1 74 BINARY MIXTURES CONTAINING AMINES THERMODYNAMICS OF BINARY MIXTURES CONTAINING AMINES BY J. L. COPP AND D. H. EVERETT Chemistry Dept., University College, Dundee (University of St. Andrews) Received 3rd February, 1953 A study has been made of the thermodynamics of the following systems: triethyl- amine + water, diethylamine + water, triethylamine + ethanol, diethylamine 4 ethanol. New measurements are reported for liquid-vapour equilibria for the last three systems, while heats of mixing have been measured calorimetrically for the first two. All four systems exhibit, as common features, negative heats of mixing and negative excess entropies of mixing. In the first three systems the excess free energies are positive while for the last, the excess free energy is negative at room temperature but becomes positive above 60" C.The relationships between excess thermodynamic functions and the conditions for critical solution phenomena in binary mixtures are outlined and a rough rule is proposed, according to which the excess free energy at a mole fraction of 0.5 should reach a value of about T cal/mole at the critical temperature. This leads to an elementary demonstra- tion of the reasons for the relativeIy frequent occurrence of upper consolute phenomena compared with lower consolute phenomena. The limited experimental data provide qualitative support for the criterion suggested. A brief account is given of the relation- ship between the thermodynamic criteria and the structural factors which have been shown to govern the appearance of lower consolute phenomena.Examples of liquid systems which either exhibit a lower consolute temperature (LCT) or in which the solubility of one liquid in the other decreases with increase in temperature, appear to be restricted, with few exceptions, to mixtures of water with secondary or tertiary amines,I ketones, ethers or alcoholic ethers?* 41 These systems must exhibit a common thermodynamic behaviour which is presumably determined by a common pattern of molecular interactions in solu- tion. It is important, therefore, to note that the organic constituents of these mixtures contain either a nitrogen atom, or an oxygen atom, which can interact through a hydrogen bridge with a hydroxyl group of a water molecule. OnJ . L. COPP AND D. H . EVERETT 175 mixing the components, profound changes in the labile hydrogen-bonded structure of liquid water can be expected.This qualitative feature, held in common by binary liquid mixtures with retrograde mutual solubility curves, has long been recognized,3 but further progress toward a quantitative theory of the phenomenon has been delayed by the lack of adequate thermodynamic data. It is hoped that determinations of the excess thermodynamic functions for mixtures of (i) water and diethylamine (LCT - 140" C) together with the values reported by Kohler 4 and supplemented by the present work for mixtures of (ii) water and triethylamine (LCT = 18.3" C ) will contribute to a discussion of the origin of lower consolute temperatures, and that the values reported for the excess functions in the related mixtures (iii) ethanol and diethylamine, and (iv) ethanol and tri- ethylamine may be more immediately amenable to detailed theoretical analysis.EXPERIMENTAL The thermodynamic results reported in this paper are based on three sets of experiments. (i) Measurements of the vapczur pressures of diethylamine and of triethylamine from room temperature to their normal boiling points. (ii) Direct measurements of the heats of mixing of (a) water and diethylamine, and (b) water and triethylamine. (iii) Determinations of isothermal vapour-liquid equilibrium diagrams for mixtures of (a) water and diethylamine, (b) ethanol and diethylamine, (c) ethanol and tri- ethylamine. MATERIALS.- Water, once distilled, was further purified, as required, by passage through an ion-exchange column.Ethanol was obtained by fractionating absolute alcohol. The distillate was dried and stored over magnesium ethylate.5 Diethylamine and triethylamine were obtained from commercial products of high quality by repeated fractionation from KOH pellets. The fractions used distilled at temperatures constant to within 0.01 " C, and weighed samples of these materials neutral- ized the theoretical amounts of standard acid (& 0.1 %). Temperature measurements were made with mercury-in-glass thermometers placed in wells with their bulbs completely immersed to a constant level in mercury. The emergent stems were jacketed with tap water, and stem corrections were applied to all readings. The thermometers were calibrated under the conditions of use by recording readings when pure water (or benzene) boiled at a series of measured pressures in an ebulliometer of standard design.6 The true boiling temperature at each fixed pressure was obtained from vapour pressure equations for water 7 and for benzene.* Calibrations were checked at intervals.Although thermometer readings could be made with an accuracy of about 0.01", the corrected temperatures on the absolute scale may be uncertain to f 0.05". Pressure measurements were made with a mercury-in-glass U-type manometer (diam. 13 mm), and a cathetometer reading to 0.05 mm. Readings were corrected to standard conditions of temperature and gravity. (i) VAPOUR PRESSURES OF PURE comoNENTs.-Only fragmentary vapour pressure data are available in the literature for diethylamine 9 and triethylamine.10 New measure- ments required for this work were made (a) by the static isoteniscope method,ll and (b) by recording boiling points under fixed pressures of dry nitrogen in an ebulliometer of small capacity.12 The isoteniscope was charged by distilling the base in vacuo from a side tube which was subsequently sealed off.The specimen was thoroughly degassed before each pressure reading. Diethylamine.-The static (15' to 55" C) and dynamic (35" to 55" C) measurements are too numerous to report in detail. For both sets, the observed equilibrium tem- perature at each experimental pressure is given to within f 0.04" C by eqn. (1). loglo P(mm) = 6.97237 - 1127-0/(t "C + 220). (1) This also reproduces to f 1 mm the vapour pressures measured by Pohland and Mehl9 between - 40" G and 20' C.The normal boiling point of diethylamine is 55.45' C by eqn. (l), whereas Timmermans 13 quotes values of 55.5" C and 55.9" C.176 BINARY MIXTURES CONTAINING AMINES TriethyZurnine.-The static vapour pressures were greater than the corresponding dynamic values, the difference increasing from 0.5 mm at 25" C, to 20 mm at 90" C. The vapour pressures determined by Lattey 10 from 0" to 50" C are even larger than our static values. The equilibrium temperature at 1 atm accepted by Timmermans 13 is 89.35" C, and the three values obtained here are 89-50' C (fractionation during purifica- tion), 89.55" C (dynamic) and 88.6" C (isoteniscope). The obvious discrepancy in the static measurements possibly arises from instability of the base at these temperatures.Whatever the products, they clearly accumulate in the small vapour space of the isoteni- scope, whereas in the dynamic method they may be continually removed. We therefore accept the dynamic measurements as the best vapour pressures available for triethylamine. They are represented by eqn. (2), which reproduces the boiling points recorded at each experimental pressure to within (2) 0.02" C. loglo P(mm) = 740853 - 1307*8/(t "C + 272.3). (ii) HEATS OF MIxING.-The heats evolved on mixing weighed amounts of water and triethylamine at 15" C, and of water and diethylamine at 25" C, were determined in a simple calorimeter. The mixing system was a modification of the inverted bell and inner vessel, proposed by Tompa 14 for eliminating vapour space corrections.The amine (distilled in vacuo) was contained in an ampoule drawn out and sealed at both ends. This replaces the inner vessel in Tompa's design. The lower tip of the ampoule, which was mounted vertically on a movable carriage and centred under the fixed inverted bell, was broken under dry mercury contained in a silvered Dewar vessel (20 x 5 cm). The trapped air was pumped out, and a known weight of water was injected into the bell through bent capillary tubes. Finally, this assembly, with a Nichrome heater and a screw stirrer, was lowered into the calorimeter and fixed in position. The calorimeter and a similar reference vessel were placed in a thermostat and the temperature difference between them was measured to rt 0*002" with a six junction copper- constantan thermocouple connected in the amplifying circuit described by Meares 15 (I" C - 1 V).The liquids were mixed by first raising the ampoule to shatter its neck and by subsequently lowering and raising the ampoule ten times. After each mixing, the apparatus was calibrated electrically by the method of Braham and McInnes,ll the temperature rise in both experiments being obtained in the usual manner from voltage against time curves. 4 % and the figures in table 1 are means of several determinations. The deviations may arise from the extreme difficulty of ensuring complete mixing of components of widely differing densities with this mixing system. The figures given in table 1 may therefore by systematically lower than the true values. The results showed a scatter of about TABLE HEATS OF MIXING x MOLES OF TRIETHYLAMINE WITH 1 - x MOLES OF WATER X 0.080 0.086 0.100 0.142 0.204 0.258 0.306 AT 15" C IN CAL/MOLE - H E 290 310 375 490 550 595 590 X 0.370 0.400 0.472 0.560 0.607 0.676 - HE 585 565 550 510 495 450 TABLE HEATS HEATS OF MIXING x MOLES DIETHYLAMINE WITH 1 - x MOLES OF WATER AT 25" c IN CAL/MOLE X 0.029 0.106 0.200 0-282 0-353 0-425 0.523 0.620 0.726 0.856 - HE 210 500 690 750 795 810 795 720 650 400 (iii) VAPOUR PRESSURES OF BINARY MIXTURES.-The isothermal equilibrium properties of three binary amine solutions were determined by operating a recycling still, essentially similar to that of Brown and Ewald.17 The auxiliary apparatus used, and the experi- mental procedure adopted, were based on the recommendations of these authors.To prevent oxidation of the amines dry nitrogen was used as the confining gas. With the alcoholic amine solutions, steady states were attained after 2-3 h. To approach a steady state with mixtures of water and diethylamine (sp. gr. 0-67), it was essential to keep the contents of each trap well mixed with a simple magnetic stirrer.J . L . COPP AND D. H. EVERETT 177 Even so, because of erratic functioning of the Cottrell pump unreliable vapour composi- tions were obtained with this system. With the other systems, for which the relative volatility of the components was nearer unity, no difficulty was experienced. I I 1 I I I FIG. 1.-Total vapour pressures for mixtures of water and diethylamine at (a) 56-80" C, (b) 49-10" C, (c) 38-35' C ; vapour composition curves calculated.FIG. 2.-The excess thermodynamic functions for mixtures of (a) water and triethyl- amine at lo" C (data from Kohler) and (6) water and diethylamine at 49.10" C. Calori- metric heats of mixing are denoted by open circles. After each determination of pressure and temperature, samples of the liquid phase and of the condensed vapour phase were withdrawn slowly into chilled syringe pipettes, and transferred to test-tubes with ground-glass stoppers. The weight percentage of amine in each sample was determined in duplicate by slowly injecting a known weight178 BINARY MIXTURES CONTAINING AMINES of the solution into a measured excess volume of standard hydrochloric acid (0.5 N). The excess acid was titrated with standard caustic soda to the grey end point of screened methyl red.The duplicate analyses invariably agreed to within 1 part in 500. For the most unfavourable system, water (mol. wt. 18) and diethylamine (mol. wt. 73), this error corresponds to an uncertainty in the mole fraction x2 of amine which increases from 1 in 500 when x2 is small, to about 3 in 500 when x2 is greater than 09. In presenting the results, x2 and y~ will denote respectively, the mole fraction of amine in binary liquid and vapour phases which are in equilibrium at a temperature T, and a total pressure P. (a) Water + triethyZumine.-Three sets of isothermal vapour-liquid equilibrium measurements have been reported for this system at temperatures below its critical solution temperature. The measurements of Lattey,lo and of Roberts and Mayer 18 show that the excess free energy change on mixing the components is positive for all values of xp, but the results are not sufficiently accurate for estimates of the excess heat ccntent and entropy functions to be made.More reliable measurements of total pressure as a function of x2 have been made at 0", 10" and 18" C by Kohler,4 and summarized in a table of derived values for the excess functions GE, HE and TSE, at 10" C . The dependence of these functions on x2 is shown by the full curves in fig. 2(a). The general correctness of this thermodynamic description TABLE 2.-EXCESS FUNCTIONS FOR MIXTURES OF WATER AND DIETHYLAMINE IN CALIMOLE to c x2 38.35 0.0 0.05 010 0.20 0-30 0.40 0.50 0.60 0.70 0.80 0.90 0.95 1.00 49-10 0.0 0-05 0 10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.95 1-00 0.05 0.10 0.20 0.30 0.40 0-50 0.60 0.70 0.80 0.90 0.95 1.00 56-80 0.0 YZ 0.0 0-653 0.715 0.766 0.809 0.846 0.877 0.905 0.928 0.947 0.968 0.980 1 *oo 0.0 0.665 0.7 1 1 0.755 0.792 0-826 0.858 0.887 0.91 1 0-935 0,958 0.974 1 *oo 0.0 0.68 1 0.720 0.753 0.784 0.814 0.843 0.870 0-894 0-917 0.946 0.986 1-00 P 50.7 140.3 167.7 197-2 227.0 257.1 287.0 316.9 344.5 367.2 388-1 397.9 407.9 88.5 255.0 291.0 333.0 373.0 413.5 454.0 493.5 528.5 558.0 5 84.0 596.4 608.6 128-6 388.5 438.0 485.5 532-3 579.5 626.5 672.0 709.0 740.5 769.0 782.5 795.9 GE 0 53 93 140 162 170 168 157 139 111 69 39 0 0 64 110 166 192 202 200 187 165 127 77 43 0 0 72 125 189 222 234 232 21 8 191 148 86 46 0 - TSE 0 330 560 855 1050 1125 1120 1060 900 640 300 120 0 -HE 0 266 450 689 858 923 920 873 735 513 223 77 0J .L. COPP AND D . H . EVERETT 179 of the system 8" C below its critical solution temperature, is confirmed by our calorimetric determinations of HE at 15" C (open circles in fig. 2(u)). (6) Wafer + diethylamine.-The mutual solubilities of water and diethylamine in the liquid state are limited, if at all,19 only at temperatures above 120" C.20~ 21 Hitherto, no vapour-liquid equilibrium measurements over a wide range of composition have been reported for this system. The results of three P, x2 isotherms, at the temperatures 38-35.' C, 49.10" C and 56.85" C are shown in fig. 1. Since the measured vapour compositions were erratic, values for 372 were calculated at intervals of 0.025 in x2 by the numerical integration method of Boissanas 22 from P, x2 values interpolated from curves drawn on a large scale.This method of calculation does not allow of the introduction of cor- rections for vapour imperfection. The excess chemical potentials pf and pf, and the excess free energy function GE were calculated at round values of x2, by means of the following equations : (3) (4) The values of P, x2 and y2, used to calculate GE at each experimental temperature, are given in table 2, together with estimates of TSE and HE at the middle temperature. Vapour pressures of the pure components were obtained, P1 from the literature,? and P2 from PiE = RT In (Pyi/PiXj), GE = XI$ + ~2p;. iqn. (1). to c 64-85 49-60 34-85 xz O~OOOO 0.1040 0.2405 0.3040 0.3705 0-441 5 0.6055 0.6540 0.7130 0.7730 0.8485 0.9280 1 *oooo 0~0000 0.1 305 0,2105 0.3260 0.4185 0.4575 0.5510 0.6740 0.7930 0.8690 0.9455 1 *moo 0-0000 0.08 10 0.1875 0.2865 0.3450 0.40 10 0.5265 0.5825 0.7250 08905 0.941 5 1 .oooo TABLE 3.-ETHANOL + TRIETHYLAMINE YZ 0*0000 0.1270 0.2640 0-3185 0.3705 0.4230 05370 0.5740 0.6170 0.6655 0-7480 0.8570 1~0000 0~0000 0.1655 0.2480 0.3585 0.4345 0.4645 0.53 15 0.6190 0-7 170 07955 0.9040 1~0000 O-oooO 0.1090 0.2435 0.3535 0.4050 0.4550 0-5490 0-5905 0.6930 0.8440 0-9 100 1 -0Ooo P mm 435.50 447.25 459.15 462.10 463-30 462.70 451.15 445.55 437.60 428.35 409-70 377-80 340-70 217.00 225.15 230.80 236.25 238.55 238.95 238.50 234.45 227.25 219.10 205.10 193.10 102.00 104.80 109.15 113.10 1 14-90 1 16-25 1 18.20 1 18-80 1 17.60 112.75 109.15 104.60 I.P cal/mole 0.0 0.0 140 25.0 41.0 620 130.5 155.0 197.5 2495 301.5 367.0 0.0 (- 2.5) 8.0 22.5 42.5 52.5 87-5 149.0 2305 292.5 327.5 0.0 (- 2.4) (- 2.6) - - 2-8 14.0 21.5 59.5 80-5 154-0 276.5 305-5 - 4 cal/mole 313.0 2575 229.5 200.0 170.5 1025 u .5 66.0 48.5 35.5 14.0 0.0 249.0 216.5 187.5 156.5 144.0 109-5 67.5 37.5 23.0 9.0 0.0 182.5 186.0 175.0 154.5 141-0 99.5 85.5 43.0 13.0 5.0 0.0 - - - GE cal/mole 0.0 32.5 72.5 87.5 100.0 110-0 113-5 110.5 103-5 94.5 76-0 39.5 0.0 0.0 30.0 520 76.5 90.0 94.5 99.5 94.0 77.5 60.5 26.5 0.0 12.5 33.0 520 62-5 69.5 80.5 83.5 73.5 42-0 22.5 0.0 -180 BINARY MIXTURES CONTAXNING AMINES The excess functions GE, T S E and H E for mixtures of water and diethylamine at 49.1 "C are represented by smooth curves in fig.2(b). Calorimetric determinations of the heat of mixing the components at 25" C (open circles) are in fair agreement with the values derived from the total pressure isotherms. (c) Ethanol + triethyZamine.-The results obtained in three series of measurements are given in table 3. In calculating the excess chemical potentials pf and $, corrections for vapour phase imperfections were introduced by eqn. (5) : ( 5 ) These correction terms may well be unreliable for systems of this kind but it seems prefer- able to make some correction rather than ignore vapour imperfections. 1 4 7 = RT In (Pyi/Pixi) + ( Vi - pj)(Pj - PI. TABLE ~.-EXCES FUNCTIONS FOR MIXTURES OF ETHANOL AND TRIETHYLAMINE IN CAL/MOLE AT 49.6" c x2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 G E 0 25 49 72 88 97 99 92 76 48 0 -TSE 0 160 283 334 369 367 328 305 283 191 0 - H E 0 135 234 262 281 270 229 213 207 143 0 TABLE 5.-AZEOTROPIC SOLUTIONS IN MIXTURES OF ETHANOL AND TRIETHYLAMINE P* mm 119.0 239.1 463.3 759.9 t * O c 34.85 49.60 64.85 77-10 ** 2 - - Y 2 8 0.605 0.480 0.371 0.284 TABLE EXCESS FUNCTIONS FOR MIXTURES OF ETHANOL AND DIETHYLAMINE IN CAL/MOLE x2 - GE - GE - GE - GE - TSE - H E t = 30.15" C t = 40.25" C t = 50*00° C t = 59-95'' C t - 50.00" C 0.0 0.1 0.2 0.3 0-4 0-5 0.6 0.7 0.8 0.9 1.0 0 125 143 146 135 115 85 50 0 I - 0 68 110 128 128 118 95 65 38 0 - 0 57 92 106 107 95 73 51 31 0 - 0 49 73 82 81 70 53 36 - 0 0 0 330 390 585 677 700 806 700 807 710 805 670 743 500 55 1 320 351 0 0 - - Vapour pressures P1 and P2 of the pure components 23 were calculated from empirical equations, and the molar volumes of the liquids were derived from published densities.24 25 The second virial coefficient of ethanol was calculated from its critical constants and a reduced equation of state.26 That of triethylamine was derived from the equation given by Lambert and Strong? The internal concordance of the results was tested by the method of Redlich and Kister.28 The areas A2 and A1 under smooth curves drawn separately through the points (pf, x2) and (pf, X I ) differed by about 18 %. In view of the uncertainty in pf and pf in dilute solutions, this agreement is satisfactory.Interpolated values of GE at rounded values of x2, together with estimates of TSE and H E at 49.6" C are shown in table 4. The excess functions for mixtures of ethanol and triethylamine at 49.6" C, represented by the smooth curves in fig.4(a) follow the pattern established for aqueous solutions of both di- and tri-ethylamines (cf. fig. 2(a) and 2(b)). Mixtures of ethanol and triethylamine, and of water and triethylamine, form positive azeotropes. The azeotropic characteristics determined for the former system at four temperatures are given in table 5.J . L. COPP AND D. H. EVERETT 181 (d) Ethanol + diethyZamine.-Four series of isothermal measurements of x2, y2 and P are shown in fig. 3. Corrections for vapour imperfection, which in this case were relatively large, were made as before (eqn. (5)). For diethylamine P2 was obtained from eqn. (1) ; V2 was derived from the density against temperature equation given by Swift,29 and /I2 was interpolated from the measurements of Lambert and Strong.27 FIG.3.-Total vapour pressures (0) and vapour compositions (0) for mixtures of ethanol and diethylamine at (a) 59.95" C, (b) 50.00" C, (c) 40.25" C, (d) 30.15" C. I - (a) (b) FIG. 4.-The excess thermodynamic functions for mixtures of (a) ethanol and amine at 49.6" C, and (b) ethanol and diethylamine at 50.0" C. triethyl- The areas under the curves (pf, X I ) and ( p t , x2) differ by 20 % at 40" C and 29 % at 50" C. This relatively large discrepancy at 50" C may reflect inaccuracies in either the primary measurements of P, x2 and y2 in dilute solution, or in the corrections for vapour imperfection.182 BINARY MIXTURES CONTAINING AMINES The values for GE given in table 6 were interpolated from smooth curves drawn through each isothermal set of (GE, x;?) points.Estimated mean values of SE were taken from the slopes of the best straight lines drawn through the points (GE, T,,), and assumed to apply at 50" C. By combining the interpolated values of GE at 50" C with the values for SE, the values for HE shown in table 6 were calculated. The excess functions for mixtures of ethanol and diethylamine at 50" C are shown in fig. 4(6). This mixture shows negative deviations from the ideal solution laws in the temperature range examined. Since, however, G E is increasing with temperature, it presumably becomes positive above 60" C. The four amine solutions considered in this paper thus belong to a thermodynamic group which is characterized by negative excess heat content and entropy functions.DISCUSSION The main object of the present work is to elucidate the thermodynamic charac- teristics of solutions which exhibit lower consolute temperatures. While certain thermodynamic properties can be established rigorously for solutions at the critical point, others can be deduced only if the system obeys certain simplifying condi- tions. The thermodynamic properties associated with simpler systems are dis- cussed below and compared with the available experimental data. In this way we hope to show that a simple approximate thermodynamic treatment is useful in throwing light on the main factors involved in critical solution phenomena, and in suggesting further work. points of a binary solution may be defined thermodynamically in terms of the behaviour of the excess functions.30 At an upper consolute point GENERAL THERMODYNAMIC CONSIDERATIONS.-The upper and lower COnSOlUte while at a lower consolute point (7) 32GE - R T .3 2 H E > O ; -- 32SE R where GE, HE and S E are respectively the excess Gibbs free energy, enthalpy and entropy per mole of solution. If, furthermore, GE(x2), HE(x2) and SE(x2) maintain the same sign for all x2 at a given T, it follows that at an upper consolute point : and at a lower consolute point : Subject to the above assumption these conditions are necessary, but not, of course, sufficient. Since for a phase to be stable 3 2 6 / 3 x 2 2 must be positive, it also follows that at the critical composition but at temperatures just above the upper consolute temperature and just below the lower consolute temperature - 13x22 x1x2' 3x22 3x22 G E > 0 ; HE > 0 ; SE > 0, or < 0 but satisfying (6) ; (8) G E > 0 ; H E < 0 ; SE < 0, and satisfying (7).(9) that is, the curvature of GE(x2) is less than at the critical point. Conditions (8) and (9) may be summarized 31 by saying that upper consolute temperatures are related to large positive deviations of the energy of the system from ideality, while lower consolute phenomena result from sufficiently large negative deviations of the entropy from ideality. This simple statement conceals, however, the subtle interplay of factors which leads to lower consolute points and which explains why such phenomena are so rare in comparison with upper consolute behaviour.The following discussion emphasizes the important thermo- dynamic factors leading to a lower consolute point.J . L. COPP AND D. H. EVERETT 183 If GE(x2) has a reasonably simple algebraic form, and the few available data seem to justify this assumption, then an increase in the curvature of GE(x2) at a given composition must follow from an increase in the magnitude of GE at this point. As the temperature changes towards the critical temperature the G E curve will bulge upwards until at some point on it x 1 ~ 2 ( 3 2 G E / 3 ~ 2 2 ) reaches the critical value of - RT. This point, which need not necessarily be that of maximum curvature, identifies the critical point of the system. At the critical temperature the GE(x2) curve will be at a critical stage in its upward growth, beyond which two phases will appear.For a curve of given shape the actual value of GE at some given concentration, x2 = 0.5 for example, may be used to test whether the GE(x2) curve has reached this stage. This criterion can be applied strictly only to a series of systems for which the G E curves are of closely similar shapes. It is interesting to examine the problem for the simple form for which the critical value of GE at x2 = 0.5 is RT/2, and the critical composition is 0.5. For a surprisingly large number of binary systems G(x2) is roughly sym- metrical about x2 = 0.5, often despite very marked asymmetry in HE and SE. We may expect, therefore, as a rough working rule, to encounter phase separation when the excess free energy at the middle of the concentration range reaches a value of about Tcal/mole.This criterion is well known for regular solutions (K(T) = or) but it also applies rigorously to all systems obeying (11). At an upper consolute point this critical value of C E can arise solely from simple energetic factors which affect the enthalpy of the solution, while not necessariIy affecting its entropy : thus regular solutions (SE = 0) can exhibit upper consolute phenomena. On the other hand, a lower consolute point will be observed only if the system has a large negative excess entropy accompanied by a relatively small negative excess enthalpy; a consideration of the nature of molecular inter- actions in solution shows that such conditions will not be of frequent occurrence.From a purely thermodynamic point of view the difficulty of satisfying the conditions for a lower consolute point can be illustrated in the following way. Consider a stable one-phase system satisfying the conditions (9) and which is therefore potentially able to separate into two phases when the temperature is raised. Suppose, for simplicity of argument, that the excess free energy is of the form (11) and at some reference temperature, TO, has a value, at x2 = 0.5, of Gf (0 in fig. 5). Since the excess entropy is negative, G E increases with T. However, if C: is positive (which as we shall see below is probable for most actual systems showing lower consolute points) S E falls with increase of T and the slope of GE(T) decreases. The curvature of GE(T) will be greater the larger the value of CIS: in comparison with Sf, and may be large enough to prevent G E reaching the critical value.This is illustrated in fig. 5 where GE (x2 = 0.5) is shown as a function of T for four values of the ratio S f / C f . System A will have a lower consolute temperature, system B a closed loop and D will not show phase separation. For system C, where the excess free energy curve just touches the critical line, no bulk phase separation will be expected although turbidity of the solution might be observed over a short temperature range. This has very recently been reported for mixtures of a- and p-picoline with water by Andon and C0x.32 Clearly, lower consolute behaviour will be shown only by those systems for which the correct balance between HE, SE and Cf is maintained.On the other hand, almost any system at 0 having excess entropy greater than - R/2 will separate into two phases on lowering the temperature : e.g., OE, OF (corresponding to a regular solution), and OG. It also follows that for a system to have a closed solubility loop Cf must be positive. This is in fact easily seen from (8) and (9), since HE has to change from a negative or zero value at the lower consolute184 BINARY MIXTURES CONTAINING AMINES temperature to a large positive value at the upper; hence, on the average at least, the excess heat capacity must be positive in this range of temperature. This argument assumes in effect that it is justifiable to extrapolate through the two- phase region by a smooth curve representing the state of a hypothetical unstable one-phase system.This procedure does not affect the conclusions drawn regarding the appearance of consolute points, but only the relationship between the upper and lower points, which can in fact be established by a more lengthy but rigorous argument if we move from the lower to upper consolute point through the one- phase region of the diagram. FIG. 5.-Schematic representation of variation of GE (x2 = 0.5) starting from 0, leading OA to lower consolute temperature, OB to closed solubility loop, OC to incipient phase separation, OD to no phase separation, OE, OF, OG to upper consolute temperatures, OF corresponds to a regular solution. Vertical dotted line separates lower consolute temperatures (on right) from upper consolute temperatures (on left).If the free energy does not follow (1 l), then the line relating the critical value of GE (x2 = 0.5) with temperature in related systems will be different, but without further knowledge of the algebraic forms of GE curves, the deviations from this line cannot be assessed. The most direct way of investigating the validity of the above conclusions is to use what few existing data there are to predict the positions of critical temperatures. This is done in fig. 6, where GE(x2 = 0.5) is plotted against temperature. Where the thermodynamic data are available only at temperatures at which x2 = 0.5 lies in the two-phase region, the excess free energy at this composition has been obtained by extrapolation from dilute solutions using the empirical equations given by Scatchard and his CO-workers.339 343 33 For diethylamine + water, if Cf were zero, a lower critical point would be expected at 100" C; as discussed below it seems almost certain that C' will be positive for this system, so the critical temperature will be somewhat higher.The observed value is about 140" C. For triethylamine + water a critical temperature of 0" C would be predicted as against 18" C observed. For both these systems it is remarkable that the criterion should be even approximately satisfied since, although the excess free energy curves are not particularly asym- metrical, the critical compositions are at mole fractions of amine of 0.30 and 0.07 respectively which indicates a small local deviation of G E from a symmetricalJ.L. COPP AND D. H. EVERETT 185 curve. Neither of the alcoholic solutioas studied appears likely to show a lower consolute point. For the systems benzene + methanol,33 and carbon tetrachloride + methanol 33 the excess free energies lie close to the critical values, but neither is known to exhibit a critical solution point although the former separates into two layers on addition of a small amount of potassium iodide. The upper critical temperature of the systems cyclohexane + methanoI,33 aniline + hexane 35 and platinum + gold 35 are given closely by the present criterion. Without more extensive data no more definite conclusions can be drawn. FIG. 6.-Experimental values of GE(x2 = 0.5) in relation to the line GE = RT/2. (1) water + diethylamine ; (3) ethanol + triethylamine ; ( 5 ) methanol + cyclohexane ; 33 (7) methanol + carbon tetrachloride ; 33 (2) water + triethylamine 4 ; (4) ethanol + diethylamine ; (6) methanol + benzene ;33 (8) hexane + aniline ; 35 (9) platinum 4- go1d.35 temperatures are indicated by *.Points (0) refer to one-phase data ; (0) to two-phase results ; experimental consolute STRUCTURAL CONSIDERATIONS.-The thermodynamic requirements which must be satisfied if a system is to show a lower consolute temperature can be summarized as (i) large negative excess entropy, (ii) small negative heat of mixing, (iii) the excess heat capacity, if positive, to be smaller than a critical value These generalizations are limited by our initial assumption that the excess function curves as functions of x2 do not exhibit double inflections.For those systems for which data are available this condition is satisfied, and we shall retain it in the present discussion.186 BINARY MIXTURES CONTAINING AMINES The first requirement immediately limits the possible systems to associated solutions, in which the two components can interact with one another to form a complex. Unfortunately systems of the kind which exhibit a large negative excess entropy, usually have a large negative excess enthalpy, so that a sufficiently high value of G E is not attained. As examples we may quote chloroform + acetone and ethanol + water ; 36 for the system ammonia + water HE < TSE and negative deviations from Raoult's law are observed. TABLE 7.-sUMMARY OF AQUEOUS SYSTEMS SHOWING LOWER CONSOLUTE TEMPERATURE OR A CLOSED SOLUBILITY LOOP (temperatures in "C) aliphatic amines (lower consolute point only) R= H CH3 C2Hs C3H7 C4H9 R2NH misc.misc. >12020,21 < - 243 < - 243 RN(CzH5)z > 120 20921 ? 18 1 ? ? N-substituted piperidines 37 (lower consolute point only) immisc. at 18 immisc. at 18 R= H CH3 C2HS C3H7 RNC5HlO > 150 48 7 <O ring-substituted piperidines 3 2 ~ 3 7 ~ 38, 39 R= H 2-CH3 3-CH3 4-CH3 HNtC5H9R) Tu - 227 23 5 189 TI > 150 80 57 86 substituted pyridines 32 R= H 2-CH3 3-CH3 4-CH3 picolines N(CsH4R) Tf misc. 80( ?) 110(?) misc. R= 2 : 4-CH3 2 : 5-CH3 2 : 6-CH3 lutidines NCsH3(R)2 T, 188-7 206.9 230.7 Ti 23.4 13.1 34.0 R= 2 : 4 : 6-CH31 cuIlidine NCsH2(R)3 T, TI alcoholic ethers 4h42 R = n-C4Hg ROCH2. CH2. OH Tu 128.0 Tr 49.0 C3H7O CH .CH2OH TU 162-0 I TI 43.0 CH3 C3H70 CH2CHOH TU 172.0 I fi 34.5 CH3 190 6 iso-CsH9 150-0 24.5 A survey of the literature indicates, however, that, among aqueous systems, solutions of both amines and alcohols can exhibit lower consolute phenomena, often associated with a closed loop (table 7). Empirically, this is achieved by introducing a sufficiently large number of hydrocarbon groupings into the amine or alcohol molecule. A detailed discussion of the results collected together in table 7 must await further understanding of the structure of aqueous solutions, and of the relative magnitude of HE, S E and C'. The discussions of Butler,44 Eley,4s and of FrankJ . L. COPP AND D. H. EVERETT I87 and Evans46 outline various ways in which such a theory might be developed.It appears that transfer of a molecule containing a substantial hydrocarbon grouping from the pure liquid state into aqueous solution will be accompanied both by a negative heat and negative entropy change. It appears, however, that the entropy effect predominates so that the increments for an additional CH2 group lead to a small increase in the excess free energy of the system; by adding sufficient hydrocarbon groups the excess free energy may be raised to the critical value. There is also a considerable body of evidence47 to indicate that addition of hydrocarbon groupings to a molecule will enhance its partial molar heat capacity in aqueous solutions. Consequently we shall expect, qualitatively, that addition of hydrocarbon groupings will both decrease the lower critical temperature and also tend to lead to closed solubility loops.These tendencies are clearly shown in the table. CoNcLusI0Ns.-The above discussion shows that the presence of lower consolute behaviour in aqueous media is closely related to two important phe- nomena (i) association between the components usually by a hydrogen bonding mechanism, (ii) heat, entropy and heat capacity effects arising from the inter- action of the " inert " hydrocarbon grouping of the second component with the water structure. A fuller understanding of the phenomenon is thus to be sought in a more fundamental study of these two effects separately ; when they are under- stood then the explanation of lower consolute temperatures will follow immediately. Essentially similar considerations will apply to systems containing aIcohols instead of water ; here the requisite balance of thermodynamic functions seems to occur in mixtures of polyhydric alcohols with aromatic amino compounds.1 Rothmund, 2. physik. Chem., 1898,26,433. 2 Rothmund, Loslickheit u. Loslichkeitbeeinflusszing (Barth, Leipzig, 1907), pp. 69-73. 3 e.g. Hirschfelder, Stevenson and Eyring, J. Chem. Physics, 1937, 5, 912. 4 Kohler, Monatsh., 1951, 82, 913. 5 Lund and Bjerrum, Ber., 1931, 64, 210. 6 Swietoslawski, Ebulfiometric Measurements (Reinhold, New York, 1943, p. 29. 7 Keyes, J. Chem. Physics., 1947, 15, 602. 8 Selected Values of Properties of Hydrocarbons, A.P.I. project 44 (Nat. Bur. Stands., 9 Pohland and Mehl, 2. physik. Chem. A, 1933, 164,48. 10 Lattey, J .Chem. SOC., 1907, 91, 1959, 1971. 11 Smith and Menzies, J. Amer. Chem. SOC., 1910, 32, 1412. 12 Swietoslawski, ref. (6), p. 19. 13 Timmermans, Physico-Chemical Constants (Elsevier, London, 1950), pp. 521, 523. 14 Tompa, J. Polymer. Sci., 1952, 8, 51. 15 Meares, Trans. Faraday SOC., 1949,45, 1066. 16Braham and McInnes, J. Amer. Chem. SOC., 1917, 39, 2116. 17 Brown and Ewald, Austral. J. Sci. Res., 1950, 3, 306. 18 Roberts and Mayer, J. Chem. Physics, 1941, 9, 852. 19 Friendlander, 2. physik. Chem., 1901, 38, 389. 20 Lattey, Phil. Mag., 1905 (vi), 10, 398. 21 Guthrie, Phil. Mag., 1884 (v), 18, 495. 22 Boissanas, Helv. chim. Acta, 1939, 22, 541. 23 Kretschmer and Wiebe, J. Amer. Chem. SOC., 1949, 71, 1793. 24 Kretschmer, Nowakowska and Wiebe, J. Amer. Chem. SOC., 1948, 70, 1785. 25 Friend and Hargreaves, Phil. Mag., 1944, 35, 619. 26 Scatchard and Raymond, J. Amer. Chem. SOC., 1938, 60, 1282. 27 Lambert and Strong, Proc. Roy. SOC. A , 1950, 200, 566. 28 Redlich and Kister, Ind. Eng. Chem., 1948, 40, 345. 29 Swift, J. Amer. Chem. SOC., 1942, 64, 1 15. 30 Prigogine and Defay, Thermodynamique Chimique (Desoer, Liege, 1950), p. 294 ; English trans. (in press). Cf. Kuenen, Verdampfung und Verflussigung von Gemischen, (Barth, Leipzig, 1906), p. 159. Washington, D.C., table 5K). 31 Prigogine and Defay, Thermodynamique Chimique, p. 419.188 CRITICAL SOLUTION TEMPERATURES 32 Andon and Cox, J. Chem. SOC., 1952,401. 33 Scatchard, Wood and Mochel, J . Amer. Chem. SOC., 1946, 68, 1957. 34 Scatchard and Raymond, J. Amer. Chem. SOC., 1938, 60, 1282. 35 Scatchard and Hamer, J . Amer. Chem. SOC., 1935, 57, 1805. 36 Prigogine and Defay, Thermodynainique Chimique, pp. 415, 455. 37 Flaschner, 2. physik. Chem., 1908, 62,493. 38 Flaschner, J . Chem. SOC., 1909, 95, 668. 39 Flaschner and McEwan, J . Chem. Soc., 1908,93, 1000. 40 Rothmund, see ref. (1). 41 Cox and Cretcher, J. Amer. Chem. SOC., 1926, 48, 451. 42 Cox, Nelson and Cretcher, J. Amer. Chem. SOC., 1927, 49, 1081. 43 Pickering, J . Chem. SOC., 1893,63, 141. 44 Butler, Trans. Faraday Sac., 1937, 33,229. 45 Eley, Tram. Faraday SOC., 1944,40, 184. 46 Frank and Evans, J. Chem. Physics, 1945,13,507. 47 cf. Eley, Trans. Furaday SOC., 1944, 40, 184. Frank and Evans, J. Chem. Physics, 1945, 13, 507. Everett and Wynne-Jones, Proc. Roy. SOC. A , 1941, 177, 499. Morrison, J. Chern. SOC., 1952, 3814.