J. Chem. SOC., Faraduj Trans. I , 1982, 78, 313-321 Effect of Temperature on the Limiting Excess Volumes of Amines in Aqueous Solution BY MURLIDHAR V. KAULGUD," VIJAY S. BHAGDE A N D ANJALI SHRIVASTAVA Department of Chemistry, Nagpur University, Nagpur 440 010, India Received 29th July, 1980 Limiting partial molal volumes (v:) from measurements of density in the concentration range 0.002-0.1 mol dm-, for aqueous solutions of NH,, MeNH,, EtNH,, n-PrNH,, N-BuNH,, t-BuNH,, (Me),NH and (Me,)N have been obtained at 5, 15 and 25 "C. The method of Cabani and coworkers for applying hydrolysis corrections in dilute solutions of amines had to be modified slightly in order to make it applicable to the lower concentration range used in this work. It is shown that the modified method applies equally well to both the low (0.002-0.1 mol drn-,) and slightly higher (0.1-0.3 mol dm-3) concentration ranges, yielding identical results.The present results show that limiting excess volumes become less negative with increasing temperature for lower amines, but higher amines show an opposite trend. Comparison of volumetric properties of amines with those of alcohols indicates that in monofunctional solutes the functional group plays an important role in solute-solvent interaction. It is found in particular that the -NH, group tends to offset the structure promoted by the hydrophobic group in amines. Volumetric and compressibility behaviour at 20 "C of some straight chain, mono- and di-alkylamines has been previously1* , reported from this laboratory and the results discussed from the point of view of solute-solvent interaction.The limiting values were obtained by extrapolation from higher concentrations (> 0.3 mol dm-3) where the hydrolysis of amines was negligible. The results obtained indicated similarity to the behaviour of alcohols and hence amines were also said to behave as hydrophobic structure formers. Cabani et ~ 1 . ~ have studied the volumetric behaviour of amines at 25 O C in a low concentration range (but > 0.002 mol dm-3). A special correction procedure was developed4 by them to ascertain the true value of the limiting partial volume of the amine molecule from that observed by subtracting the contribution of the ions produced due to hydrolysis. Though various physicochemical properties of solutions of alcohols and amines show similarity, there are still subtle differences.Thus alcohols produce a rise in the temperature of maximum density (t.m.d.) of water while amines lower it.576 The characteristic constant ' a ' in the expression for the structural contribution of the solute to the change in t.m.d. of water A8,,, = ax+5x2 (x = mole fraction of the solute), which is an index of its structure strengthening ability, is larger for alcohols than for amines (for n-BuOH a = 237 OC, and for n-BuNH, a = 173 "C). Similarly, ACF, AGP and ASP7q8 values for amines are much less than for the corresponding alcohols. Further, solid clathrates have been isolated for some amine~,~,lO but not yet for alcohols. The polar group thus seems to be playing a role in this case.The volumetric properties of alcohols at different temperatures are well documented. Similar studies in amines especially at low temperatures are lacking, probably on account of the difficulties associated with the correction for hydrolysis. It was hence thought worthwhile to evaluate the true limiting excess volumes of amines at 5, 15 and 25 OC and see how they compare with those of alcohols. 313314 EXCESS VOLUMES OF AMINES EXPERIMENTAL The differential float balance method described and used earlier" for measurements at 25 "C for solid solutes in aqueous solution was modified in the present work as follows: A single float method using a Sartorius model 2474 single pan semi-microbalance having facility to weight below the pan was adopted. The glass float weighted with mercury (volume z 170 cm3) was suspended by a thin nylon thread into distilled water kept in a stainless-steel cylinder.The steel cylinder in turn was kept in a well-insulated and covered constant-temperature bath (capacity 30 dm3) whose temperature was regulated by circulating liquid from a MK-70 cryostat through large copper coils kept in the bath. Replacement of the glass cylinders of the earlier work" by the stainless-steel cylinder in this work meant faster thermal equilibration between solution and bath and reduction in experimentation time, leading to better stability of the bath temperature around the nominal value. n-Propylamine (Riedel-De-Haen), n-butylamine (Merck, Germany) and t-butylamine (Fluka, pract.), were dried over KOH for ca.48 h, distilled twice and the miadle fraction was used to prepare stock solutions. Ammonia (local grade), methylamine (40%), ethylamine (70 %), dimethylamine (40 %) and trimethylamine (50 %) (all Riedel-De-Haen) solutions were slightly warmed and the amine vapours were led into doubly distilled water to obtain a stock solution. Dilutions were made in situ and the concentration of the solution was determined by volumetric titration with standard AnalaR HCl using a suitable indicator. To begin with water was degassed by passing nitrogen and to avoid carbonation a layer of nitrogen gas was maintained over the solution throughout the experiment. Amine solutions of increasing concentration were obtained by adding successively 10 cm3 of concentrated amine solution to the water in the steel jar and estimating the concentration of the resulting solution by titration with standard hydrochloric acid solution by withdrawing two aliquots of 5 cm3 each.Addition of 10 cm3 of solution and subsequent withdrawal of the same for estimation each time ensured that the float dipped into the water at the same level and the small errors arising due to additional nylon thread dipping in the event of successive addition could be avoided. The volume of the plunger was determined accurately first by weighing it in air and then in distilled water held at 5, 15 and 25 OC. Measurement of the density of a given amine solution were obtained in 2 or 3 different runs, each run comprising of 5 or 6 different concentrations. The difference in the weight of the plunger in water and solution at the lowest concentration was ca.10-15 mg yielding a difference in density of 1 unit in the fifth decimal place. This coupled with the readability of the balance to 0.01 mg results in an accuracy of ca. 0.1 ppm in the measured density value. The temperature fluctuation as read on the Beckman thermometer was kO.002 O C . From the measured density, apparent molal volumes were first calculated and these were subjected to the hydrolysis correction as described below. METHOD OF CORRECTION FOR HYDROLYSIS Cabani et al.4 adopted the following procedure for hydrolysis correction. They assume that the hydrolysis of the amines (B) in aqueous solution at a concentration c takes place through a hypothetical neutral aquo-amine species BHzO as: (1-a)c ac ac where a is the degree of hydrolysis $v = z-(;- A4 I)-.I000 The fictitious apparent molal volumes &!'s, which are calculated by introducing in eqn (2) the molecular weight of the hypothetical species BHzO, can then be considered to be made up of proportionate contributions of #V(BH,o), &(BH+) and &(OH-), that is: hbSd = (1 -a) 4v(BHzo) +a(&(BH+) +&(OH-))= (1 -a) dV(BH,o) +a&(BH+OH-) - (3)M. V. KAULGUD, V. S. BHAGDE A N D A. SHRIVASTAVA 315 Since BHZO is a neutral species, the value of &(RH,o) can be assumed to depend linearly on the (4) concentration as: where &(BHro) is the value of &(BE,zo) at infinite dilution and h is the slope factor. BH+ and OH-, the hydrolytic products, were assumed to form partners of a strong electrolyte.Hence the value of &,(BH+OH ) at any concentration was found by using the modified Debye-Hiickel theory as applied to the apparent volume of 1 : 1 electrolyte: 4V(BH,<)) = -a) $,,, - 1.8682/~ = 4; + h+c &(BH+OH-) = #;(BH+oH-) + I .868y'(ac) + h+ca. ( 5 ) (5') where h+ is called the deviation constant,12 or in the present case Introducing eqn (4) and (5') in eqn (3) one gets: &bsd = (1 - a)&(BHno) + hc( 1 - + 4;(BH+oH-) + 1.8682/(ac) + h+a2c. On rearranging and dividing both sides by (1 -a) one obtains: where K; is thermodynamic hydrolysis constant and 4; represents the numerator of the 1.h.s. of eqn (6). The a values at the actual ionic strength were calculated by an iterative procedure using the known values of the thermodynamic hydrolysis constant K z and molal activity coefficient values given by the Debye-Huckel limiting law.The term &BH+oH- at 25 O C was calculated using values of &(,,,+,,-, = 16.61 cm3 mol-l and 4",,,,+,,-, = 4.60 cm3 mol-l taken from literature, while the values of &(BH+CI-) were experimentally determined. For each amine considered and for each concentration the term K z h+ is constant and negligible. Hence &(BH,o) is determined as an intercept by extrapolation of the linear plots of d:/( 1 -a) against (1 -a) c to zero concentration. The limiting partial molal volume of free amine $"VcB, is then calculated by subtracting the molar volume of pure water from &(BH,o). But if the above method is applied to our data for n-propylamine at 25 "C and in the low-concentration range, the points in the plot of &/( 1 - a) against (1 - a) cdo not lie on a straight line as shown in fig. 1 (a).Such non-linear trends are also observed for curves at 5 and 15 O C , in the lower concentration range. Evaluation of limiting volumes by use of eqn (7) is thus difficult, as unequivocal extrapolation to zero concentration cannot be made. Similar difficulty was experienced in the previous work from this laboratory while evaluating true limiting partial molal compressibilities from measurements in dilute aqueous amine s01utions.l~ Kaulgud et al. while deriving their equations for hydrolysis correction for compressibilities on the same lines as Cabani et al. tor volume, slightly modified their equation so as to yield linear extrapolations.We felt that a similar procedure could be adopted to handle density data at lower concentrations to arrive at q5;(B) unambiguously. By multiplying both sides of eqn (7) by (1 -a)c and neglecting as before the term K z h+ one gets: 4;c = (1 - ~ ) C [ ~ ; ( B H ~ O ) + ( l - ~ ) C h l . (8) Eqn (8) shows that provided the solute-solute interaction term (1 -a) ch in the square bracket is negligible, one should get a straight line passing through origin if 4; c is plotted against (1 -a) c with &(,,, o) as slope. In order to see if this is so, we have plotted in fig. l(6) points showing 4: c as a function of (1 -a) c for n-propylamine at 25 OC (full circles). The a values were evaluated by the same iterative method adopted by Cabani mentioned above.The PKb values needed for this calculation were taken from the 1iterat~re.l~ It can be seen that all the points lie on a straight line passing through the origin. Moreover, the true limiting volume of the unhydrolysed n-propylamine, 74.18 cm3, obtained by subtracting the molar volume of pure water from the slope of this straight line, agrees very well with the value 74.12 obtained by316 EXCESS VOLUMES OF AMINES ii *> 8 16- 4 12 -3 8 - 2 I I I I I I I I , 0 LO 80 120 160 ( 1 -a) c~ 103 FIG. 1 .-(u) Plot of #;/( 1 -a) against (1 -a) c for n-propylamine at 25 O C . [The scale for abscissae is same as the inner scale in (b).] (6) Plots of 4; c against (1 -a) c for n-propylamine at 25 O C . Our data (@); inner scale for ordinate and abscissae).Cabani's data (0); (outer scale for ordinate and abscissae) (see text). Cabani et al.3 by applying eqn (7) to their density measurements. To further verify if (1 -a) ch remains negligible at higher concentrations, we have applied eqn (8) to Cabani's density data* for n-propylamine at 25 "C in the concentration range up to 0.3 mol dmP3. These points are plotted in fig. 1 (b) (open circles), with a four-fold contraction in both the abscissa and ordinate. These points are seen to lie on the same straight line as ours, indicating the same value of slope and consequently the same value for d",,,,. This method applied to Cabani's density data for MeNH,, EtNH, and n-BuNH, at 25 OC at higher concentration (up to 0.3 mol dm-3) also showed good straight lines and yielded an almost identical value for d",,,, as that found by Cabani.3 These facts show the validity of eqn (8) at higher concentrations.Similar straight lines passing through the origin were obtained for ammonia and other amines handled in this work at 25 OC and our values agree with Cabani's values in all cases (table 1). We have plotted 4;c against (1 - a ) c in fig. 2 for ethylamine at 5, 15 and 25 OC and in fig. 3 for ammonia, methyl-, n-propyl-, dimethyl- and n-butyl-amine at 5 OC, to indicate the applicability of eqn (8) at lower temperatures. Though the straight line plots at 15 "C are not shown, they are all found to be so. Values of limiting partial molar volume thus evaluated are given in table 1. The evaluation of the slope was carried out in all the cases by fitting the points into a straight line by the method of least squares.The excess molar volumes at infinite dilution v:E were calculated as = Vf- V: with F: = 4;. The molar volumes at 25 "C are taken from the literature3 and at 5 and 15 OC are evaluated from density data reported in the 1iterat~re.l~ * We are grateful to Prof. Cabani for making these data available.M. V. K A U L G U D , V. S. B H A G D E A N D A. SHRIVASTAVA 317 TABLE I.-vALUES OF THE LIMITING PARTIAL MOLAL VOLUME OF AMINES AT DIFFERENT TEMPERATURES amines 25 "C 5 "C 15 "C 25 OC Cabani, ref. (3) ammonia me thy lamine ethylamine n-propy lamine n-butylamine t-but ylamine dime t hy lamine trimet hylamine 22.01 f 0.2 36.75 f 0.08 54.95 f 0.03 7 1.64 & 0.024 87.23 f 0.04 89.66 & 0.05 58.62 f 0.12 77.85 f 0.1 22.86 & 0.1 39.79 f 0.04 56.94 f 0.02 72.56f0.012 89.43 f 0.02 90.1 f0.04 58.86 f 0.1 78.32 f 0.1 24.80 f 0.2 41.98 f 0.02 58.85 f 0.02 74.18f0.01 89.84+0.01 91.24 f 0.02 59.44 f 0.1 79.34 f 0.08 24.85 41.68 58.37 74.12 89.80 59.80 78.40 - FIG.2.-Plots of q5$c against (1 - a ) c for ethylamine at 25 (O), 15 (0) and 5 O C ( 0 ) (origin shifted towards right by 5 and 10 units for 15 and 5 O C , respectively). RESULTS AND DISCUSSION The straight lines passing through the origin obtained by application of eqn (8) for all amines indicate that the solute-solute interaction term (1 -a)ch in the square bracket is negligible up to quite high concentration (0.3 mol dm+) and even at low temperatures. The h values for amines at 25 OC tabulated by Cabani4 are of the order318 EXCESS VOLUMES OF AMINES (1 -a) x 1 0 3 FIG.3.-Plots of 4; c against (1 -a) c at 5 OC for NH, (O), MeNH, (a), Me,NH (A), n-PrNH, (0) and n-BuNH, (A). of unity with negative sign for amines handled in this work. Hence the maximum value of the interaction term (1 - a) ch z - 0.3 at a concentration of 0.3 mol dmP3 where a = 0.05. This value is very small as compared with #$(BH,o) which is of the order of 50-120 cm3 and the term (1 - a ) ch is, at the worst, of the order of magnitude of experimental errors. Hence, this modification of the original method is applicable for the determination of reliable 4: values even by using data at higher concentrations. It is also found that 4; values determined using eqn (8) are independent of slight uncertainty (ko.1 if any) in the measurement of p& values for amines.This fact is to be contrasted with the Cabani's procedure, which is shown to be sensitive to small uncertainties in p&, values. In this sense, the variant proposed by us in this work [eqn (S)] can be said to be better suited for reliable evaluation of #$(R). Table 1 shows that the limiting partial molal volumes of ammonia and t-BuNH, are practically constant between 5 and 25 OC, while for other amines these show a distinct increase with temperature. This is to be contrasted with the behaviour of alcohols for which Vz are practically constant in the temperature range 0-30 OC.16 Both amines and alcohols show negative limiting excess volumes ( V,""), the magnitude being larger for amines.This means that the extent of accommodation of amines in open cage structures existing in water is greater than for alcohols. Some insight into the further differences in behaviour of alcohols and amines might be gained by considering the temperature coefficient of the limiting excess volumes d "/dT = d( - V,O)/dT where V i is the limiting partial molar volume and V: is the molar volume of the pure liquid. Neal and Goring" studied the temperature coefficients of the apparent specificM. V. KAULGUD, V. S. BHAGDE A N D A. SHRIVASTAVA 3 19 TABLE 2.-TEMPERATURE COEFFICIENTS OF THE LIMITING EXCESS VOLUMES FOR AMINES AND ALCOHOLS amines 102 d V i E/dT alcohols lo2 dV'E/dT ammonia 2.2 met hylamine 16.6 methyl alcohol - 4.6" e t h y lamine 9.1 ethyl alcohol - 6.0" n-prop ylamine 1.2 n-propyl alcohol - 7.0" t-butylamine - 3.2 t-butyl alcohol - 10.3b dimethy lamine - 8.8 trimethylamine - 6.8 n-butylamine - 6.5 n-butyl alcohol - 4.3" (' Ref.(16). Evaluated from the vo against Tcurves of F. Franks and H. G. Smith, Trans. Furaduy SOC., 1968, 64, 2962. W 0 5 15 25 T/"C FIG. 4.-Vanation of vF with temperature for NH, (a), MeNH, (O), EtNH, (A), n-PrNH, (O), n-BuNH, (A), t-BuNH, (01, Me,NH (8) and Me,N (m). volumes dd,/dT of a large number of non-electrolytes in water at low concentration and concluded that the difference (dd,/dT- d V,/dT) (where d V,/dTis the temperature coefficient of the specific volume of the pure liquid) is positive for structure-breaking solutes and negative for structure-making solutes. The correspondence between d r: E/d T and (d@,/d T - d K/d T ) is quite obvious. Values of d V: E/d T for ammonia and all amines handled in this work (table 2) can hence be subjected to similar interpretation.Since alcohols are well known to be structure stabilizers, they show negative values for d E/dT as expected (table 2). Amines, which are, like alcohols,320 EXCESS VOLUMES OF AMINES monofunctional aliphatic organic solutes, would be expected to show similar behaviour. Surprisingly, the first three members, methyl-, ethyl- and n-propyl-amine and ammonia show positive d Fi "/d7', whereas the rest of the amines including di- and tri-methylamine show negative values. Since in both alcohols and amines the hydrophobic part is the same, the observed differences must be due to the different ways in which the -NH, and the -OH groups interact with solvent water.In fact, the observed results can be rationalized by assuming that the water-structure compatible OH group reinforces water structure and the NH, group disrupts it in its vicinity due to its inability to participate in cooperative hydrogen bonding with water. It can be seen that ammonia, which can easily be accommodated into the natural cavities in water, acts as a weak structure breaker. In the case of methylamine, the effect of NH, group outweighs that of a lone CH, group on water and the overall molecule turns out to be a structure breaker according to the sign of d "/dT. The magnitude of d r t E/dT decreases with increasing chain length as in ethyl- and n-propyl-amine showing the opposite influences on water structure of the hydrophobic group and the NH, groups.With a sufficiently long hydrocarbon chain and/or bulky groups on the nitrogen atom as in n-butylamine or di- and tri-methylamine, the effect of the hydrophobic group seems to outweigh that due to NH, and the molecule behaves as a structure stabilizer. These findings are in agreement with the results of a similar comparative study of limiting partial molal compressibilities (d",) of amines and alcohols. It was shown by Kaulgud18 that the relative structure-strengthening ability of a solute could be described quantitatively by the expression d(Q)KS-Pi V,O)/dT, where Pi and VF are the compressibility and molar volume of the pure liquid. It was foundlg that this expression gave values which are considerably less for amines than for the corresponding alcohols. Concluding, it can be said that the volumetric behaviour of a monofunctional solute in water is also influenced by the nature of the polar group.In particular, comparison between the hydroxyl group (-OH) and the amine group (-NH,) shows that the latter acts as a structure breaker. Two of us (V. S. B.) and (A. S.) thank the University Grant Commission, New Delhi for a Faculty Improvement Programme Fellowship and a Junior Research Fellowship, respectively. We also thank the referees for their valuable suggestions and comments. M. V. Kaulgud and K. J. Patil, J. Phys. Chem., 1974, 78, 714. M. V. Kaulgud and K. J. Patil, J. Phys. Chem., 1976, 80, 138. S. Cabani, G. Conti and L. Lepori, J. Phys. Chem., 1974, 78, 1030. S. Cabani, G. Conti and L. Lepori, J. Phys. Chem., 1972, 76, 1338. G. Wada and S. Umeda, Bull. Chem. Soc. Jpn, 1962, 35, 646. G. Wada and S. Umeda, Bull. Chem. Soc. Jpn, 1962, 35, 1797. ' D. M. Alexander and D. J. T. Hills, Aust. J . Chem., 1969, 72, 347. J. Konicek and I . Wasdo, Acta Chem. Scand., 1971, 25, 1541. R. K. McMullan, G. A. Jeffery and T. H. Jordan, J . Chem. Phys., 1967, 47, 1229. lo F. Franks, Water, A Comprehensive Treatise (Plenum Press, New York, 1973), vol. 2, chap. 1, p. 35. l 1 M. V. Kaulgud, H. G. Dole and K. S. M. Rao, Indian J. Chem., Sect. A , 1978, 16, 955. l 2 F. J. Millero, Chem. Rec. 1971, 71, 147. l 3 M. V. Kaulgud, M. R. Awode and A. Shrivastava, Indian J . Chem., Sect. A , 1980, 19, 144. l4 D. D. Perrin, Dissociation Constants of Organic Bases in Aqueous Solution (Butterworths, Washington, l5 K. Raznjeric, Handbook of Thermodynamic Tables and Charts (Hemisphere, Washington, 1976). 1975).M. V. KAULGUD, V. S. BHAGDE AND A. SHRIVASTAVA D. M. Alexander, J . Chem. Eng. Data, 1959, 4, 252. '' J . L. Neal and D. A. I. Goring, J . Phys. Chem., 1970, 74, 658. l R M. V. Kaulgud, J . Chem. SOC., Faraday Trans. I , 1979, 75, 2246. M. V. Kaulgud, A. Shrivastava and M. R. Awode, Indian J. Pure Appl. Phys., 1980. 18, 864. 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