J. Chem. SOC., Faraday Trans. I, 1982, 78, 3203-3212 Ultrasonic Investigations of Mixtures of n-Octane with Isomeric Octanols Isoentropic Compressibility and Excess Volumes of Mixing BY AKL M. AWWAD AND RICHARD A. PETHRICK* Department of Pure and Applied Chemistry, University of Strathclyde, Thomas Graham Building, 295 Cathedral Street, Glasgow G1 1XL Received 2 1 st December, 198 1 Volumes of mixing, isoentropic compressibilities, acoustic attenuations and viscosities are reported on mixtures of various isomeric octanols and octane at 298.15 K. The data are interpreted in terms of competing effects of the alkane chain taking up the ‘free’ volume in the system and the disturbance of the distribution between cyclic and linear structures and monomer forms in the mixtures. Recent studies of the behaviour of n-alkanol + n-alkane mixtures have been undertaken in an attempt to interpret the way in which structure in the associated alcohols is modified by the addition of alkanes.’.’ Such investigations are crucial if we are ever to understand the processes which occur when water is added to alcohol.s-lo In this latter situation, large excess acoustic attenuations are often reported and attributed to the effect of the sound wave on the distribution of structural forms present at different concentrations.Returning to the ‘ simpler’ system of an alcohol in its homologous hydrocarbon, the stability of the hydrogen-bonded structures will depend on the accessibility of the hydroxy group. It has been suggested by Staveley2 that the behaviour observed in dilute solutions in benzene is associated with the ‘ interaction between the hydroxy group and the surrounding benzene molecules which underwent a change when the hydrocarbon group of the alcohol became sufficiently long to be capable of screening the hydroxy group’.In an earlier study of isomeric octanols with methanol it was observed that excesses in the attenuation similar to those reported for aqueous solutions were observed.ll This present study is an extension of these investigations. EXPERIMENTAL MATERIALS The isomeric octanols : octan- 1-01, octan-2-01, 2-ethylhexan- 1-01, 2,4-dimethylhexan-3-01, 2,3-dimethylhexan-3-01 and the n-octane were all obtained from Aldrich Chemical Co Ltd as better than 99% pure. The purity was confirmed using gas-liquid chromatography and the structuraI integrity using I3C n.m.r.spectroscopy. The liquids were all stored over type 4A molecular sieves (B.D.H.) and filtered before use. Densities and refractive indices of the pure components were measured (see table 1) and found to be in good agreement with values published in the DENSITY MEASUREMENTS The densities were determined using an Anton Paar densimeter (DMA 60) thermostatted with a precision of & 0.01 K. The overall precision of the densities measured was estimated to 32033204 ULTRASONIC STUDIES OF OCTANOL+OCTANE MIXTURES TABLE ~.-DENSITIES, p, REFRACTIVE INDICES, n,, VELOCITY OF SOUND, c, OF THE PURE COMPONENTS AT 298.15 K molecule n-octane octan-1-01 octan-2;ol 2-ethylhexan- 1-01 2,4-dimethylhexan-3-01 2,3-dimethylhexan-3-01 Plg cm-3 obs.lit. 0.698 76 0.698 67 - 0.698 61 0.821 13 0.821 39 - 0.82 157 0.81627 0.8162 0.83205 0.83272 0.834 18 0.834 8 I 0.82906 - c/ms-l ~~~ obs. lit. obs. lit. 1.395 22 1.395 18 1.395 05 I .427 24 1.427 57 - 1.427 5 1.424 34 1.424 1.42921 - 1.43022 -- - 1.42920 -- I 177.85 1177.25 1349.86 1348.83 1323.45 1321.80 1309.75 1307.75 - - 1288.50 - 1286.52 - be better than +_ 3 x of the components. kg-3. The mixtures were prepared by the addition of weighted amounts ULTRASONIC MEASUREMENTS The attenuation and velocity data reported in this paper were obtained using a swept-frequency acoustic resonator.1s- l9 The smnd velocity was determined from the separation of the resonance peaks in the frequency range 1.5-3 MHz. The attenuation was determined from the variation of the widths of the resonances in this region.A detailed study of the frequency dependence on the pure components has been reported e1se~here.I~ VISCOSITY MEASUREMENTS The viscosities of the pure components and the mixtures were determined using a suspended level viscometer. The flow times were determined electronically using an electronic stop watch with a precision of +_ 0.5 s and the temperature of the water bath was controlled to better than kO.01 K. RESULTS VOLUMES OF MIXING Values of the excess volumes of mixing VE of the binary mixtures of the isomeric octanols and octane were calculated using the following equation where X , , X2, M , , M,, V;T and V,* are, respectively, the mole fraction, molecular weight and molar volumes of the pure components designated 1 and 2.The density, p, is the measured value for the binary mixture. Values of VE for the isomeric octanol + octane mixtures were calculated using the data presented in fig. I t and fitted to an empirical equation of the form m VE =X(1-X) a, Xn-l (2) n-1 where a, is the fitting coefficient of order n obtained from a least-squares fit of the data presented in table 2. The standard deviations associated with this analysis are also presented in table 2, along with the coefficients for a,. Comparison of the plots t The data presented in the figures are available on request from the authors.TABLE 2.-cOEFFICIENTS a, AND STANDARD DEVIATIONS d VE/CM3 m0l-l FOR LEAST SQUARES REPRESENTATIONS OF EXCESS VOLUMES AT 298.15 K BY EQN (2) Qrl octan- l-ol 2-ethylhexan- l-ol octan-2-01 2,4-dirnethylhexan-3-01 2,3-dimethylhexan-3-01 0.02441 - 0.93847 - 5.94620 24.282 60 21.17675 - 32.909 25 - 5.69659 0.0004 0.00404 1.241 37 1 8.700 92 18.39394 0.0005 - 7.099 36 - 26.08026 - 5.16065 0.004 76 2.5 1494 3 1 .1 44 67 28.491 33 0.0009 - 12.91642 - 41.284 85 - 7.05422 0.095 82 3.39620 33.694 05 42.73724 0.0002 - 13.787 89 - 52.33445 - 13.808 27 0.062 16 3.997 39 - 23.419 8 1 65.892 23 76.38988 - 99.855 47 - 23.077 38 0.0007 > ?3206 ULTRASONIC STUDIES OF OCTANOL+OCTANE MIXTURES 1 I 0 0.5 X FIG. 1.-Excess volumes for [xC,H,,OH+(l -x)n-octane] at 298.15 K. 0, octan-1-01; 0, octan-2-01; A, 2-ethylhexan-1-01; A, 2,3-dirnethylhexan-3-01; a, 2,4-dimethylhexan-3-01. of the actual data and the predictions of eqn (2) indicates that the deviation is in all cases < 0.1 %.The excess volumes for the binary mixtures of branched-chain octanols with octane are all positive over the whole mole-fraction range (fig. 1). In the case of the straight-chain octan-1-01, VE values are negative except at low mole fractions, where they are positive. ACOUSTIC VELOCITY A N D ISOENTROPIC COMPRESSIBILITY The velocities of sound measured at ca. 2 MHz for the pure components are listed in table 1. The excess isoentropic compressibility was calculated using an empirical equation of the form KF = Ks(obs)-lX1 V;" KS,+X2 c Ks21 1x1 v+xz V 3 - l (3) where Xl X , c Ks, and Ks2 are, respectively, the mole fractions, molar volumes and isoentropic compressibilities of the pure components and K, (obs) is the isoentropic compressibility of the binary mixture calculated using the Laplace relation K, = be2)-' where cis the measured velocity of sound in the mixture.The isoentropic compressibility excesses so obtained are plotted in fig. 2. ULTRASONIC ATTENUATION A N D VISCOSITY MEASUREMENTS Attenuation data ( a / f 2 ) obtained over the frequency range 1.5-3 MHz are presented in fig. 3 as a function of mole fraction of the mixture. The viscosities of the mixtures are presented in fig. 4. The attenuation of an organic liquid can be separated into two parts : a relaxational element associated with the disturbance of rotational isomeric equilibria or hydrogen-bonded associated forms of the alcohol,A. M. AWWAD A N D R. A. PETHRICK 3207 -'t 0 0-5 X 1 FIG.2.-Excess isentropic compressibility K," for [xC,H,,OH +( 1 - x)n-octane] at 298.15 K. 0, octan-1-01; A, octan-2-01; 0, 2-ethylhexan-1-01; ., 2,3-dimethylhexan-3-01; 0, 2,4-dimethylhexan-3-01. 0 0 - 5 1 X FIG. 3.-Ultrasonic absorption coefficient for [xC,H,,OH +( 1 - x)n-octane] at 298.15 K and 2MHz. 0, octan-1-01; 0 , octan-2-01; A, 2-ethylhexan-1-01; 0, 2,3-dimethylhexan-3-01; ., 2,4-dimethylhexan-3-01.3208 ULTRASONIC STUDIES OF OCTANOL-kOCTANE MIXTURES 0 0.5 X 1 FIG. 4.-Variation of viscosity (poise) as a function of mole fraction, x, of octanols for [xC,H,,OH + (1 -x)n- octane] at 298.15 K. A, octan-1-01; 0, octan-2-01; A, 2-ethylhexan-1-01; ., 2,3-dimethyl hexan-3-01; 0, 2,4-dimethylhexan-3-01. I A 0 0-5 X 1 FIG. 5.-Ultrasonic absorption contribution from shear viscosity (a/p)s for [xC,H,,OH + ( 1 - x) n-octane] at 2 MHz and 298.15 K.A, octan-1-01; A, octan-2-01; *, 2ethylhexan-1-01; 0, 2,3-dimethylhexan-2-01; ., 2,4-dimethylhexan-3-01.A. M. A W W A D A N D R. A. PETHRICK 3209 and a classical contribution associated with viscous and thermal contributions. The contribution from shear relaxation can be calculated from the viscosity using the relation where vs is the shear viscosity. The calculated shear contribution is presented in fig. 5. The viscous contribution contains a volume-viscosity element, and the total attenuation contains also a thermal-conductivity loss. The latter for most organic liquids makes a contribution of 4 1 % to the observed attenuation. Estimates based (a/P)s = g7%/3pc3 (4) on very imprecise literature data indicate that this is also true in the which case the volume viscosity can be calculated from (a/P)v = (27%/PC3)V = (a/P)o,s - (a/P)s where vv is the volume viscosity of the mixture.Calculated values presented in fig. 6. present case, in ( 5 ) for (alp)" are 1 I I 0 0 . 5 1 X FIG. 6.-Ultrasonic absorption contribution from volume viscosity (alp)" for [xC,H,,OH +( 1 -x) octane] at 2 MHz and 298.15 K. e, octan-1-01; 0, octan-2-01; A, 2-ethylhexan-1-01; 0, 2,3-dimethylhexan-3-01; m, 2,4-dirnethylhexan-3-01. DISCUSSION A survey of the literature indicates that few measurements have been performed in a systematic manner of the changes in the structure of alcohols with the addition of non-polar molecules. This is in contrast to the considerable attention which has been given to alcohols with other hydrogen-bonding molecules. In this present study the isomeric octanols allow the effects of chain isomerism, hydrogen-bond accessibility and configurational mobility of the second molecule to be studied.VOLUME OF MIXING The V E values in the case of the straight-chain octan-1-01 are negative except for mole fractions < 0.02, where they become positive (fig. 1). The maximum values of the excess volumes for branched octanols decreased in the order 2,3- dimethylhexan-3-01, 2,4-dimethylhexan-3-01, octan-2-01, 2-ethylhexan- 1 -01. Accord- ing to Tresczanowicz and Benson13 the VE data for similar binary mixtures can be I04 F A R 783210 ULTRASONIC STUDIES OF OCTANOL+OCTANE MIXTURES explained qualitatively by postulating that the excess is the result of two opposing effects : self-association of the octanol and physical dipole-dipole interactions between octanol monomers and multimers, leading to increases in volume.Negative contri- butions arise from changes of ‘free volume’ in the real binary mixture. Additional contributions can be envisaged as arising from the restrictions in rotational motion15 which arise when the octane molecule is accommodated interstitially within the branched-oc tanol structure. The data presented in fig. 1 indicated that the negative contribution reaches a maximum at ca. 0.4 mole fraction of octan-1-01 and at very low dilution octan-1-01 it becomes positive owing to hydrogen-bond breaking. The positive values of VE for the branched-chain octanols are a consequence of steric interactions associated with the branched alkyl chains reducing the extent of hydrogen bonding in the system.For instance, in the case of 2,3-dimethylhexan-3-01 the hydroxy group is highly hindered by the alkyl group and gives the highest maximum excess volume values. As the steric effect of the alkyl group is increased so the positive contribution becomes more important than the negative. In octan-1-01 the octane molecules are accommodated in the octanol structure and a negative direction is observed. Similar effects have been reported by Benson for other alcohol + alkane systems. ACOUSTIC VELOCITY AND ISOENTROPIC COMPRESSIBILITIES As indicated above, the main effect of addition of octane is a change in the ‘free’ volume in the mixture compared with that in the pure components.Disruption of the alcohol structure and restriction of the rotational motion has been described as the condensation 21 Interstitial accommodation and orientational order lead to a more compact structure and to an observed decrease in the excess compressibility, fig. 2. At low alkanol concentrations the negative deviations observed are attributed to the effects of break-up of the hydrogen-bond structure and this tends to increase the compressibility and leads ultimately to the positive trend. The behaviour reported here is similar to that reported by Kiyohara and Benson2 on various n-alkanol + n- octane systems. The main conclusion with regard to the low mole-fraction data is that breaking of multimer structure leads to a positive value of K,E and a concomitant increase in the ability for interstitial accommodation of the alkane.This behaviour is modulated by the steric interactions of the alkyl group both on the stability of the multimer structure but also on the ability of the liquid to accommodate the straight-chain alkane. The infrared spectrum of these mixtures is very complex and does not allow either positive identificatior, or estimation of the concentrations of the various multilinear structures present. VISCOTHERMAL ACOUSTIC ATTENUATION COEFFICIENT The frequency dependence of the acoustic attenuation in the isomeric octanols has been reported previ0us1y.l~ In the following analysis account has been taken of the contribution associated with rotational isomerism in octan-2-01, 2,3-dimethylhexan- 3-01 and 2,4-dimethylhexan-3-01 to the acoustic attenuation.In all cases the rotational isomeric contribution decreased linearly with the concentrations of the octanol allowing the viscothermal acousticattenuation to be defined as a frequency-independent contribution. The concentration variation of the viscosity reflects the complex manner in which the ‘ hydrogen-bonded structure’ varies with concentration and reflects the extent to which ‘ associated ’ cyclic and linear hydrogen-bonded structures are destabilized by the addition of non-polar molecules. The observed deviations are negative, implyingA. M. A W W A D AND R. A. PETHRICK 321 1 break up of associated structure in all cases. The ultrasonic attenuation is observed to increase rapidly on the addition of alcohol to the alkane and a maximum in the attenuation coefficient is observed in the dilute region for octan- 1-01, octan-2-01 and 2-ethylhexan-1 -01 and implies that as the alcohol concentration is increased so the probability of formation of cyclic forms increases.The maximum is probably of similar origin to that observed in water alkanol systems, where the excess is attributed to disturbance of the distribution between cyclic and linear pure forms and mixed associated forms.s The height of the absorption maximum decreases as the steric effects of the alkyl group increase. The height decreases in the order octan- 1-01,2-ethylhexan- 1-01, octan-2-ol,2,4-dimethylhexan-3-ol and 2,3-dimethylhexan-3-01. The steric effects in the 2,4- and 2,3-dimethylhexan-3-01 lead to less self-association in these systems than in the corresponding linear systems. Introduction of n-octane to 2,3-dimethylhexan-3-01 leads to a slow increase in the attenuation, and no maximum at low concentrations is observed, hydrogen bonding between these molecules being insufficiently strong to lead to association, and hence the mechanism of relaxation observed in the other systems is excluded here.The excess absorption at low concentrations appears to be due to a structural relaxation contribution to the volume viscosity rather than to the classical shear-viscosity absorption (fig. 5-7). 0 0.05 Y 0.1 FIG. 7.-Ultrasonic absorption coefficient for [xC,H,,OH+(l -x)n-octane] at 298.15 K. 2 MHz and low mole fraction, x, of octanols < 0.1 .0, octan-1-01; A, octan-2-01; ., 2-ethylhexan-1-01; A, 2,3- dimethylhexan-3-01; 0, 2,4-dimethylhexan-3-01. As the concentration of the octanols increases, the disordering action of the n-octane molecules becomes less important in comparison with the effects of hydrogen bonding between neighbouring molecules. Studies of the temperature and frequency dependence of the attenuation in the pure alcohols have indicated that the total attenuation of the pure alcohol is a combination of contributions from rotation isomerism and processes associated with structural relaxation of hydrogen-bonded clusters and dynamics of the structural association. This analysis is further supported by the trends observed at high mole fractions of alcohol, the rotational isomeric contribution being a linear function of the concentration of alcohol.104-23212 ULTRASONIC STUDIES OF OCTANOL+OCTANE MIXTURES CONCLUSIONS This study indicates that in mixtures of alcohol and alkane the observed excesses are a consequence of a number of competing effects. In the sterically unhindered alcohols cyclic and linear associated forms can be formed. Addition of alkane allows the 'free' volume in the lattice to be filled and also will perturb the degree of clustering present. In the sterically hindered alcohols the cyclic associated forms cannot be formed and no excess features associated with critical association are observed. These latter effects are observed in the region of 0.1 mole fraction for the majority of systems studied.A lack of definitive spectroscopic data precludes a detailed analysis of these data at the present time in terms of linear and cyclic associated structures. A.M.A. thanks the Petroleum Research Institute, Iraq for sabbatical leave and financial support during the period of study. K. N. Marsh and C. Burfitt, J. Chem. Thermodyn., 1975, 7, 955. 0. Kiyohara and G. C. Benson, J. Chem. Thermodyn., 1979, 11, 861. L. A. K. Staveley and B. Spice, J . Chem. Soc., 1952, 406. G. Dharmaraju, G. Nayayanaswamy and G. K. Raman, J . Chem. Thermodvn., 1979, 11, 861. H. C. Van Ness, C. A. Soczek and N. K. Kochar, J. Chem. Eng. Data, 1962, 12, 346. M. Diaz Pena and D. Rodriguez Cheda, An. R. Soc. ESP. Fis. Quim. Ser. B, 1970, LXVI, 637. G. N. Swamy, G. Dharmaraju and G. K. Raman, Can. J. Chem., 1980, 58, 229. J. Emery and S. Gasse, Acustica, 1979, 43, 205. S. Nishikawa, M. Mashima and T. Yasunaga, Bull. Chem. Soc. Jpn, 1976, 49, 1413. '" M. J. Blandamer and 0. Waddington, Adv. Mol. Relaxation Processes, 1970, 2, 1. l 1 C. Dugue, J. Emery and R. A. Pethrick, Mol. Phys., 1981, 42, 1453. l 2 A. J. Tresczanowicz and G. C. Benson, J . Chem. Thermodyn., i978, 10, 967. l 3 A. J. Tresczanowicz and G. C. Benson, J . Chem. Thermodyn., 1980 12, 173. l4 J. L. Hales and J. H. Ellender, J. Chem. Thermodyn., 1976, 8, 1177. 15 C. Dugue, J. Emery and R. A. Pethrick, Mol. Phys., 1980, 41, 703. l 6 E. Alcart, G. Tardajou and M. Diaz Pena, J . Chem. Eng. Data, 1980, 25, 140. l 7 Selected Values of Properties of Hydrocarbons and Related Compounds, API Project 44 (Thermodyn- amics Research Centre, Texas A & M University, College Station, Texas, October 31, 1952 and October 3 1, 1963). F. Eggers, Acustica, 1967, 19, 323. I 9 R. A. Pethrick, J . 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