S.LINDENBAUM
8 14
initial particle radius. The data collected in the early stages of reaction exhibited anomalies which were apparently caused by the cracking and flaking off of the initially formed fluoride film. It is believed that this was the result of initial exposure of the oxide to fluorine a t room temperature rather than at the elevated reaction temperature. The reaction rate was proportional to the square root of the fluorine pressure. Since this pressure dependence can be explained by assuming either fluorine atoms or copper ions to be the diffusing species, the data do not allow identification of the diffusing species.
Acknowledgments. The authors wish to express their appreciation to Drs. H. A. Bernhardt and R. M. McGill of the Oak Ridge Gaseous Diffusion Plant, Union Carbide Corporation, Nuclear Division, for their helpful suggestions during the course of this work. The authors are indebted to Mr. J. W. Grisard, who designed and constructed the thermobalance employed in this investigation. Thanks are also extended to Mr. T. W. Bartlett, who prepared the electron micrographs associated with this work, and to Mr. P. G. Dake, whose Powder Analyses Group furnished the required surface area measurements.
Thermodynamics of Aqueous Solutions of Tetra-n-alkylammonium Halides. Enthalpy and Entropy of Dilution'
by S. Lindenbaum Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 97831
(Received September 84, 1966)
Heats of dilution of tetramethyl-, -ethyl-, and -n-propylammonium chloride, bromide, and iodide and tetra-n-butylammonium chloride and bromide were measured a t 25" from near saturation to 0.2 m, or lower, to final concentrations of less than 0.003 m. The apparent molal heat contents, I&, were combined with the previously reported free energy data (osmotic and activity coefficients) to obtain the excess apparent molal entropies. A comparison of the apparent molal free energy, enthalpy, and entropy reveals that the values of the free energy are small compared to the enthalpy and entropy. It is suggested, therefore, that structural inferences drawn from free energy information alone can be misleading and that structural models describing these solutions must account for the very pronounced entropy and heat effects observed.
Introduction I n a recent paper from this laboratory,2 osmotic and activity coefficients of tetraalkylammonium halides
at 250 were reported. ~twas found for dilute solutions of the chloride salts that the osmotic coefficients increased with the size of the cation, whereas for the bromides and iodides the reverse order was obtained. This reversal had been noted previously3v4for measurements of dilute solutions of these salts a t the freezing The J O U T Wof~ Physical Chemistry
point. Data a t higher concentrations2 yielded osmotic coefficient curves which crossed each other in a (1) Presented before the Division of Physical Chemistry, 150th National Meeting of the American Chemical Society, Atlantic City, N. J., Sept 12-17, 1965. Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp. (2) 9.Lindenbaum and G . E. Boyd, J. Phys. Chem., 68, 911 (1964). (3) L. Ebert and J. Lange, 2. Physik. Chem. (Leipsig), 139A, 584 (1928). . , (4) J. Lange, ibid., MSA, 147 (1934).
THERMODYNAMICS OF SOLUTIONS OF TETRA-n-ALKYLAMMONIUM HALIDES
~~~
815
~
Table I : Experimental Calorimetric Data for Dilution of Tetraalkylammonium Chlorides
Q
m21/2
0.339 0.589 0.857 0,888 0.907 1.014 1.168 1.396 1.476 1.669 2.174 2.585 2.816 3,241 3.615 4.412 4.412
(CHs)aNCl 0.0493 68 0.0500 172 0.0529 338 0.0760 360 0.0781 375 0.0456 413 0.0776 528 0,0791 666 0.0772 7 09 0.0794 812 0.0749 1035 0.0760 1088 0 0734 1117 0,0693 1059 0.0785 1005 0.0797 644 0.0756 630
0.384 0.634 0.640 0.821 1.152 1.269 1,538 1.915 2,307 3,024
(CzH5)aNCl 0.0616 77 0.0419 241 0.0751 212 0.0600 304 0.0727 468 0.0605 49 1 0.0788 543 0.1017 476 0.1007 254 0.0784 -544
- 438 - 466 -510 - 436 -214 +576
0,566 0.651 0.746 0,770 1.344 1,417 1.764 2.098 3.216 3.216 3.216
(n-CsH7)aNCI 0.0362 - 59 0.0403 - 156 0.0394 -217 - 200 0.0556 0.0575 - 1142 - 1486 0.0391 0.0568 - 2469 0.0699 - 3707 0,0570 - 6418 0,0556 -6517 - 6359 0.0316
74 173 234 224 1166 1503 2493 3736 6442 6540 6373
-47 - 151 -316
- 329 - 343 - 393 - 496 - 635
-677
- 779
- 1004 - 1057 - 1087 - 1030 - 973 -610 - 599
-51
- 223
- 181 - 278
( n-CaH9)aNCl
0.229 0.473 0.537 0.597 0.857 1,008 1,008 1.008 1,008 1.203 1.581 2.271 3.276 3.983
0.0312 0.0510 0.0502 0.0112 0.0506 0,0284 0.0624 0.0203 0,0360 0.0506
0.0612 0.0731 0 0728 0.0526
- 133 -457 - 561 -786
- 1705 -2421 - 2443 -2415 - 2453 -3645 -6011 -8597 -9366 -9645
146 480 582 791 1726 2433 2469 2423 2468 3666
6033 8627 9396 9667
complicated fashion. Tentative explanations of these phenomena were offered in terms of the organizing effect of these large paraffinlike ions on the water struct ~ r e , the ~ , ~ formation of “water-structure-enforced ion pairs,”’ and the presence of micelles. It is the purpose of this work to report heats of dilution of the tetraalkylammonium halides and to combine this enthalpy data with the previously reported free energies to obtain entropies of dilution.
Experimental Section Materials. The tetra-n-alkylammonium halides are the same as those used for the isopiestic vapor equilibration measurements reported in an earlier publication.2 Calorimetric Measurements. The calorimeter and associated circuitry are the same as previously describeds with the exception of the amplifier which has been replaced with a Keithley Model 150 AR Microvoltammeter. The temperature sensitivity of the calorimeter was about All solutions were prepared by weight and measured into the calorimeter pipet from weight burets. The pipet had a capacity of about 3 ml, and the volume of water in the calorimeter dewar at the beginning of the experiment was about 500 ml accurately measured by weight. -411 dilutions thus resulted in final concentrations of 0.01 m or less, requiring only small corrections to infinite dilution. The energy calibration of the calorimeter was performed as previously described, and the heat of solution of KC1 was determined periodically and compared with literature datag as an over-all check of the calorimetric system. A correction for the heat of opening of the pipet (0.015 cal) was applied. All results are expressed in terms of defined calories (1 cal = 4.1840 absolute joules). In several cases replicate measurements were made of the heat absorbed on dilution of the same initial stock solution as a check on the reproducibility of the calorimeter.
Results and Discussion The calorimetric data obtained are summarized in Tables 1-111. The initial and final concentrations (moles/kg of water) are ml and msr respectively. Q is the heat absorbed (cal/mole of solute), and 4L (5) H. S. Frank and M. W. Evans, J . Chem. Phys., 13, 507 (1945). (6) H. S. Frank and W.-Y. Wen, Discussions Faraday SOC.,24, 133 (1957). (7) R . hf. Diamond, J . P h y s . Chem., 67, 2513 (1963). (8) S. Lindenbaum and G. E. Boyd, ibid., 69, 2374 (1965). (9) G. Somsen, J. Coops, and M. W. Tolk, Rec. Traa. Chim., 82, 231 (1963). (10) T. F. Young and 0. G. Vogel, J . Am. Chem. Soc., 54, 3030 (1932).
Volume 70, A’umber 3 March 1966
S . LINDENBAUM
816
is the apparent molal heat content. The correction from m2 to infinite dilution was made by assuming that at the lowest final concentration (0.003 m or less) the salts all have r$L values equal to that of NaC1.10 The error introduced by this assumption is probably no greater than 5 cal/mole. The I # I ~values in Tables 1-111 are estimated in most cases to be accurate to 2% or 10 cal/mole, whichever is larger.
Table I1: Experimental Calorimetric Data for Dilution of Tetraalkylammonium Bromides 7TLl’/2
mz1/2
Q
0.479 0.690 0.919 1.164 1.541 1.914 2.343
(CHdaNBr 0.0318 167 0.0472 324 0.0590 512 0.0853 714 0.0839 988 0.0953 1240 0.0867 1494
0.489 0,672 0.696 0.966 0,970 1.329 1.499 2,148 2.649 3.467
(CzHd4NBr 0.0327 0.0482 0.0462 0.0596 0.0663 0.0816 0.0924 0.114 0.114 0.118
0.522 0.697 0.971 1.078 1.648 2.098 2.934
(n-CaH,)4NBr 0.0561 52 0.0462 63 0.0472 -89 0.0576 - 255 0,0579 - 1226 0.0836 - 2547 0.0822 -4253
0.380 0.493 0.711 0.783 1.070 1.456 1.997 2.300 2.811 3.846
(n-C4Hs)4NBr 0.0253 - 191 0,0324 -317 - 962 0.0476 0.0473 - 1225 0.0467 - 2482 -4460 0.0673 0.0672 -6332 0.0903 - 6951 0.0902 - 7462 0.0659 - 7836
201 343 360 572 576 794 861 921 764 136
9L
m11/2
-304 -487
- 691 - 954 - 1202 - 1449
- 187 - 323 - 340 - 552 - 556 -772 - 838 - 898 - 741 - 114
Q
mz1/2
0.337 0.481 0.481 0.471 0.546 0.631 0.805 0.970 1,349 1,349
(CzH6)4NI 0.0585 0.0727 0.0730 0.0504 0.0576 0.0722 0.0716
227 292 363 516 644 931 969
- 203 - 294 - 365
0.406 0.467 0.702 0.702
(n-CaH7hNI 0.0416 0.0329 0.0439 0.0397
92 117 138 150
-74 - 103 -119 - 133
202 331 982 1245 2502 4488 6360 6988 7499 7863
- 110
- 198 -216
-514 -643 - 933 971
-
El = - ( l / z m a / * / j j . 5 1 ) ( d ~ L / b ~ m ) (1) 1 2 = +L 1/zm”2(~4L/dv‘ii) (2) The smoothed & us. l/m curves were interpolated and differentiated” to provide values of $L, El, and .Ez
+
at even values of the molality. These data are presented in Tables IV-VI. The values of & were combined with the previously reported osmotic and activity coefficients to determine the excess apparent molal according to eq 3 and 4. entropies, SEX,
- 29 - 44 $109 f279 f1250 f2581 +4287
91
(CH3)4NI 0.0460 129 0.0348 213 0.0344 230
- 153
Values of the relative partial molal heat contents of the solvent and solute, 11and 12,respectively, were calculated from the equations’” The Journal of Physical Chemistry
Table I11 : Experimental Calorimetric Data for Dilution of Tetraalkylammonium Iodides
GEX = 2RT(1 - 4
+ In 7 )
(4) where 4 and y are the osmotic and activity coefficients, respectively. The thermodynamic functions calculated in this way are compared in Figure 1. Values of the entropy are plotted in Figure 2 together with those calculated for HC1, LiC1, NaC1, KC1, and KN03. The values of 4, y, and 4L for these calculations were obtained from tabulations in the literature. l 4 Tables 2 are provided to enable the calculation of of 11 and 1 relative partial molal entropy functions used by other authors: 31 - Sol = E1/T - R In al/N1 for the solvent15 and 32 - S O 2 = E z / T - 2R In y for the sol(11) The author is indebted to Dr. A. Schwarz for programming this calculation for the CDC 1604 computer. (12) H.L. Friedman, J . Chem. Phys., 32, 1351 (1960). (13) V. P. Vasil’ev, Russ. J. Phys. Chem., 36, 1077 (1962). (14) H.Harned and B. B. Owen, “The Physical Chemistry of Electrolyte Solutions,” 3rd ed, Reinhold Publishing Corp., New York,
N. Y.,1958.
THERMODYNAMICS OF SOLUTIONS OF TETRA-WALKYLAMMONIUM HALIDES
817
Table IV : Apparent Molal and Relative Partial Molal Heat Contents of Tetraalkylammonium Chlorides (C Ha)4N C19L
Zl
(-36) - 89 - 134 - 182 - 223 - 262 - 303 - 338 - 359 - 390 - 447 - 501 - 550 - 597 - 640 - 738 - 821 - 887 - 940 - 979 - 1010 - 1030 - 1050 - 1070 - 1080 - 1070 1060 1040 -1010 - 976 - 892 - 775 - 638
m
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6 m
8 9 10 11 12 13 15 17 19
-
7 -
(CzH,)-4NCl---
10-2L2
+L
Ll
...
...
( - 10)
0.4 0.8 1.3 1.8 2.6 3.2 3.4 3.8 5.4 7.2 9.1 11 13 15 20 24 26 26 24 23 21 19 14 2 - 14 - 31 - 53 - 80 -110 - 200 - 330 - 470
-1.9 -2.7 -3.6 -4.2 -5.0 -5.6 -5.7 -5.9 -6.9 -7.8 -8.6 -9.3 -10 -10 -12 -13 -13 -13 -13 -13 -12 -12 -12 -11 -9.9 -8.8 -7.7 -6.4 -5.1 -1.4 3.0 7.5
- 164 -215 -256 - 286 -317 - 341 - 364 - 383 - 415 - 444 - 466 - 480 -492 -510 -502 - 456 - 405 - 347 - 272 - 178 - 75 132 340 546
- 100
10-22.2
9L
...
...
0.6 0.9 1.3 1.6 2.0 2.4 2.7 3.1 3.2 4.0 4.5 4.2 3.8 3.8 1.1 -8.8 -21 - 31 - 48 - 76 - 110 - 130 - 180 - 240 - 300
-2.5 -3.4 -4.0 -4.3 -4.7 -5.1 -5.3 -5.5 -5.6 -6.0 -6.2 -6.1 -6.0 -6.0 -5.4 -3.4 -1.2 0.3 2.5 5.7 9.1 12 16 20 24
(25) (56) 91 124 165 215 261 315 370 433 570 735 932 1180 1470 2070 2560 3000 3420 3800 4160 4450 4710 5170 5580 5960 6330
ute.16J7 Values of L1 and 1 2 may also be applied to the calculation of temperature coefficients for osmotic and activity coefficients. These values have been used to estimate the correction for the freezing point measurements of the tetraalkylammonium iodides3 to 25”, and it has been found in agreement with the experimental evidence2that this correction is negligible over the concentration range covered. Several features of the HEXcurves of Figure 1 are of interest. The heats evolved on dilution of the tetrabutyl- and tetrapropylammonium chlorides and bromides are the largest of any 1-1 electrolytes previously reported. For a given halide, the order of heat evolved is (C4H&N+ > (C3H7)4Nf > (C2&)4T\T+ > (CH&N+ over the entire concentration range. For a given tetraalkylammonium ion, the order is C1- > Br- > I-. This regularity is quite striking in view of the apparent disorder observed in the activity coefficient curves. This order is also the one which would be expected
E1
10 -%
...
... ...
... -0.6 -1.1 -2.0 -3.1 -4.4
-6.3 -8.6 -12 -20 -32 -51 -79 -99 -120 -150 -190 -230 -270 -290 -300 -320 -380 -460 -550 -660
1.9 2.7 3.9 5.0 6.1 7.5 9.0 11 15 20 27 36 42 48 54 60 66 71 74 75 77 82 88 94 100
9L
185 400 625 850 1100 1350 1610 1830 2070 2340 2810 3480 4200 4750 5200 6040 7590 8040 8290 8470 8590 8690 8790 8950 9090 9220 9320 9420 9500 9570 9650
(n-C4 Ho) - 4NC 1 - 7 L1 10 -%
-0.4 -1.6 -3.6 -6.8 -11 -17 -21 -27 -37 -47 -74 -120 -150 -150 -150 -270 -330 -150 -120 -110 -100 -110 -120 -130 -160 -170 -180 -200 -190 -180 -110
3.9 8.4 13 18 24 29 33 37 44 49 62 83 93 93 94 120 140 100 100 98 97 98 99 100 100 100 100 100 100 100 100
according to the “competition principle” suggested by Fajans and Johnson,1gwhich states that the interaction of a salt with water is greater, the more the cation and anion hydration energies differ. The entropy curves also decrease in the order (C4H9)4N+> (C3H7)4N+ > (CzHJqN+ > (CH,)qN+. The values of SEX reported for the tetrapropyland tetrabutylammonium halides are larger than those of any 1-1 electrolyte previously reported. This large entropy effect, due to the (C3H7)4N+ and (C4He)4N+ ions, is in qualitative agreement with the
(15) H. S. Frank and A. L. Robinson, J. Chem. Phys., 8 , 933 (1940). (16) R.H.Wood, J . Phgs. Chem., 6 3 , 1347 (1959). (17) F. R. Jones and R. H. Wood, ibid., 67, 1576 (1963). (18) K. S. Pitrer and L. Brewer, “Thermodynamics,” 2nd ed, McGraw-Hill Book Co., Ino., New York, N. Y.,1961. (19) K. Fajans and 0. Johnson, Trans. Electrochem. Soc., 8 2 , 27
(1942).
Volume 70. Number S March 1966
S. LINDENBAUM
818
Table V : Apparent Molal and Relative Partial Molal Heat Contents of Tetraalkylammonium Bromides
m
0.1
0.2 0.3 0.4 0.5 0.6 0.7
0.9 0.9 1. 0
1.2 1.4 1.6 1.8 2.0 2 .B 3.0 3.5 4.0 4.5 5.0 5.5 6 7 8 9 10 11 12 13 14
L1
(-68)
...
(-140) -196 -254 -320 -370 -430 -470 -520 -560 -634 -704
-770 -830 -881 -987 -1080 -1180 -1260 -1330 -1400 -1450
-(C%H&NBr---
-
+L
...
...
...
0.9 1.8 2.6 3.6 4.4 5.2 6.6 7.0 9.3 12 15 16 17 23 30 38 46 51 53 54
-3.7 -5.0 -6.1 -7.0 -7.8
-8.3 -9.3 -9.5 - 11 - 12 - 13 - 13 - 14 - 15 - 16 - 18 - 19 - 20 -20 - 20
-(n-CsH7)4NBr---
+L
L1
( -80) ( - 150)
... ...
... ...
1.2 2.0 2.5 3.2 3.9 4.6 5.8 6.8 7.7 7.9 8.8 9.8 10 11 7.8 2.6 -3.7 13 24 33 - 44 -71 -110 170 240 - 330 450
-4.5 -5.8 -6.4 -7.1 -7.7 -8.2 -9.0 -9.6 - 10 - 10 - 10 -11 -11 -11 - 10 - 10 -8.6 -7.5 -6.1 -5.1 -4.1 -1.8 1.1 4.9 9.3 14 20
-220 - 300
-360 -412 - 460 - 500 - 540 - 580 - 648 - 699 - 738 -775 - 805 - 868 -902 - 916 -914 - 903 - 879 -850 -818 -744 - 658 - 553 - 426 - 281 - 121
-
-
10-%2
-
15) (-25) - 35 - 40 - 40 -35 50 60 135 195 300 400 510 620 740 1070 1480 1930 2320 2650 2940 3200 3430 3830 4140
(
-----(n-C,Hp),NBr-
LI
10-2Z2
...
...
... ...
0.1 0.1 -0.1 -1.5 -4.2 -7.5 -9.8 - 10 - 13 - 19 -25 -34 - 44 -83 - 140 - 180 -210 - 230 -250 - 270 - 290 -310 - 300
-0.6 -0.5 -0.3 1.0 3.4 5.8 7.4 7.7 9.2 11 14 17 20 29 41 49 52 55 57 59 61 63 62
+L
+L
(130) 290 450 680 900 1190 1480 1740 1980 2220 2670 3170 3600 3980 4310 4940 5500 5990 6360 6660 6870 7050 7180 7370 7300 7590 7660 7720 7780 7820 7850
21
lo-%
...
...
-1.2 -3.2 -6.5 -11 -19 -24 -29 -35 -42 -62 -82 -93 -100 -110 -130 -170 -190 -190 -190 -180 -170 -150 -140 -130 -120 -120 -130 -130 -110 -88
6.1 10 16 22 29 34 37 41 46 55 64 68 72 74 79 87 90 90 90 88 88 86 85 84 83 83 84 84 83 82
Table V I : Apparent Molal and Relative Partial Molal Heat Contents of Tetraalkylammonium Iodides
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8
(-97) 182
-
I . .
0.6
...
-3.4
... ...
...
( - 170)
-294 - 382 - 445 -498 - 545 - 587 - 625 - 661 - 729 - 798 -872 - 956
1.7 2.2 2.6 3.2 3.9 4.6 5.4 6.4 8.9 13 18 28
-6.1 -6.8 -7.4 -8.0 -8.6 -9.1 -9.6 - 10 -11 - 13 - 15 - 18
(-70)
ideas of Frank and Wen,6who have suggested that these large paraffinlike ions promote the structure of water. A surprising result of the comparison of the entropy The J O U Tof ~Ph&d
Chemhtry
...
(-59) - 84 - 103 - 120
...
...
0.2 0.3 0.5
-1.3 -1.6 -1.8
curves in Figure 2 is the fact that those of tetrapropylammonium chloride, bromide, and iodide fall very close together, and, similarly, the tetrabutylammo-
THERMODYNAMICS OF SOLUTIONS -OFTETRA-WALKYLAMMONIUM HALIDES
%;
c
Ef-6000
'OoO 4000
1
819
( GH3 l4 N GI
- p NGI
G X
-20000 2
8 40 12
4 6
7000-
2
6000- (CH314 N Br
' 5000cn
E
4000-
5 9
0 2 4 6 8 10 12
2000-
- 1000 2 4 6 8 40 12
3 2 4 6 8 1042
4
(nC4HJ4N Br
3000-
-20000
t , , , , , ,u
1 2 4 6 81012
G EX 0 2 4 6 8 1012
L
3 2 4 6 8 1012
G
:
'
,
0 2 4 6 81012
- 2000 MOLALITY
Figure 1. Excess apparent molal thermodynamic functions for tetraalkylammonium chlorides, bromides, and iodides at 25".
6oool f 5000
4
2
3 m
Figure 2. Concentration dependence of the apparent molal excess entropy function TSEXat 25" for tetraalkylammonium halides and some other 1-1 electrolytes.
nium chloride and bromide curves coincide within the experimental error. This suggests that structural effects accompanying the solution of these salts in water are largely independent of which particular
anion is associated with these large tetraalkylammonium cations. This observation apparently conflicts with the explanation offered earlier2$'for the fact that the activity coefficients of the tetra-n-alkylammonium chlorides increase with increasing cation size, while the opposite order is observed for t.he bromides and iodides. Diamond suggested that large hydrophobic cations and anions tend to combine with each other to minimize their interaction with the water. It was further suggested that iodide and, perhaps, bromide ions participate in the formation of these "waterstructure-enforced ion pairs," whereas the chloride ion would not. It might have been expected that such a difference in ability to form water-structure-enforced ion pairs would result in a considerable difference in the entropy. The fact that this difference is not observed suggests that the concept of water-structure-enforced ion pairs should not be used to explain the difference in the order of the activity coefficients. This is not to say necessarily that water-structure-enforced ion pairs do not occur; it does suggest, however, that the degree to which this phenomenon occurs is largely independent of the size of the anion or that the water-structureVolume 70,Number d March 1966
820
promoting property of the tetraalkylammonium cation6 overshadows the differences due to the sizes of the anions. Alternatively, it is suggested that the contribution to the entropy and enthalpy due to the structural effect of these salts on the solvent is so great as to obliterate completely the entropy and enthalpy differences due to the sizes of the anions or their relative abilities to form ion pairs. Whereas these differences may be swamped out in the entropy and enthalpy, they show up as significant portions of the much smaller free energy. It is conceivable, therefore, that
The Journal of Physical Chemistry
S. LINDENBAUM
differences in the abilities of the halides to participate in ion-pair formation are reflected in the reversals of the order of the activity coefficients and that this effect is not observed in the enthalpy and entropy.
Acknowledgments. The author is grateful to Dr.
G. E. Boyd for his continued interest and encouragement in this work, to Dr. Fred Vaslow for his help and advice in setting up the calorimetric system, and to both of them for many illuminating discussions of this problem. Thanks are also due to Dr. 14. A. Bredig for his careful review of the article and valuable suggestions toward its improvement.
