied with zero enthalpy of solvation. Consequently, we need not consider Esol(AH) in the calculation of ∆pK. With experimental enthalpy of hydration of proton11,12 as 1100.4 kJ mol-1, and ε (at 298 K) of water and acetonitrile as 78.54 and 35.72 respectively9, Esols(H+) − Esolw(H+) is calculated as 16.60 kJ mol-1. For large anions, since van der Waals’ radii will be large, the difference Esols(A-) − Esolw(A-) is expected to be negligible. As such, S terms are small (T∆S for proton in water12 is only 12.1 kJ mol-1) and their difference is also expected to be small enough. Further, along a series, S is expected to be roughly a constant. Thus, with S → 0, ∆pK is going to be determined solely by Esols(H+) − Esolw(H+) which is 16.60 kJ mol-1. This energy difference is equivalent to 2.89 pKa unit which is in excellent agreement with the average ∆pK value obtained in Table 2. Thus, pKa of an AH molecule in acetonitrile will be higher than that in water. This is because water being more polar than acetonitrile facilitates greater dissociation. Since Esols(A-) − Esolw(A-), and S are likely to have positive values albeit small. For all practical purposes, ∆pK is likely to be greater than 2.89 pKa unit. Another factor that is likely to result

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in a higher value, is formation of ion pair which will decrease the molar conductance. Formation of ion pair cannot be stopped even in water, which has a rather high value of ε. The association constant of a 1:1 electrolyte in water13 is close to 3.82 mol-1 dm3. It is expected to be higher in acetonitrile as the ε of acetonitrile is significantly less than that of water. A factor that can lower the value of ∆pK is preferential solvation of AH by water compared to acetonitrile (e.g. by H-bonding). Acknowledgement S N thanks the Council of Scientific & Industrial Research, New Delhi for providing the fellowship. References 1

Ghasemi J, Nayebi S, Kubista M & Sjogreen B, Talanta, 68 (2006) 1201. 2 Kaljurand I, Rodima T, Leito I, Koppel I A & Schwesinger R, J Org Chem, 65 (2000) 6202. 3 Sooväli L, Kaljurand I, Kütt A & Leito I, Anal Chim Acta, 566 (2006) 290. 4 Sanz-Nebot V, Toro I, Benavente F & Barbosa J, J Chromatogr A, 942 (2002) 145. 5 Oh H K & Jeong J, Bull Korean Chem Soc, 22 (2001) 1123. 6 Henry B, Tekely P & Delpeuch J -J, J Am Chem Soc, 124 (2002) 2025. 7 Kolthoff I M & Chantooni M K, Jr, J Phys Chem, 72 (1968) 2270. 8 Greary W J, Coord Chem Rev, 7 (1971) 81. 9 CRC Handbook of Chemistry and Physics, edited by D R Lide, 83rd Edn (CRC Press, Florida) 2002. 10 Naskar J P & Datta D, Indian J Chem A, 44 (2005) 2202. 11 Basolo F & Pearson R G, Mechanisms of Inorganic Reactions, 2nd Edn (Wiley Eastern, New Delhi) 1973, Table 2.10. 12 Camaioui D M & Schwerdtfeger C A, J Phys Chem A, 109 (2005) 10795. 13 Datta D, Hill H A O & Nakayama H, J Electroanal Chem 324 (1992) 307.