J. Chem. SOC., Faraday Trans. I , 1982, 78, 1177-1187 Effect of Temperature on the Ionisation Constants of 2-, 3- and 4-Nitrobenzoic, Phthalic and Nicotinic Acids in Aqueous Solution BY LESLEY A. ASHTON AND JOSEPH I. BULLOCK* Cecil Davies Laboratory, Department of Chemistry, University of Surrey, Guildford GU2 5XH Received 18th May, 1981 The association constants (equivalent to pKd on the molar scale for the equilibria between hydrogen ion and the 2-, 3- and 4-nitrobenzoate, phthalate, hydrogen phthalate and nicotinate anions and the nicotinic acid zwitterion have been determined in aqueous solution at constant ionic strength from spectrophotometricdata at various temperatures between 288 and, in some cases, 473 K. 3- and 4-nitrobenzoic acids were stable to 473 K, 2-nitrobenzoic acid decomposed at 423 K and nicotinic acid at 408 K, and the absorption spectrum for the phthalic acid system was unsuitable for use above 448 K. Only one reaction, namely the protonation of the nicotinate anion [C,H,NO,]-, was isoelectric and the association constant describing the formation of the zwitterion decreased with increasing temperature.The plot of pK, against reciprocal temperature was linear within experimental error leading to temperature-invariant values of AH (exothermic) and A S with AC, = 0 for the association reaction. To 408 K, the association constant for the protonation of the zwitterion changed little in terms of the experimental errors. For 2-nitrobenzoic acid the plot of pK, against reciprocal temperature was also approximately linear. In this case the abnormally high acid strength at room temperature is caused largely by the highly endothermic nature of the association reaction and the acid becomes appreciably weaker at high temperature.For the rest the association constants (pK,) were greater at the highest temperatures employed than at 298 K which was largely caused by the high, positive entropy change for the association reaction resulting from a decrease in the dielectric constant of the bulk solvent as the temperature increased. Plots of pK, against reciprocal temperature were markedly non-linear with minima observed in some cases. These plots were analysed in terms of continually varying values of AH, A S and AC, over the temperature range although in some cases the changes in AC, were hardly significant in terms of the likely experimental errors.Previous from this laboratory has employed spectrophotometric data to study the protonation of heterocyclic nitrogen bases and, in some cases, the stability constants of iron@) complexes of the bases. The upper temperature limit was usually 473 K except where decomposition at a lower temperature occurred. An extension is to study the effect of temperature on the equilibria between the anions of organic acids and hydrogen ion. The computer program SQUAD^.^ allows the determination of association constants from spectrophotometric data alone and does not require predetermined extinction coefficients or the free hydrogen ion activity, and is thus particularly suitable for use above 373 K. Polyfunctional species can also be studied4 even if stages of the association reactions are overlapping across wide pH ranges.For ion-consuming reactions, e.g. the association of an acid anion or a zwitterion with a hydrogen ion, plots of pK, (log,, association constant) against 1/T are expected' to be non-linear and many show minima at relatively low temperatures. Continually varying values of A H and A S are expected with AC, interpreted as having a constant, non-zero value8 or varying over the temperature range9 or not reported at all1* depending on the precision of the experimental results. On the other hand, isoelectric reactions, e.g. the protonation of a neutral or the dissociation of 11771178 EFFECT OF TEMPERATURE ON IONISATION CONSTANTS a zwitterion, may give near-linear plots of ply, against 1/T with the extent of association decreasing with temperature in either case.EXPERIMENTAL The acids were used as supplied or recrystallised from water depending on the analytical purity of the materials supplied. The following analytical figures refer to the acids used in our experiments. Found: 2-nitrobenzoic acid, C 50.1, H 2.8, N 8.3%; 3-nitrobenzoic acid, C 50.4, H 2.9, N 8.4%; 4-nitrobenzoic acid, C 50.2, H 2.9, N 8.1 %; C,H,N04 requires: C 50.3, H 3.0, N 8.4%. Phthalic acid, found: C 57.4, H 3.4%; C,H,04 requires: C 57.8, H 3.6%. Nicotinic acid, found: C 58.5, H 4.0, N 11.5%; C,H,NO, requires: C 58.5, H 4.1, N 11.4%. Other materials were as described previo~sly.~ The spectrophotometers, high- and low-temperature cells, fumace4p l1 and the computer program SQUAD were used as b e f ~ r e .~ A summary of experimental conditions is given in table 1. The upper temperature limits were : 473 K, 3- and 4-nitrobenzoic acids, set4 by the experimental design; 423 K, 2-nitrobenzoic acid TABLE 1 .--SUMMARY OF EXPERIMENTAL CONDITIONS total total organic ionisable compounda no. of no. of range r acid hydrogen ion no. solutions wavelengths /nm /mol dm-3 mol dm-3 /mol dm-3 I 7 8 240-310 0.01 0.743 5.328 x 7.427 x I1 7 8 250-320 0.01 1.301 9.646 x I11 7 7 250-310 0.01 1.499 9.536 x 1.499 x IV 9 11 270-290 0.02 5.994 1.697 x 2.028 x V 10 7 244-268 0.05 2.046 1.553 x 1.301 x 10-4 1.044 x 10-4 a I, 4-nitrobenzoic acid; 11, 3-nitrobenzoic acid; 111, 2-nitrobenzoic acid; IV, phthalic acid; V, nicotinic acid.and 408 K, nicotinic acid, decomposition noted by observation of absorbance drift with time at higher temperatures; 448 K, phthalic acid, observed absorption envelope narrowed and flattened above this temperature making the spectrum unsuitable for use. The ionic strengths (table 1) were adjusted to constant values with AnalaR sodium chloride. With the nitrobenzoic acids series of solutions at fixed organic acid concentration but with varying hydrogen ion concentration (adjusted with standardised, AnalaR hydrochloric acid) were prepared. The absorbance of each solution was measured at various wavelengths at each temperature (table 1) and allowance made for the absorbance of the water-filled cell, which was large at high temperature because the cell windows are made from ~apphire.~ The procedures for phthalic and nicotinic acids were the same except that standardised, AnalaR sodium hydroxide solution was added to some solutions to generate high concentrations of the phthalate dianion or nicotinate anion.It was necessary to use more solutions and to measure them at a greater number of wavelengths for the dibasic than for the monobasic acids as the association reactions overlap over an appreciable part of the total acid concentration employed. The SQUAD input data consisted of the absorbance-wavelength matrix, the total organic acid concentration, the total conckntration of ionisable hydrogen ion, the expected species and an estimate of the equilibrium constant(s). No other information is required and a set of absorbance data can be readily obtained from a set of solutions prepared within the reagent conceqtrations outlined in table 1.L. A.ASHTON AND J. I. BULLOCK 1179 RESULTS AND DISCUSSION As b e f ~ r e l - ~ ~ l ~ the molar concentration scale was used throughout and it was assumed that the solutions expanded as would pure water.2*13 The density of water at each temperature was incorporated into the computer program. Constants were calculated for the association reactions : (i) for the nitrobenzoic acids, H+ + L- + HL loglOKF = pK, (ii) for phthalic acid, H+ + L2- HL- log,,K~ = pK,, and 2H+ + L2- e H2L log,,#F (iii) for nicotinic acid, H+ + L-" HL* log,,K~ = pK,, and 2H+ + L- e H2L+ logl,$? from which where HL* is the zwitterion. These values at the stated ionic strengths are listed in table 2.The uncertainties in parentheses were derived from the degree of fit between the experimental and computed spectra, and the true experimental errors must be greater than these. The fit was best for 4-nitrobenzoic acid because the observed absorption envelope (table 1) was well-separated from the tail of a much more intense short-wavelength absorption and for 3- and 2-nitrobenzoic acids the envelope shifted progressively to shorter wavelength so that for 2-nitrobenzoic acid there was appreciable mixing of the short- and longer-wavelength absorptions. TABLE ACIDITY CONSTANTS FOR THE ACIDS AT VARIOUS TEMPERATURES (a) 4-nitrobenzoic acid, (b) 3-nitrobenzoic acid (c) 2-nitrobenzoic acid, Z = 0.01 mol dm-3 Z = 0.01 mol dm-a Z = 0.01 mol dm-s 288 298 312 323 348 373 398 423 435 448 460 473 3.32 (1) 3.41 288 3.31 (1) 3.40 298 3.31 (1) 3.41 305 3.33 (0) 3.43 323 3.38 (1) 3.48 348 3.47(1) 3.58 373 3.55 (1) 3.67 398 3.68 (2) 3.82 423 3.75(2) 3.89 435 3.80 (7) 3.95 460 3.86 (3) 4.02 473 4.01 (1) 4.18 - 3.44(1) 3.53 288 3.40(2) 3.49 293 3.39(1) 3.48 298 3.42 (0) 3.52 305 3.43 (2) 3.53 323 3.48 (5) 3.59 335 3.50(5) 3.62 348 3.62 (4) 3.75 360 3.76 (1) 3.90 368 3.84(5) 4.00 373 3.99 ( 5 ) 4.16 398 - 423 - 1.93 (5) 2.02 2.05 (6) 2.14 2.16 (2) 2.25 2.28 (3) 2.38 2.39 (3) 2.49 2.55 (6) 2.65 2.61 (4) 2.71 2.67(1) 2.78 2.72 ( 5 ) 2.83 2.85 (6) 2.97 3.00(12) 3.13 2.11 (1) 2.201180 EFFECT OF TEMPERATURE O N IONISATION CONSTANTS TABLE 2.-continued (d) phthalic acid, I = 0.02 moldm-3 temp/K log,,KP PGl P G 288 298 305 323 348 373 398 423 435 448 460 4.65 (5) 4.69 (5) 4.65 (5) 4.76 (6) 4.91 (8) 5.15 (11) 5.25 (5) 5.41 (8) 5.50 (10) 6.56 (29) 5.55 (8) 7.48 (3) 7.50 (8) 7.40 (5) 7.64 (6) 7.83 (6) 8.10 (9) 8.36 (4) 8.59 (5) 8.70 (8) 8.77 (7) 9.85 (28) 5.13 5.17 5.14 5.28 5.46 5.75 5.90 6.13 6.25 6.35 2.95 2.93 2.87 3.00 3.05 3.09 3.27 3.36 3.38 3.42 (e) nicotinic acid, Z = 0.05 mol dm-3 288 298 303 318 333 348 363 378 393 408 4.78 (1) 4.72 (2) 4.68 (1) 4.63 (2) 4.57 (1) 4.47 (2) 4.39 (3) 4.24 (10) 4.14 (5) 4.10 (8) 6.90 (5) 6.71 (7) 6.67 (4) 6.60 (6) 6.58 (5) 6.45 (4) 6.35 (5) 6.24 (1 7) 6.17 (13) 6.22 (19) 4.96 4.88 4.85 4.80 4.75 4.66 4.58 4.45 4.36 4.33 2.12 1.99 1.99 1.97 2.01 1.98 1.96 2.00 2.03 2.12 For both phthalic and nicotinic acids it is possible to determine the equilibrium constants for the successive protonation reactions separately by working at very low or very high pH.However, as the association constants are temperature-dependent, at each temperature it would be necessary to check that the total acidity employed was sufficient to effectively remove the unwanted form. Using the program SQUAD this is unnecessary and the same total acidities and therefore the same set of solutions can be used for the entire temperature range. This simplifies the experimental procedures and is particularly useful above 373 K. Log KF and log /3F are correlated, in the computational method and for this reason overlapping pK, values for polybasic acids will always be less well-defined than those for monobasic acids assuming other factors to be comparable.In addition, the absorption envelope for phthalic acid was relatively narrow and small absorbance changes were observed. Above 448 K, the fit became very poor (table 2). For nicotinic acid, three forms are found across the acidity range, namely the zwitterion, [C,H,NO,] * , the protonated cation, [C,H,NO,]+, and the deprotonated anion, [C,H,NO,]-. At 298 K all three species coexisted to an appreciable extent in five of the ten experimental solutions. As with phthalic acid the observed absorption envelope was narrow and only small absorption changes were noted. Mean ionic activity coefficients calculated from the Davies equation1* (substituting the appropriate Debye-Huckel coefficient at temperatures other than 298 K) wereL. A.ASHTON A N D J. I. BULLOCK 1181 applied with the activity coefficients of the neutral or zwitterionic forms put equal to unity to give the so-called thermodynamic constants pKL shown in table 2. No correction was made to pKa2 for nicotinic acid on the assumptions that the activity coefficient of the zwitterion15 is equal to unity and that of the nicotinate cation is equal to that of the hydrogen ion at a given ionic strength. The contributions of the ions derived from the organic acids to the mean ionic strength were calculated using approximate pK, values at each temperature. The differences in ionic strength found when the refined values of pK, were used had a negligible effect. It was not possible to vary the ionic strength over a wide range by changing the concentration of the organic acids because the concentration required is largely determined by the extinction coefficients of the acid and its anion.However, by adding an inert electrolyte (in our case sodium chloride) it was possible to increase the ionic strength. This was done for 4-nitrobenzoic acid at 298 and 423 K (table 3). The values of pK, decreased with increasing ionic strength as expected, and on applying Davies activity coefficients14 there was a reasonable constancy when the possible sources of error were considered. TABLE EFFECT OF IONIC STRENGTH ON THE DISSOCIATION OF 4-NITROBENZOIC ACID 298 K 423 K I/mol dm-3 0.01 0.05 0.10 0.50 0.01 0.05 0.10 0.50 log,oKF 3.31 3.30 3.18 3.17 3.68 3.64 3.55 3.41 PK', 3.40 3.47 3.39 3.43 3.83 3.92 3.90 3.85 The values of pKi for all the acids compare reasonably well with the critical values of Martell and Smithls for 298 K and I = 0.These are: 4-nitrobenzoic acid 3.442 f 0.001 3-nitrobenzoic acid 3.449 0.001 2-nitrobenzoic acid 2.179 f 0.006 phthalic acid pK;, 5.408 pKL2 2.950 nicotinic acid pKL, 4.81 0.03 pKa2 2.05 _+ 0.03 The quoted deviations referle to agreement between different workers rather than to the significance of an individual measurement. Of the nitrobenzoic acids the 2-nitro-dekivative is much the strongest at 298 K and as the temperature is raised above ca. 320 K all of them become appreciably weaker. To 423 K, pK; for 2-nitrobenzoic acid decreases by an order of magnitude whereas for 3- and 4-nitrobenzoic acids the decreases to that temperature are much smaller.As the temperature is raised presumably the increasingly poor solvation of the proton more nearly offsets the steric hindrance in 2-nitrobenzoic acid. Phthalic acid (pKi,) is also comparatively strong. In the solid state" both carboxylic acid groups are inclined at 45.8O to the plane of the benzene ring, but in the acid anion1* (pH,]+ salt) the -COOH group is inclined at 26' and the -COO- group at 74O to the ring. As might be expected, pK;, for phthalic acid decreases with increasing temperature to a much greater extent than does pK,,. The second stage of ionisation of phthalic acid1182 EFFECT OF TEMPERATURE O N IONISATION CONSTANTS 4.2 4 .O lo3 KIT FIG. 1.-Variation of pG with 1/T. Curve A, 4-nitrobenzoic acid, left-hand scale; curve B, 3-nitrobenzoic acid, right-hand scale.(pK,,) is highly ionic-strength dependent.1° Lumme and KarilO found pK,, = 5.358 (298 K) from a least-squares treatment of the experimental pK, values and two expressions for activity coefficients with Z in the range 0.2668-2.0150 mol dm-3. At Z = 0.0570 mol dm-3 and 298 K they found pK,, = 4.963 which is higher than our value at Z = 0.02 mol dm-3. DERIVED THERMODYNAMIC QUANTITIES These were determined by the temperature variation method (fig. 1-3). As stated earlier, the protonation of the nicotinate anion is an isoelectric reaction on the assumption of the formation of the zwitterion. Earlier workla supports this and our plot of pK,, against 1 / T was linear. Temperature-invariant values of AH and A S were calculated (table 4) with the assumption that ACp = 0.The second stage! i.e. the protonation of the zwitterion, is non-isoelectric so that a non-linear plot of pKaz against 1/T might be expected. However, the equilibrium constant (table 2) changed little with temperature in terms of the degree of fit. This meant that AH, x 0 in terms of the experimental error. According to Christensen and co-workersZo AH, is ionic-strength independent in the range Z = 0.01 -0.09 mol dm-3 at 298 K which would seem to support our view that corrections to pKaz for activity coefficients need not be made. The critical valuesls for nicotinic acid are: 298 K, Z = 0, AH in kJ mol-l, A S in J K-l mol-l AH1=-11.7&1; AS1=5O AH, = - 3.3; There is good agreement with respect to AH, and AS, (table 3). ASz = 29.L.A. ASHTON AND J. I. BULLOCK 1183 5 . 0 1 4 I 1 I I I 1 I I 2.3 2.7 3 1 3.5 lo3 KIT FIG. 2. 3.0 2 . 8 - m % 2.6 2.4 2 . 2 2 .o I 1 I I 1 I I 2.4 2.8 3.2 3.6 103 KIT FIG. 3. FIG. 2.-Variation of pkf, with 1/T for phthalic acid. Curve (a) p&; curve (b) pkf,,. FIG. 3.-Variation of p G with 1/T for 2-nitrobenzoic acid: 0, present work; 0, Schaller, ref. (24). For 2-nitrobenzoic acid a plot of pKa against 1/T (fig. 3) was approximately linear so that a temperature-invariant value of AH was calculated from a least-squares treatment of this plot on the assumption that ACp = 0. AH and the calculated, constant value of AS are reported in table 4. Figures in' parentheses are derived from the standard deviation of fit for the pKa against 1/T plot. The enthalpy change is markedly positive for the association reaction and is the main cause of the abnormally high acid strength [see table 4, parts (u)-(c)].The solid-state structure of the acid reveals that the planes containing the carboxylic acid and nitro-groups are both inclined2' at high angles with respect to the plane of the benzene ring (24.1O and 54.3O, respectively) compared with the angles for the 3-nitro- (means 3O and 13S0, respectively22) and 4-nitro- (1.6' and 13.8O, re~pectively~~) benzoic acids. Presumably steric hindrance is reduced in the 2-nitrobenzoate anion although the structure is unknown. Whilst it is always possible to analyse data in terms of a constant, non-zero value of ACp [ref. (8) quotes 99.2 J K-l mol-'1 the possible sources of error hardly justify this in our case.The critical values16 for 2-nitrobenzoic acid are: 298 K, I = 0, AH = 14.1 kJ mol-l, AS = 89.1 J K-l mol-l, so that only fair agreement was found. These were determined by Everett and Wynne-Jonesa based on conductivity data of Schalleri4 reported in 1898. In order to determine AGO means of pKa at various dilutions were takenS8 However, the data24 show clear evidence of small but regular increases in pKa with dilution in the 2-nitrobenzoic acid range 7.81 x 10-3-9.77 x mol dm-3. For the most dilute solution pKa (298 K) = 2.19 and pKa (372 K) = 2.81; we found that the1184 EFFECT OF TEMPERATURE ON IONISATION CONSTANTS TABLE 4.-sELECTED THERMODYNAMIC QUANTITIES FOR THE ACIDSa* ' A H A S ACP temp/K /kJ mol-l /J K-l mol-l /J K-l mol-l 288 298b 312 323 348 373 398 423 435 448 460 473 288 298b 305 323 348 373 398 423 435 460 473 (a) 4-nitrobenzoic acid - 2.2 58 1.1 69 2.8 74 6.7 86 10.9 98 15.4 109 20.2 121 22.6 126 25.3 132 27.8 138 30.7 144 (b) 3-nitrobenzoic acid - 5.7 48 -3.1 57 -0.1 66 4.2 79 8.9 92 13.9 105 19.3 118 22.0 124 27.8 137 30.9 144 -0.8 (1 .O) 63 (3) -4.2 (1.1) 53 (9) 134 139 (1 1) 145 151 162 174 186 197 203 209 214 221 (27) 150 155 (43) 159 168 181 194 207 220 (61) 226 239 246 (c) 2-nitrobenzoic acid A H = 18.4 (0.5) kJ mol-l; A S = 103 (6) J K-l mol-l (d) phthalic acid 288 298b 305 323 348 373 398 423 435 448 8.3 9.3 (2.0) 10.0 11.9 14.7 17.7 20.9 24.3 26.0 27.9 ~ 119 123 (19) 125 131 139 148 156 164 168 173L. A.ASHTON AND J. I. BULLOCK 1185 TABLE 4.-continued (di) phthalic acid temp/K /kJ mol-l /J K-l mol-l AH2 AS2 288 29gb 305 323 348 373 398 423 435 448 2.6 3.3 (2.0) 3.8 5.2 7.2 9.4 11.8 14.3 15.6 17.0 65 67 (19) 69 73 79 85 91 98 100 104 (e) nicotinic acid (i) AH, = - 11.8 (0.7) kJ mol-l; ASl = 54 (3) J K-l mol-I (ii) 298 K: AH, x 0; AS, x 38 J K-l mol-l a Calculations based on pK', with AG = - 2.3026 RT pK', except AH, and AS, for nicotinic acid.Estimated errors in parentheses (see text). plot of PKa against reciprocal temperature was approximately linear. Our (pKa) results and those of S ~ h a l l e r ~ ~ are plotted together in fig. 3. Schaller did not employ solutions at constant ionic strength, but at the lowest acid concentLation the activity coefficients must be close to unity. For the rest, plots of pKa and (pK,) against reciprocal temperature (fig.1 and 2) were non-linear and were fitted to the polynomials shown below: 4-nitrobenzoic acid 2.3026 R ply: = 2.150 x lo4 T'-76.41+0.2331 T 3-nitrobenzoic acid phthalic acid 2.3026 R pKL = 2.725 x lo4 T'- 101.7+0.2600 T 2.3026 R pKal = 5.437 x lo3 T1+23.69+0.1662 T 2.3026 R pKa2 = 7.534 x lo3 T1-5.681 +0.1220 T from which values of AH, AS and ACp can be readily calculatedz5 at each temperature. The error in ACp is particularly large using this procedure25 with values of pKa derived from spectrophotometric data. In the present work, pKa values are best defined for 4- and 3-nitrobenzoic acids (see above) and ACp as well as AH and AS at each temperature are included in table 4. The standard deviations in these quantities may be estimated using a procedure outlined by King25 for equally spaced temperature intervals.Previous application^^^ used a mean temperature at or close to 298 K, where the deviations in A H and AS would be least, and therefore a very limited temperature range. In our experiments the mean temperature was much higher than 298 K so that at 298 K the calculated standard deviations in A H and AS are at their greatest; the deviation in ACp would increase with increasing temperature. Another disadvantage is that the method does not allow the low-temperature data, which were the most 39 FAR 11186 EFFECT OF TEMPERATURE O N IONISATION CONSTANTS precise, to be favourably weighted in the analysis. The method was applied to eight temperatures for 4-nitrobenzoic acid with pKa f 0.02 and six temperatures for 3-nitrobenzoic acid (pKa & 0.04) separated by 25 K intervals to give the results shown in parentheses in table 4.For phthalic acid (pKi&-O.10) seven temperatures were available but A H and A S (table 4) are less well defined because of the greater uncertainties introduced in pKa. Values of ACp are not included. The critical valuesl8 are : 298 K, Z = 0, A H in kJ mol-l, A S in J K-l mol-l; 4-nitrobenzoic acid A H = - 1.80f 1.3, A S = 59.8 3-nitrobenzoic acid A H = - 1.55 0.2, A S = 61.1 AH, = 2.68+0.04, AS, = 65.3. phthalic acid AHl = 2.09+0.17, AS, = 110 In general, the critical values were obtained from more precise measurements of PKa than ours but from very much smaller temperature ranges. For 3-nitrobenzoic acid A H was obtained directly26 from calorimetry but polynomial fits for pKL and T were also used2' as was the case28 for 4-nitrobenzoic acid.For phthalic acid it was foundlo that pKa = a+ bT. There is reasonably good agreement between our results and the critical values at 298 K except for A H for 3-nitrobenzoic acid and AH, for phthalic acid. The disagreement for phthalic acid arises from our apparently low value of pXal. A H is endothermic for 2-nitrobenzoic acid and for the rest becomes more endothermic for the association reaction as the temperature increases so that the decrease in acid strength is controlled by changes in A S which is always positive and becomes increasingly so as the temperature is raised (constant, positive A S for 2-nitrobenzoic acid). These findings are in keeping with the crude suggesting that AG is in a linear relationship with 1/e (where E is the bulk dielectric constant of AG = A+B/E water) leading26 to a proportionality between AG and A S and that the increase in A S is mainly a result of environmental effects largely concerned with the increasingly poor solvation of the proton as the temperature increases.At temperatures above 300 K plots of AG against l/e were approximately linear for 4- and 3-nitrobenzoic acids but curvature was observed above 400 K for both stages of ionisation of phthalic acid. In the range 298-473 K, E The uncertainty in the absorbance measurements is smaller below 373 K than above because of the reliabilities of the spectrophotometers used. For 4-nitrobenzoic acid, which was the best defined experimentally, the pKa values obtained from the SP 3000 used at low temperatures (288-348 K) were fitted to a polynomial of the type shown above and the equation used to predict pK, at 473 K. A value of 4.01 was obtained which was the same as the experimental quantity. Our results suggest that precise determinations of pKa over a limited, low-temperature range ( e g .278-333 K) may well be useful in predicting acidities to temperatures at least 100 K greater. For example, the best available data28 for 4-nitrobenzoic acid were fitted to give the results in table 5. At each temperature these results are indistinguishable in terms of the likely experimental errors. 4-Nitrobenzoic acid has28 a minimum value of pKa near 300 K and the data from ref. (28) consist of six determinations in the range 288-313 K separated by 5 K temperature intervals.For phthalic acid, the best literature values1* consist of four measurements in the range 288-308 K but in this case plots of pKa against T were linear for both stages 4 from 78.36 to 34.59.L. A. ASHTON A N D J. I. BULLOCK TABLE 5.-mDICTION OF VALUES FOR 4-NITROBENZOIC ACID 1187 AH AS T/K PK', /kJ mol -l /J K-l mol-l 473 4.14b 4.18' 28Sb 30.7' 139.7b 144' 298 3.441" 3.41' -0.51" -0.8' 64.2" 63' " Ref. (27); predicted from low-temperature data of ref. (27); ' this work. of ionisation. In the absence of a minimum value for pKi or marked curvature in the low-temperature range it is unlikely that the data will be of much value in pre- dicting high-temperature results.Financial support from the Central Electricity Generating Board and the S.R.C. is gratefully acknowledged. R. D. Alexander, D. H. Buisson, A. W. L. Dudeney and R. J. Irving, J. Chem. Soc., Faraday Trans. I , 1978, 74, 1081. D. H. Buisson and R. J. Irving, J. Chem. Soc., Faraday Trans. I , 1977, 73, 157. R. D. Alexander, A. W. L. Dudeney and R. J. Irving, J. Chem. SOC., Faraday Trans. 1,1978,74,1075. J. I. Bullock and P. W. G. Simpson, J. Chem. Soc., Faraday Trans. I , 1981, 77, 1993. D. J. Leggett and W. A. E. McBryde, Talanta, 1975,22, 781. Acetic acid, for example, H. S. Harned and R. W. Ehlers, J. Am. Chem. Soc., 1933, 55, 652. D. H. Everett and W. F. K. Wynne-Jones, Trans. Faraday Soc., 1939, 35, 1380. (I D. J. Leggett and W. A. E. McBryde, Anal. Chem., 1975, 47, 1065. @ F. S. Feates and D. J. G. Ives, J. Chem. Soc., 1956, 2798. lo P. Lumme and E. Kari, Acta Chem. Scand., Ser. A, 1975,29, 1 17. l1 R. D. Alexander, A. W. L. Dudeney and R. J. Irving, J. Phys. E, 1980, 13, 22. l2 A. S. Quist and W. L. Marshall, J. Phys. Chem., 1968, 72, 684. l3 G. C. Kennedy, W. L. Knight and W. T. Holser, Am. J. Sci., 1958, 256, 590. l4 C. W. Davies, Ion Association (Butterworths, London, 1962), p. 41. B. P. Kelley and T. H. Lilley, J. Chem. Soc., Faraday Trans. I , 1978, 74, 2779. l6 R. M. Smith and A. E. Martell, Critical Stability Constants (Plenum Press, London, 1976), vol. 1 and 3. l7 W. Nowacki and H. Jaggi, Z. Kristallogr., 1957, 109, 272. R. A. Smith, Acta Crystallogr., Sect. B, 1975, 31, 2508. R. W. Green and H. K. Tong, J. Am. Chem. Soc., 1956,78,4896. 2o J. J. Christensen, R. M. Izatt, D. P. Wrathall and L. D. Hansen, J. Chem. SOC. A, 1969, 1212. 21 S. S. Tavale and L. M. Pant, Acta Crystallogr., Sect. B, 1973, 29, 2979. 22 N. N. Dhaneshwar, S. S. Tavale and L. M . Pant, Acta Crystallogr., Sect. B, 1974, 30, 583. 23 S. S. Tavale and L. M. Pant, Acta Crystallogr., Sect. B, 1971, 27, 1479. 24 R. Schaller, Z. Phys. Chem., 1898, 25, 497. 2b E. J. King, Aci6Base Equilibria, International Encyclopedia of Physical Chemistry and Chemical Physics (Pergamon, Oxford, 1965), topic 15, vol. 4, chap. 8. T. Matsui, H. C. KO and L. G. Hepler, Can. J. Chem., 1974, 52, 2906. 27 P. D. Bolton, K. A. Fleming and F. M . Hall, J. Am. Chem. Soc., 1972,94, 1033. 28 J. M. Wilson, N. E. Gore, J. E. Sawbridge and F. Cardenas-Cruz, J. Chem. Soc. B, 1967. 852. 2@ (a) B. B. Owen, R. C. Miller, C. E. Milner and H. L. Cogan, J. Phys. Chem., 1961, 65, 2065; (b) G. C. Akerlof and H. I. Oshry, J. Am. Chem. Soc., 1950,72, 2844. (PAPER 1/800) 39-2