Thermodynamics of ketone + amine mixtures

Thermochimica Acta 512 (2011) 86–92 Contents lists available at ScienceDirect Thermochimica Acta journal homepage: www.elsevier.com/locate/tca Thermodynamics of ketone + amine mixtures Part IV. Volumetric and speed of sound data at (293.15; 298.15 and 303.15 K) for 2-butanone +dipropylamine, +dibutylamine or +triethylamine systems Iván Alonso, Ismael Mozo, Isaías García de la fuente, Juan Antonio González ∗ , José Carlos Cobos G.E.T.E.F., Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid, 47071 Valladolid, Spain a r t i c l e i n f o Article history: Received 19 June 2010 Received in revised form 1 September 2010 Accepted 2 September 2010 Available online 15 September 2010 Keywords: Densities Speeds of sound Compressibilities 2-Butanone Amines Interactions Structural effects a b s t r a c t Densities, , and speeds of sound, u, of 2-butanone +dipropylamine, +dibutylamine or +triethylamine systems have been measured at (293.15, 298.15 and 303.15 K) and atmospheric pressure using a vibrating-tube densimeter and sound analyser Anton Paar model DSA-5000. The  and u values were used to calculate excess molar volumes, VE , at the three temperatures, and the excess functions at 298.15 K for the speed of sound, uE , the thermal expansion coefficient, ˛EP , and for the isentropic compressibility, SE . VE , SE and ˛EP are positive magnitudes. When replacing dipropylamine by dibutylamine or triethylamine in the studied mixtures, the excess functions increase. This may be ascribed to the interactions between unlike molecules are more important in the former solutions. From the comparison with similar data obtained for propanone or 2-butanone +aniline, +N-methylaniline, or +pyridine systems, it is concluded that interactions between unlike molecules are stronger in mixtures containing aromatic amines. The replacement of 2-butanone by propanone in mixtures with dipropyl, dibutyl or triethylamine leads to increased VE values, which may be explained assuming that the higher positive contribution to VE from the disruption of the propanone–propanone interactions overcompensates the larger negative contribution related to stronger interactions between unlike molecules. Calculations in the framework of the Flory model support this conclusion. Free volume effects are present in solutions with dipropyl or dibutylamine as the VE curves are shifted towards higher mole fractions of 2-butanone. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Amides, amino acids, peptides and their derivatives are of interest because they are simple models in biochemistry. Secondary amides possess the basic (−CO) and acidic (−NH) groups of the very common, in nature, peptide bond [1]. For example, proteins are polymers of amino acids linked to each other by peptide bonds. Consequently, the understanding of liquid mixtures involving the amide functional group is necessary as a first step to a better knowledge of complex molecules of biological interest [2]. Thus, the aqueous solution of dimethylformamide is a model solvent representing the environment of the interior of proteins. In addition, amides have many other practical applications. Dimethylformamide and N-methylpyrrolidone are used as highly selective extractants for the recovery of aromatic and saturated hydrocarbons from petroleum feedstocks [3], and ␧-caprolactam is used for the production of nylon 6, which is a polycaprolactam formed ∗ Corresponding author. Tel.: +34 983 423757; fax: +34 983 423136. E-mail address: jagl@termo.uva.es (J.A. González). 0040-6031/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.tca.2010.09.004 by ring-opening polymerization. The study of alkanone + amine mixtures, which contain the carbonyl and amine groups in separate molecules, is pertinent in order to gain insight into amide solutions. In this article, we report , u and VE data at (293.15, 298.15, 303.15 K), and uE , ˛EP , and SE at 298.15 K for the mixtures 2-butanone +dipropylamine (DPA), +dibutylamine (DBA) or +triethylamine (TEA). Previously, we have provided similar data for systems containing propanone, or 2-butanone and aniline, Nmethylaniline, or pyridine [4,5], as well as for the propanone +DPA, +DBA, or +TEA mixtures [6]. 2. Experimental 2.1. Materials 2-Butanone (≥0.995) and TEA (≥0.995) were from Fluka, DPA (≥0.99) and DBA (≥0.995) were from Aldrich (purities expressed in mass fraction), and were used without further purification. The  and u values of the pure liquids are in good agreement with those from the literature (Table 1). I. Alonso et al. / Thermochimica Acta 512 (2011) 86–92 87 Table 1 Physical properties of pure compounds, 2-butanone, dipropylamine, dibutylamine and triethylamine at temperature T: , density; u, speed of sound; ˛P , isobaric thermal expansion coefficient; S , adiabatic compressibility; T , isothermal compressibility and CP , isobaric heat capacity. Reduction parameters used in the Flory model for volume, V* , and pressure, P* , are also included. Property T/K 2-Butanone This work 3 /g cm Dipropylamine Lit This work a b Triethylamine Lit This work c 0.805351 0.80495 0.738188 0.73720 0.759571 0.762022 0.727515 298.15 0.800077 0.7997f 0.79974a , i 0.79992l 0.733683 0.73336g 0.73368h 0.73333m 0.755457 0.722822 303.15 0.794779 0.79464l 0.79448a 0.729087 0.72820b 0.73121k 0.73019n 0.751329 0.75553g 0.75570j 0.75572h 0.75595k 0.75194k 0.75248n 1212.3 1191.0 1213a 1192a 1209.2 1187.7 T /TPa−1 CP /J mol−1 K−1 303.15 298.15 293.15 298.15 303.15 298.15 298.15 1170.8 1.32 844.9 881.2 917.9 1175.9 1171a 1.31a 844a 880a 918a 1188d 159.2p 1167.1 1.24 926.5 966.2 1006.9 1216.4 V* r /cm3 mol−1 P* r /J cm−3 298.15 298.15 68.80 574.2 106.51 509.6 103 ˛P /K−1 S /TPa−1 This work 293.15 293.15 298.15 u/m s−1 Dibutylamine Lit 135.15 491.2 1198k 1174k 1.201k 947k 992k 1183k 252.84d 0.718201 1261.2 1241.3 1269.47c 1248k 1132.77 1111.1 1222.5 1.09 827.7 859.0 890.6 1060.1 1246.7c 1227k 1.059k 814.31c 849k 883k 1039k 302k 1090.7 1.29 1071.2 1120.7 1170.5 1441.0 Lit 0.7276d 0.72753e 0.72318h 0.72376k 0.71836e 1123k 1115.1o 1101k 1.24o 1113o 1135k 1404o 216.43q 107.33 454. V* = 54.69 cm3 mol−1 ; P* = 619.1 J cm−3 ; values obtained using ˛P and T from Ref. [4]. a [37]. b [38]. c [39]. d [10]. e [40]. f [41]. g [42]. h [24]. i [43]. j [44]. k [45]. l [46]. m [47]. n [48]. o [49]. p [50]. q [51]. r For propanone. 2.2. Apparatus and procedure Binary mixtures were prepared by mass in small vessels of about 10 cm3 . Caution was taken to prevent evaporation, and the error in the final mole fraction is estimated to be less than ±0.0001. Conversion to molar quantities was based on the relative atomic mass table of 2006 issued by IUPAC [7]. The densities and speeds of sound of both pure liquids and of the mixtures were measured using a vibrating-tube densimeter and sound analyser, Anton Paar model DSA-5000, automatically thermostated within ±0.01 K. Temperature measurements were taken using a Pt-100, calibrated at the triple point of water (0.01 ◦ C) and at the melting point of gallium (29.7646 ◦ C) according to the ITS-90 scale [8,9]. The calibration of the densimeter was carried out with deionised double-distilled water, heptane, octane, isooctane, cyclohexane and benzene, using  values from the literature [10–12]. The accuracy for the  and u measurements are ±1 × 10−5 g cm−3 and ±0.1 m s−1 , respectively, and the corresponding precisions are ±1 × 10−6 g cm−3 and ±0.01 m s−1 . The experimental technique was checked by determining VE and u of the standard mixtures: cyclohexane + benzene at the temperatures (293.15, 298.15 and 303.15 K) and 2-ethoxyethanol + heptane at 298.15 K. Our results agree well with published values The accuracy in VE is   [13–16]. E  + 0.005) cm3 mol−1 , where believed to be less than ±(0.01 Vmax E | denotes the maximum experimental value of the excess |Vmax molar volume with respect to the mole fraction. The accuracy of the deviations of u from the ideal behaviour is estimated to be 0.3 m s−1 . 3. Equations The thermodynamic properties for which values are derived most directly from the experimental measurements are the density, , the molar volume, V, the coefficient of thermal expansion, ˛P = − (1/)( ∂ /∂ T)P and the isentropic compressibility, S . In this work, ˛P values were obtained from a linear dependence of  with T. Assuming that the absorption of the acoustic wave is negligible, S can be calculated using the Newton–Laplace’s equation: S = 1 u2 (1) For an ideal mixture at the same temperature and pressure than the system under study, the values Fid of the thermodynamic prop- I. Alonso et al. / Thermochimica Acta 512 (2011) 86–92 88 Table 2 Densities, , molar excess volumes, VE , and speeds of sound for 2-butanone(1) + amine(2) mixtures at temperature T. u/m s−1 x1 /g cm−3 VE /cm3 mol−1 u/m s−1 2-Butanone(1) + dipropylamine(2); T/K = 293.15 0.0539 0.740359 0.043 0.1021 0.742443 0.069 0.1497 0.744612 0.088 0.1982 0.746936 0.101 0.2459 0.749311 0.112 0.2983 0.752034 0.122 0.3504 0.754874 0.130 0.4012 0.757757 0.137 0.4495 0.760619 0.142 0.5068 0.764200 0.142 1208.02 1207.27 1206.70 1206.17 1205.69 1205.17 1204.86 1204.58 1204.35 1204.30 0.5551 0.6014 0.6568 0.6968 0.7555 0.8009 0.8573 0.9010 0.9479 0.767388 0.770563 0.774567 0.777603 0.782275 0.786111 0.791158 0.795276 0.799908 0.139 0.136 0.128 0.120 0.107 0.092 0.068 0.049 0.027 1204.38 1204.49 1204.76 1205.12 1205.87 1206.59 1207.83 1208.90 1210.29 2-Butanone(1) + dipropylamine(2); T/K = 298.15 0.0592 0.736042 0.050 0.1027 0.737924 0.071 0.1509 0.740108 0.087 0.2001 0.742441 0.101 0.2446 0.744623 0.114 0.2958 0.747263 0.123 0.3545 0.750410 0.134 0.4003 0.753000 0.139 0.4625 0.756591 0.145 0.5006 0.759040 0.143 1186.64 1185.88 1185.19 1184.66 1184.17 1183.84 1183.33 1183.16 1182.49 1182.88 0.5539 0.5992 0.6474 0.6987 0.7531 0.8048 0.8557 0.9041 0.9471 0.762376 0.765587 0.769011 0.772610 0.777151 0.781469 0.785991 0.790463 0.794714 0.142 0.136 0.130 0.115 0.105 0.089 0.066 0.050 0.025 1182.71 1183.16 1183.43 1183.49 1184.56 1185.36 1186.62 1188.02 1189.12 2-Butanone(1) + dipropylamine(2); T/K = 303.15 0.0658 0.731678 0.055 0.0988 0.733107 0.067 0.1106 0.733626 0.072 0.2146 0.738432 0.104 0.2595 0.740626 0.118 0.3098 0.743197 0.129 0.3630 0.746053 0.138 0.4131 0.748859 0.143 0.4570 0.751472 0.149 0.5154 0.755069 0.149 1165.92 1165.40 1165.23 1164.09 1163.49 1163.09 1162.78 1162.50 1162.37 1162.30 0.5554 0.6081 0.6657 0.7041 0.7517 0.8032 0.8513 0.8958 0.9448 0.757601 0.761161 0.765248 0.768129 0.771855 0.776094 0.780312 0.784355 0.789085 0.145 0.139 0.132 0.124 0.110 0.094 0.071 0.055 0.029 1162.39 1162.63 1163.01 1163.52 1163.99 1164.84 1166.07 1166.99 1168.60 2-Butanone(1) + dibutylamine(2); T/K = 293.15 0.0568 0.760739 0.053 0.1152 0.762014 0.105 0.1488 0.762814 0.129 0.1968 0.764024 0.158 0.2539 0.765570 0.188 0.3056 0.767093 0.209 0.3564 0.768675 0.228 0.4105 0.770501 0.243 0.4545 0.772103 0.245 0.5005 0.773872 0.256 1258.16 1254.96 1252.90 1250.30 1247.19 1244.42 1241.62 1238.72 1236.36 1233.96 0.5553 0.6022 0.6554 0.7036 0.7554 0.8022 0.8598 0.9001 0.9513 0.776145 0.778277 0.780870 0.783444 0.786435 0.789404 0.793411 0.796544 0.800881 0.259 0.254 0.245 0.231 0.211 0.186 0.147 0.109 0.055 1231.06 1228.89 1225.75 1223.35 1220.79 1218.72 1216.34 1214.96 1213.50 2-Butanone(1) + dibutylamine(2); T/K = 298.15 0.0681 0.756775 0.066 0.1038 0.757539 0.097 0.1625 0.758950 0.139 0.2034 0.759972 0.163 0.2603 0.761475 0.194 0.3112 0.762929 0.216 0.3523 0.764175 0.232 0.3937 0.765506 0.246 0.4420 0.767105 0.260 0.5018 0.769396 0.264 1237.35 1235.31 1232.05 1229.94 1226.66 1223.83 1221.60 1219.44 1216.58 1213.32 0.5455 0.6036 0.6514 0.7003 0.7473 0.7978 0.8456 0.9022 0.9482 0.771147 0.773698 0.775963 0.778472 0.781050 0.784142 0.787356 0.791581 0.795385 0.267 0.261 0.253 0.241 0.226 0.198 0.164 0.112 0.064 1211.00 1207.71 1205.23 1202.70 1200.27 1197.91 1195.86 1193.73 1192.26 2-Butanone(1) + dibutylamine(2); T/K = 303.15 0.0621 0.752548 0.055 0.1098 0.753539 0.098 0.1666 0.754759 0.151 0.2074 0.755736 0.178 0.2593 0.757080 0.205 0.3090 0.758454 0.228 0.3551 0.759790 0.250 0.4045 0.761368 0.262 0.4566 0.763133 0.275 0.4957 0.764551 0.280 1218.87 1216.11 1212.59 1210.29 1207.25 1204.69 1201.97 1199.30 1196.39 1194.07 0.5402 0.6005 0.6493 0.7004 0.7486 0.8005 0.8456 0.899 0.953 0.766282 0.768842 0.771091 0.773646 0.776288 0.779398 0.782362 0.786254 0.790578 0.282 0.276 0.267 0.253 0.232 0.202 0.169 0.122 0.061 1191.57 1188.20 1185.58 1182.87 1180.45 1177.89 1175.94 1173.70 1171.96 2-Butanone(1) + triethylamine(2); T/K = 293.15 0.0684 0.730666 0.066 0.1169 0.733080 0.098 0.1627 0.735417 0.132 1134.48 1136.03 1137.96 0.5572 0.6100 0.6519 0.761332 0.765576 0.769122 0.144 0.135 0.124 1162.26 1166.74 1170.56 x1 /g cm−3 VE /cm3 mol−1 I. Alonso et al. / Thermochimica Acta 512 (2011) 86–92 89 Table 2 (Continued) x1 /g cm−3 VE /cm3 mol−1 u/m s−1 x1 /g cm−3 VE /cm3 mol−1 u/m s−1 0.2218 0.2686 0.3141 0.3549 0.4154 0.4636 0.5054 0.738705 0.741430 0.744214 0.746818 0.750867 0.754264 0.757343 0.149 0.162 0.167 0.168 0.165 0.161 0.154 1140.60 1142.96 1145.52 1147.86 1151.74 1155.05 1158.17 0.7051 0.7603 0.8057 0.8586 0.9019 0.9451 0.773808 0.778962 0.783447 0.788929 0.793679 0.798586 0.112 0.097 0.079 0.061 0.042 0.028 1175.66 1181.38 1186.51 1192.76 1198.33 1204.10 2-Butanone(1) + triethylamine(2); T/K = 298.15 0.0709 0.725999 0.082 0.1149 0.728152 0.115 0.1580 0.730378 0.138 0.2181 0.733668 0.159 0.2610 0.736151 0.167 0.3203 0.739738 0.175 0.3605 0.742292 0.178 0.4159 0.745987 0.175 0.4607 0.749113 0.171 0.5106 0.752756 0.163 1112.73 1114.19 1115.89 1118.52 1120.74 1123.91 1126.28 1129.87 1132.99 1136.68 0.5701 0.6039 0.6600 0.7122 0.7604 0.8023 0.8437 0.8921 0.9456 0.757323 0.760048 0.764735 0.769362 0.773883 0.777983 0.782252 0.787444 0.793453 0.154 0.145 0.134 0.119 0.099 0.084 0.063 0.042 0.025 1141.48 1144.46 1149.45 1154.62 1159.77 1164.44 1169.62 1175.66 1182.84 2-Butanone(1) + triethylamine(2); T/K = 303.15 0.0686 0.721221 0.082 0.1149 0.723470 0.116 0.1643 0.726011 0.143 0.2101 0.728487 0.161 0.2639 0.731565 0.172 0.3102 0.734326 0.181 0.3502 0.736816 0.185 0.3869 0.739189 0.185 0.4500 0.743482 0.180 0.5081 0.747667 0.172 1092.17 1093.65 1095.56 1097.57 1100.29 1102.73 1105.13 1107.37 1111.65 1115.97 0.5652 0.6051 0.6561 0.7087 0.7630 0.7945 0.8542 0.8987 0.9500 0.752023 0.755192 0.759446 0.764061 0.769188 0.772200 0.778238 0.783012 0.788818 0.159 0.151 0.137 0.121 0.107 0.087 0.062 0.043 0.021 1120.58 1124.04 1128.72 1134.02 1139.97 1143.48 1150.54 1156.33 1163.38 erty, F, are calculated using the equations [13,17]: F id (F = V ; CP ) = x1 F1 + x2 F2 (2) and  (F E ) = F id = 1 F1 + 2 F2 (F = ˛P ; T ) (3) where CP is the isobaric heat capacity, i = xi Vi /Vid the volume fraction, T , the isothermal compressibility, and Fi , the F value of component i, respectively. For S and u, the ideal values are calculated according to [17]: Sid = Tid − an F-test [18] at the 99.5% confidence level. Table 4 lists the parameters Ai obtained in the regression, together with the standard deviations , defined by: TV id ˛id2 P CPid  1 N−k  E E (Fcal − Fexp ) 2 1/2 (8) where N is the number of direct experimental values. Results on VE and SE are shown graphically in Figs. 1 and 2. No data have been encountered in the literature for comparison. Hereafter, we are referring to values of the excess molar properties at equimolar composition and 298.15 K. (4) and uid =  1 id Sid 1/2 (5) where id = (x1 M1 + x2 M2 )/Vid (Mi , molecular mass of the i component). In this work, we have determined the excess functions: F E = F − F id (6) 4. Results and discussion Table 2 lists values of densities, calculated VE and of u vs. x1 , the mole fraction of the 2-butanone. Table 3 contains the derived quantities SE , ˛EP and uE . The data were fitted by unweighted leastsquares polynomial regression to the equation: k−1  F E = x1 (1 − x1 ) Ai (2x1 − 1)i (7) i=0 where F stands for the properties cited above. The number of coefficients k used in Eq. (7) for each mixture was determined by applying Fig. 1. VE for the 2-butanone(1) + amine(2) systems at atmospheric pressure and 298.15 K. Full symbols (this work): (䊉), DPA; (), DBA; (), TEA. Solid lines, calculations with Eq. (7) using the coefficients from Table 4. Dashed lines, results form the Flory model (see text). I. Alonso et al. / Thermochimica Acta 512 (2011) 86–92 90 Table 3 Excess functions at 298.15 K for S , adiabatic compressibility, u, speed of sound, and ˛P , isobaric thermal expansion coefficient of 2-butanone(1) + amine(2) mixtures. SE /TPa−1 uE /m−1 ˛EP /10−6 K−1 2-Butanone(1) + dipropylamine(2) 0.0592 1.89 0.1027 3.14 0.1509 4.26 0.2001 5.11 0.2446 5.91 0.2958 6.46 0.3545 7.33 0.4003 7.67 0.5006 8.30 0.5992 8.14 0.6474 7.92 0.7531 6.78 0.8048 5.96 0.8557 4.48 0.9041 2.97 0.9471 1.86 −0.95 −1.63 −2.25 −2.71 −3.15 −3.45 −3.94 −4.13 −4.52 −4.48 −4.39 −3.82 −3.39 −2.58 −1.69 −1.12 1.37 0.73 −0.23 −0.73 −0.48 0.51 2.25 3.63 5.35 4.19 2.86 0.23 0.07 0.85 2.19 2.64 2-Butanone(1) + dibutylamine(2) 0.0681 2.90 0.1038 4.25 0.1625 6.18 0.2034 7.23 0.2603 9.09 0.3112 10.46 0.3523 11.41 0.3937 12.12 0.4420 13.39 0.5018 14.18 0.5455 14.55 0.6036 15.10 0.6515 15.01 0.7003 14.69 0.7473 14.17 0.7978 12.88 0.8456 11.08 0.9022 8.04 0.9482 4.81 −1.81 −2.65 −3.88 −4.51 −5.66 −6.48 −7.04 −7.43 −8.16 −8.64 −8.82 −9.14 −9.04 −8.80 −8.44 −7.65 −6.56 −4.76 −2.85 0.88 1.77 3.61 5.19 7.59 9.76 11.46 13.04 14.73 16.11 16.79 17.01 16.64 15.70 14.32 12.19 9.68 6.25 3.28 2-Butanone(1) + triethylamine(2) 0.0709 2.73 0.1149 3.67 0.1580 4.19 0.2181 4.62 0.2610 4.45 0.3203 4.40 0.3605 4.17 0.4159 3.63 0.4607 3.16 0.5106 2.60 0.5701 1.86 0.6039 1.31 0.6600 0.90 0.7122 0.31 0.7604 −0.28 0.8023 −0.50 0.8437 −1.12 0.8921 −0.99 0.9456 −0.55 −1.03 −1.38 −1.55 −1.69 −1.57 −1.52 −1.40 −1.13 −0.89 −0.63 −0.26 0.01 0.19 0.47 0.73 0.79 1.07 0.89 0.52 7.90 9.82 10.47 10.41 10.18 10.21 10.53 11.34 12.19 13.08 13.67 13.56 12.44 10.11 6.88 3.51 −0.03 −3.42 −4.52 x1 Mixtures of 2-butanone with a given alkane are characterized by strong dipolar interactions between the ketone molecules. Thus, for the heptane system, HE and VE values are 1338 J mol−1 [19] and 0.794 cm3 mol−1 [20], respectively. The large positive VE value indicates that the interactional contribution to this excess function, due to the disruption of the ketone–ketone interactions upon mixing, is much more important than those related to effects which contribute negatively to VE (structural effects arising from interstitial accommodation of one component into the other and free volume effects). Dipropylamine and dibutylamine are secondary amines, and are weakly self- Fig. 2. SE for the for the 2-butanone(1) + amine(2) systems at atmospheric pressure and 298.15 K. Full symbols (this work): (䊉), DPA; (), DBA; (), TEA. Solid lines, calculations with Eq. (7) using the coefficients from Table 4. associated [21]. Accordingly, the mixtures with alkanes show relatively low HE values: 456 J mol−1 for DPA + heptane [22], and 277 J mol−1 for DBA + heptane (at 303.15 K) [23]. The corresponding VE values are lower than in the case of 2-butanone solutions: 0.258 cm3 mol−1 (DPA + heptane) and 0.052 cm3 mol−1 (DBA + heptane) [24]. The latter value suggests that structural effects may become important, which is supported by the negative VE of the DBA + hexane system, −0.185 cm3 mol−1 [24]. Such effects are also relevant in mixtures including TEA [25], a weakly polar tertiary amine. In solutions with heptane, HE = 112 J mol−1 and VE = 0.1255 cm3 mol−1 [26], while in the hexadecane system, HE = 322 J mol−1 [27] VE = −0.0979 cm3 mol−1 [28]. We note that for the studied mixtures, VE is positive. Therefore, the contribution to VE from the breaking of the interactions between like molecules upon mixing is predominant over the negative contributions from structural effects and interactions between unlike molecules. The existence of such interactions is supported by the VE decrease observed in 2-butanone mixtures when heptane is replaced by DPA, two solvents of similar size. It is remarkable that the VE , ˛Ep and SE magnitudes are positive for propanone, or 2-butanone +DPA, +DBA or +TEA systems (Tables 2 and 3 Figs. 1–3), while they are negative quantities for propanone or 2-butanone +aniline, +N-methylaniline, or +pyridine [5,6]. For example, in the case of the 2-butanone + aniline and SE = −113.4 TPa−1 . This means that interactions between unlike molecules are much stronger in mixtures including aromatic amines. In fact, the strength of the 2-propanone–aniline interactions has been estimated to be −30.50 kJ mol−1 [4], a higher absolute value than that of the H-bonds between 1-alkanol molecules (−25 kJ mol−1 ). In addition, it is known that negative (∂V E /∂T )P values are encountered in systems characterized by complex formation, as amine + chloroform, and are interpreted in terms of a decrease in the molar volume of complex formation (with increasing temperature), which overcompensates for the decrease in the extent of complex formation [29,30]. The VE increase observed when replacing DPA by DBA may be ascribed to the interactions between 2-butanone molecules are broken more easily by DBA, due to its larger aliphatic surface. Moreover, the creation of the amine–ketone interactions is more difficult as the amine group is more sterically hindered in I. Alonso et al. / Thermochimica Acta 512 (2011) 86–92 91 Table 4 Coefficients Ai and standard deviations, (FE ) (Eq. (8)) for representation of the FE, a property at 298.15 K for 2-butanone(1) + amine(2) systems by Eq. (7). System T/K 2-Butanone + dipropylamine 293.15 298.15 2-Butanone + dibutylamine 303.15 293.15 298.15 2-Butanone + triethylamine 303.15 293.15 298.15 303.15 a Property FE E V VE uE SE ˛EP VE VE VE uE SE ˛EP VE VE VE uE SE ˛EP VE A0 0.562 0.576 −17.99 33.0 21.8 0.594 1.024 1.058 −34.4 56.43 64.42 1.121 0.624 0.664 −2.72 10.84 52.9 0.692 A1 0.018 −0.006 −4.3 6.3 3.5 0.022 0.141 0.168 −15.7 28.2 40.0 0.170 −0.318 −0.273 11.1 −22.7 35 −0.296 A2 0.127 −0.04 −2.3 3.6 −138 −0.03 0.159 0.161 −10.3 17.9 −30.5 0.11 0.218 0.223 0.7 4.0 −28 0.205 A3 −0.21 −0.20 3.3 −7.4 7 −0.21 −10.6 −0.27 5.6 −11.3 −197 −0.22 ␴(FE ) A4 0.27 201 0.23 0.002 0.002 0.07 0.11 0.18 0.002 0.002 0.002 0.06 0.11 0.04 0.003 0.002 0.002 0.06 0.12 0.3 0.002 FE = VE , units: cm3 mol−1 ; FE = uE , units: m s−1 ; F E = SE , units: TPa−1 ; F E = ˛EP , units: 10−6 K−1 . this amine. On the other hand, VE is higher for the TEA solution than for the DPA mixture. This reveals that the interactions between unlike molecules are more important in the latter system, which is confirmed by the larger ˛Ep value encountered for the TEA solution (Table 3). We note that the VE curves are shifted to higher mole fractions of 2-butanone, the smaller component, in solutions with DPA, or DBA (Fig. 1), which is typical of systems where free volume effects are present [19]. Similar trends are found for propanone +DPA, +DBA, or +TEA mixtures. The parame2 ter  = (u/uid ) − 1 is widely used to estimate the non-ideality of a system, [31–34] as solutions with strong deviations from the ideal behaviour are characterized by high  values. For example, for 2pyrrolidone mixtures, (methanol) = 0.8 and (ethanol) = 0.35 [32]. For systems with 2-butanone, (DPA) = −0.008; (DBA) = −0.014; (TEA) 0.001; (aniline) = 0198; (N-methylaniline) = 0.120; and (pyridine) = 0.070. This is in agreement with our previous findings: interactions between unlike molecules are weaker in DBA solutions, and such interactions are much stronger in those systems with aromatic amines. The replacement of 2-butanone by propanone in mixtures with DPA, DBA or TEA leads to increased VE values (see Figs. 1 and 3). This may be interpreted assuming that the higher positive contribution to VE from the disruption of the propanone–propanone interactions overcompensates the larger negative contribution related to stronger interactions between unlike molecules. On the other hand, structural effects increase with the size of the alkanone, as it is revealed by VE < 0 for the 2-heptanone + TEA mixture (I. Alonso, personal communication). Finally, we have applied the Flory model [35] to propanone or 2-butanone +DPA, +DBA, or +TEA systems. The reduction parameters for volume, V* and for pressure, P* , of pure substances are given in Table 1. A graphical comparison between experimental data and theoretical results is shown in Figs. 1 and 3. The model represents fairly well the VE curves, except that of the 2butanone + TEA mixture. Discrepancies may be due to structural effects related to the globular shape of TEA, which are also encountered in systems with 1-alkanols [36], or n-alkanes (see above). The Flory interaction parameters, X12 , determined in this work are (in J cm−3 ): 6.35 (2-butanone + DPA); 9.5 (2-butanone + DBA) and 7.05 (2-butanone + TEA), and 7.75 (propanone + DPA); 14.85 (propanone + DBA) and 10.4 (propanone + TEA). This newly points out that interactions between like molecules are more relevant in propanone solutions, or in mixtures with DBA compared with those including DPA. 5. Conclusions In this work, we have determined VE , SE and ˛Ep for 2-butanone +DPA, +DBA, or +TEA. These excess functions are positive, and increase when replacing DPA by DBA or TEA. This may be attributed to interactions between unlike molecules are more important in the DPA solution. The replacement of 2-butanone by propanone leads to increased VE values, which may be attributed to interactions between like molecules are more relevant in propanone systems, which is confirmed by Flory calculations. Data suggest that the interactions between unlike molecules are weaker in the studied systems than in 2-butanone + aromatic amine mixtures. Acknowledgements E Fig. 3. V for the propanone(1) + amine(2) systems at atmospheric pressure and 298.15 K. Full symbols [6]: (䊉), DPA; (), DBA; (), TEA. Solid lines, results form the Flory model (see text). The authors gratefully acknowledge the financial support received from the Consejería de Educación y Cultura of Junta de Castilla y León, under the Project VA052A09 and from the Ministerio de Educación y Ciencia, under the Project FIS2007-61833. I.A. 92 I. Alonso et al. / Thermochimica Acta 512 (2011) 86–92 also gratefully acknowledges the grant received from the Junta de Castilla y León. References [1] P. Bour, C.N. Tam, J. Sopková, F.R. Trouw, J. Chem. Phys. 108 (1998) 351–359. [2] E.S. Eberhardt, R.T. Raines, J. Am. Chem. Soc. 116 (1994) 2149–2150. [3] B. Blanco, M.T. Sanz, S. Beltrán, J.L. Cabezas, J. Coca, Fluid Phase Equilib. 175 (2000) 117–124. [4] I. Alonso, V. Alonso, I. Mozo, I. García de la Fuente, J.A. González, J.C. Cobos, J. Chem. Eng. Data 55 (2010) 2505–2511. [5] I. Alonso, I. Mozo, I. García de la Fuente, J.A. González, J.C. Cobos, J. Chem. Eng. Data (submitted for publication), doi:10.1021/je100472t. [6] I. Alonso, I. Mozo, I. García de la Fuente, J.A. González, J.C. Cobos, J. Mol. Liq. 155 (2010) 109–114. [7] IUPAC: Atomic weights of the elements 1995 (IUPAC technical report), Pure Appl. Chem., 68 (1996) 2339–2359. [8] M.L. McGlashan, J. Chem. Thermodyn. 22 (1990) 653–663. [9] H. Preston-Thomas, Metrología 27 (1990) 3–10. [10] J.A. Riddick, W.B. Bunger, T.K. Sakano, in: A. Weissberger (Ed.), Organic Solvents, Techniques of Chemistry, vol. II, Wiley, New York, 1986. [11] J. Nath, J. Chem. Thermodyn. 30 (1998) 885–895. [12] K.N. Marsh, Recommended Reference Materials for the Realization of Physical Properties, Blackwell Scientific Publications, Oxford, 1987. [13] G.C. Benson, C.J. Halpin, A.J. Treszczanowicz, J. Chem. Thermodyn. 13 (1981) 1175–1183. [14] E. Junquera, G. Tardajos, E. Aicart, J. Chem. Thermodyn. 20 (1988) 1461–1467. [15] K. Tamura, K. Ohomuro, S. Murakami, J. Chem. Thermodyn. 15 (1983) 859–868. [16] K. Tamura, S. Murakami, J. Chem. Thermodyn. 16 (1984) 33–38. [17] G. Douheret, M.I. Davis, J.C.R. Reis, M.J. Blandamer, Chem. Phys. Chem. 2 (2001) 148–161; G. Douheret, C. Moreau, A. Viallard, Fluid Phase Equilib. 22 (1985) 277–287. [18] P.R. Bevington, Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, 1969. [19] O. Kiyohara, Y.P. Handa, G.C. Benson, J. Chem. Thermodyn. 11 (1979) 453–460. [20] K. Ohomuro, K. Tamura, S. Murakami, J. Chem. Thermodyn 19 (1987) 163–169. [21] S. Villa, J.A. González, I. García de la Fuente, N. Riesco, J.C. Cobos, J. Solut. Chem. 31 (2002) 1019–1038. [22] F. Sarmiento, R. Bravo, M.I. Paz Andrade, R. Kechavarz, H. Tachoire, Thermochim. Acta 68 (1983) 273–281. [23] I. Velasco, S. Otín, C. Gutiérrez Losa, J. Chim. Phys. 75 (1978) 76–78. [24] T.M. Letcher, J. Chem. Thermodyn. 4 (1972) 159–173. [25] N. Riesco, J.A. González, S. Villa, I. García de la Fuente, J.C. Cobos, Phys. Chem. Liq. 41 (2003) 309–321. [26] M. Bender, J. Hauser, A. Heintz, Ber. Bunsenges. Phys. Chem. 95 (1991) 801–811. [27] R. Philippe, G. Delmas, Int. Data Ser. Sel. Data Mixtures Ser. A 2 (1983) 154–168. [28] N. Riesco, S. Villa, J.A. González, I. García de la Fuente, J.C. Cobos, Fluid Phase Equilib. 202 (2002) 345–358. [29] J.G. Magalhaes, R.B. Tôrres, P.L.O. Volpe, J. Chem. Thermodyn. 40 (40) (2008) 1402–1417. [30] A. Chand, Y.P. Handa, D.V. Fenby, J. Chem. Thermodyn. 7 (1975) 401–402. [31] A.K. Das, B.L. Jha, J. Mol. Liq. 50 (1981) 155–186. [32] S.K. Mehta, R.K. Chauhan, R.K. Dewan, J. Chem. Soc. Faraday Trans. 92 (1996) 1167–1173. [33] R. Mehra, Z. Phys. Chem. 219 (2005) 425–437. [34] J.A. González, I. Mozo, I. García de la Fuente, J.C. Cobos, N. Riesco, Phys. Chem. Liq. 46 (2008) 390–407. [35] P.J. Flory, J. Am. Chem. Soc. 87 (1965) 1833–1838. [36] S. Villa, N. Riesco, I. García de la Fuente, J.A. González, J.C. Cobso, Fluid Phase Equilib. 216 (2004) 123–133. [37] B. González, A. Domínguez, J. Tojo, J. Chem. Thermodyn. 38 (2006) 707–716. [38] C.M. Kinart, A. Cwiklinska, W.J. Kinart, A. Bald, J. Chem. Eng. Data 49 (2004) 1425–1428. [39] A. Pal, R. Gaba, S. Sharma, J. Chem. Eng. Data 53 (2008) 1643–1648. [40] P. Kokkonen, J. Chem. Thermodyn. 14 (1982) 585–591. [41] A.B. Pereiro, E. Tojo, A. Rodríguez, J. Canosa, J. Tojo, J. Chem. Thermodyn. 38 (2006) 651–661. [42] I.M.S. Lampreia, E.F.G. Barbosa, Fluid Phase Equilib. 71 (1992) 125–142. [43] F. Comelli, R. Francesconi, J. Chem. Eng. Data 40 (1995) 808–810. [44] S. Villa, N. Riesco, I. García de la fuente, J.A. González, J.C. Cobos, Fluid Phase Equilib. 198 (2002) 313–329. [45] S.L. Oswal, P. Oswal, R.L. Gardas, S.G. Patel, R.G. Shinde, Fluid Phase Equilib. 216 (2004) 33–45. [46] L.-S. Lee, M.-L. Chuang, J. Chem. Eng. Data 42 (1997) 850–853. [47] S. Villa, N. Riesco, I. Garcia de la Fuente, J.A. González, J.C. Cobos, Fluid Phase Equilib. 190 (2001) 113–125. [48] F. Ratkovics, L. Domonkos, Acta Chim. Acad. Sci. Hung. 89 (1976) 325–330. [49] P. Goralski, M. Wasiak, A. Bald, J. Chem. Eng. Data 47 (2002) 83–86. [50] J.-P.E. Grolier, G.C. Benson, P. Picker, J. Chem. Eng. Data 20 (1975) 243–246. [51] J.-P.E. Grolier, G. Roux-Desgranges, M. Berkane, E. Jiménez, E. Wilhelm, J. Chem. Thermodyn. 25 (1993) 41–50.