1600
H. WOLFFAND R. WWRTZ
assumptions concerning the temperature dependence of the heats of transitions. If, for example, the temperature interval, 8, is so small that the transition entropies may be taken as constant within it-a likely situation for high polymers-then (12) and (13) become
e
= (V1CRT2/LFMn)exp[rzc/(l
-k g’rzc)l (12a)
for the freezing point depression, 8, and
8 = (vlcRT2/L,Jl,) exp[rzc/(l
+ g ’ r ~ c ) ] (13a)
for the boiling point elevation, 8. In these expressions, LF and L, are the latent heats per mole of fusion and
vaporization, respectively, at the transition temperature, T . Acknowledgment. The measurements reported on here from our laboratory were made by J. R. Donaldson.
Hydrogen Bonding and Vapor Pressure Isotope Effect of Dimethylamine by H. Wolff and R. Wiirtz Physikalisch-Chenisches Institut, Universitlit Heidelberg, 69 Heidelberg, Germany (Received August 6,1060)
The vapor pressure isotope effect of two isotopic compounds in solution is given by the ratio p / p ’ of their partial pressures in the same solvent, where p and p’ are the partial pressures of the heavy and of the light compound, respectively. The temperature and concentration dependence of this ratio has been determined for solutions in n-hexane of (CH&NH, (CH&ND, (CD3)2NH, and (CD&ND between 1-20 and -50”. The ratio decreases with increasing temperature and is independent of concentration for pairs with equal amino groups but different methyl groups. These observations and the values indicate that the ratio is not influenced by association and depends primarily on the difference of the methyl group vibrations. However, for pairs with equal methyl groups but different amino groups the ratio increases with iucreasing temperature as well as with dilution, which shows that the ratio depends upon association and is determined by the intermolecular vibrations and the internal amino group vibrations. When methyl and amino groups both differ, the ratio is determined by the external and internal amino group vibrations as well as the internal methyl group vibrations. The values of the ratios and their temperature dependence differ from the results for methylamine, because in dimethylamine the number of methyl groups is increased and the association is decreased. Taking into account the association equilibrium, the ratio of partial pressures is given by a two-state function. From this function it has been calculated that the undiluted dimethylamine contains approximately 60-40ojO of free N H or N D groups in the temperature range of f20 to -20”. Similar results have been obtained from infrared measurements in the first harmonics.
A. Introduction and Measurements Methylamine is the only hydrogen-bonded molecule for which the temperature dependence as well as the recently detected concentration dependen~el-~ of the ratio p/p’ of vapor pressures ( p is the pressure of the heavy compound, p’ is the pressure of the light compound) have been investigated for the variously deuterated forms.2 The results depended on whether the hydrogen-bonding group or another group of the mole cule was deuterated. To extend these ideas and to study the effect of the second methyl group and of the weaker association, we measured the temperature and concentration dependence of p / p ‘ for the isotopic dimethylamines (CB&NH, (CH3)2ND, (CD&JSH, and (CD&ND. The association constant K,” = x,/ x,-lxl (2, is the mole fraction of the v-mer) has only half the value for dimethylamine in n-hexane than for T h e Journal of Physical Chemiatry
methylamine in n-hexane.6 As in the measurements of the methylamines we investigated solutions in nhexane between +20 and -50’. The ratios of the undiluted compounds were given directly by the measured pressures. The ratio of partial pressure at a mole fraction x1 of dimethylamine mere determined by eq 1 (fi and fi‘ are the activity cocffi-
(1) H. Wolff and A, Hopfner, Ber. Bunsenges. Phys. Chem., 69, 710 (1965). (2) H. Wolff and A. Hopfner, ibid., 71, 461 (1967). (3) H. Wolff and H.-E. Hoppel, ibid., 72, 722 (1968). (4) H. Wolff and A . Hopfner, ibid., 73, 480 (1969). (5) H. Wolff and R. Wllrtz, 2. Phys. Chem, (Frankfurt am Main), 67, 115 (1969). (6) H . Wolff and H.-E. Hoppel, Ber. Bunsenges. Phys. Chem., 70, 874 (1966).
VAPORPRESSURE ISOTOPE EFFECTOF DIMETHYLAMINE
1601
Table I : Vapor Pressures of the System (CHa)zNH-n-Hexane in Torra pressure
- 100
00
+ 100
26.7 45.6 87.5 108.4 136.1 160.8 187.7 188.3 224.9 268.2 289.4 349.8
45.5 73.3 133.5 164.9 206.5 245.3 289.1 290.1 350.4 424.7 461.5 560 7
75.6 113.5 198.2 243.1 303.5 360.7 428.3 430.4 522,7 644.0 704.0 862.4
7
I -
XI
- 50°
- 40°
-30°
- 200
0 0,0206 0,0706 0.1014 0.1508 0.2008 0.2707 0.2720 0.4031 0.6022 0.7157 1.o
2.2 4.7 10.4 12.8 15.3 17.3 19.6 19.6 21.9 24.3 25.7 30.3
3.8 9.0 19.1 23.2 29.1 33.2 37.6 37.7 43.2 49.4 52.4 61.7
7.7 15.9 33.4 41.5 51-8 59.9 68.6 68.8 79.6 92.1 98.8 117.4
14.3 27.4 55.2 68.7 86.1 98.8 116.5 117.2 137.7 162.1 174.2 208.9
I
+zoo
121.3 171.6 285.9 347.7 428.8 512.4 612.0 615.0 750.0 939.9 1031.1 1276.9
a Our previous measurements* were repeated as they did not meet the high standard of precision which is essential for the determination of the ratio of partial vapor pressures when the mole fraction of amine approaches zeio. However, only the pressures below ZI = 0.1014 have to be taken from the above Table I. The previous values6 can be used for pressures above XI = 0.1014. 21 is the mole fraction of (CH8)zNH in the liquid phase.
Table I1 : Vapor Pressures of the System (CHa)zND-n-Hexane in Torra 21
- 50"
- 40°
0 0.0048 0.0075 0,0207 0.0254 0,0484 0.0708 0.0922 0.1541 0.2535 0,3053 0.3526 0,4109 0.4494 0.5077 0 6055 0.6554 0.7038 0.7538 0.8037 0.8545 0.9021 1
2.2 2.5 3.0 4.9 5.6 8.2 10.2 11.8 15.2 18.3 19.1 20.1 20.9 21.5 22.2 23.1 23.8 24.6 25.0 25.7 26.6 27.3 28.8
3.8 5.0 5.7 9.0 10.0 15.2 18.9 22.5 28.9 35.7 37.7 40.1 41.8 43.2 44.6 47.3 48.4 49.7 50.9 52.5 54.2 55.6 58.9
I
a
__ Pressure-----------
-30'
7.7 9.4 10.8 15.3 18.0 26.6 33.3 39.1 51.7 64.9 69.6 73.9 78.2 80.2 83.6 88.8 91.6 94.0 96.7 100.5 102.4 105.7 112.2
- 200
- 100
00
+ 100
+200
14.3 17.3 19.7 27.9 30.5 44.3 55.0 64.7 86.6 111.3 119.8 128.3 135.5 140.4 147.1 157.3 162.0 167.3 172.2 177.3 182.6 188.3 201.0
26.7 30.8 33.8 45.3 50.4 70.6 87.4 102.3 137.5 178.2 194.5 209.5 223.0 231.1 243.4 262.1 268.6 279.6 288.2 297.6 307,2 316.8 338.4
45.5 52.4 56.6 74.1 79.9 108.9 133.6 156.3 209, 8 276.6 301.9 327.1 350.7 364.3 384.6 417.3 432.1 447.4 461 5 477.2 493.1 509.3 545.1
75.6 85.2 91.0 114.8 122.7 163.2 198.3 231.1 307.9 409.5 448.8 484.9 527.6 549.6 582.0 635.5 659.8 685.0 708.6 734.1 759.0 784.9 841.1
121.1 133.4 141.3 173.2 183.6 238.6 286.4 331.8 437.8 584.6 642.3 706.3 765.1 798.5 846.3 932.2 970.1 1009.4 1046.4 1086.1 1125.1 1164.8 1249.2
I
x1 is the mole fraction of (CH&ND in the liquid phase.
cients of heavy and light dimethylamine in hexane,
P and P' are the pressures of the undiluted isotopic compounds). Equation 1 follows from the equations for the partial pressures p
XlfiRP
p' = xlfilRIP1
(2a)
The activity coefficients were obtained from measurements of the vapor pressure isotherms. These coefficients were calculated according to Barker' by means of the equations of Redlich and Kisters Inf1
=
+
Cxz2(1 - 8x1
(2b)
(R and R' are corrections for gas imperfection) when corrections for gas imperfections are taken to be equal.
Axz2- Bxz2(1- 4x1)
(7)
J. A,
+ 12x19
(3a)
Barker, Aust, J , Chen., 6 , 207 (1953).
(8) 0. Redlioh and A. T. Kister, I n d . Eng. Chem., 21, 345 (1948).
Volume 74, Number 7 April 8, 1970
1602
H. WOLFFAXD R. WURTZ
Table 111: Vapor Pressures of the System (CDa)tNH-n-Hexane in Torra 7
XI
0 0.0103 0.0254 0.0509 0.0763 0.1016 0,1504 0,2525 0 2685 0 2778 0.3539 0 4063 0.4258 0.5014 0.5529 0.6053 0.6531 0.7044 0.7546 0.8024 0.8529 0.9218 1 I
I
I
a 21
-50'
- 40'
-30"
-200
2.2 3.5 5.8 8.9 11.5 13.6 16.2 20.1 20.3 20.8 22.6 23.4 23.7 24.8 25.4 26.9 27.0 28.5 28.6 29.3 29.9 31.2 32.8
3.8 6.7 10.5 16.4 20.9 25.1 30.6 38.8 39.8 40.2 44.1 46.1 46.8 49.5 50.9 52.3 53.9 55.3 56.9 58.2 60.1 63.0 66.0
7.7 12.1 18.6 28.2 36.4 43.3 54.0 70.1 72.2 73.0 80.7 84.5 86.5 91.5 94.8 97.8 100.9 103.8 106.8 109.7 113.1 118.4 124.8
14.3 21.6 31.4 46.4 59.8 71.7 90.3 118.8 122.0 123.8 138.5 146.0 149.4 159.5 167.3 172.2 177.1 182.5 188.1 193.9 200.1 209.2 221.1
Presmr----
00
+ 100
+20"
26.7 36.7 51.2 73.9 94.4 112.3 141.8 190.2 195.3 198.7 223.8 237.7 243.9 260.9 272.1 283.4 292.8 303.3 312.9 322.7 333.5 349.8 369.8
45.5 60.4 81.9 113.6 143.9 170.9 214.7 291.1 299.3 305.5 347.5 370.4 380.2 409.4 428,2 447.9 463.9 480.9 497 9 514.4 531.8 558.7 591.5
75.6 96.0 124.7 169.9 212.1 250.9 312.9 428.5 441.2 449 * 7 516.1 553.2 569.3 615.2 646.3 677.9 703.8 732.0 759.1 785.0 813.5 855.0 906.6
121.1 148.5 185.9 247.1 304.1 357.6 442.3 609.1 626.0 638.5 739.9 795.8 819.9 891.3 938.3 987.1 1029.4 1072,d 1114 .,5 1156.3 1198.5 1262.2 1339.4
- 100
00
+ 100
+200
26.7 36.9 31.9 73.9 94.6 112.5 142.9 166.7 187.6 203.4 218.0 232.0 242.9 263.3 264.6 274.3 284.9 293.4 303.6 312.5 323.2 333.4 356.5
45.5 60.7 82.1 114.1 144.3 171.3 218.0 254.9 285.6 314.5 339.6 363.0 381.6 398.9 418.1 435.5 453.2 468.0 484.9 499.7 517.9 535.5 572.9
75.6 96.5 125.7 170.5 212.7 251.8 320,3 374.0 426.0 466.8 506.8 544.4 572.8 602.3 633.7 661 .O 690.7 714.2 741.7 766.3 795.7 823.0 882 * 1
121.1 148.6 187.6 247.5 305.8 3B9.7 456 3 528.9 605.5 666.6 727.3 785. 2 827.7 873.4 924.4 966.9 1012 .o 1050.0 1092, ,5 1130.4 117.5.8
I
is the mole fraction of (CD3)zNH in the liquid phase.
Table IV: Vapor Pressures of the System (CD&ND-n-Hexane in Torra XI
0 0.0103 0.0256 0.0503 0.0761 0.1012 0.1516 0,2028 0.2538 0.3003 0.3512 0.4005 0.4504 0.5019 0.5485 0.6022 0.6533 0.7011 0.7533 0.8003 0.8519 0.9012 1 a
21
-
- 100
---
- 50'
- 40°
2.2 3.1 5.9 8.9 11.6 13.0 15.9 18.4 19.8 20.1 21.4 22.2 22.9 23.2 24.1 25.1 25.5 26.0 26.8 27.4 28.7 29.4 30.8
3.8 6.5 10.4 16.1 21.1 24.4 30.4 34.9 37.9 39.9 42.2 43.8 45.7 47.2 48.5 50.0 51.2 52.8 54.3 55"s 57.6 59.3 62.4
-30'
7.7 12.7 18.7 28.0 36.2 42.9 53.9 62.3 68.7 73.2 77.8 81.7 84.8 88.1 91.1 93.9 96.8 99.6 102.5 105.5 108.6 112.0 119.0
- 20" 14.3 21.6 31.8 46.6 60.0 71.4 90.3 104.7 117.0 125.6 133.7 141.9 148.1 153.8 159.8 165.5 171.3 176 0 181.7 186.7 192.8 199.0 212.3 I
Pressure-
-
I
1219.0
1309.7
is the mole fraction of (CD3)sND in the liquid phase.
lnf2 = Az12
+ B~1~(1 - 4x2) +
'"
Cz12(112z22) (3b) where A , B , and C are constants, using the mole volumes and the virial coefficients which were applied in a preThe Journal of Physical Chemistry
vious investigation of the (CH&KH-n-hexane systomVG Measurements of the pressures and preparation of the compounds were performed as described for methylamine and other arnines.lv2 The vapor pressures of the first and last fraction of the compounds within the
VAPORPRESSURE ISOTOPE EFFECT OF DIMETHYLAMINE
1603
Table V : Constants for the Calculation of the Activity Coefficients with Eq 3a and 3b A
B
C
A
0.048 0.050 0.057
0.828
0.055 0.086 0,089 0.124 0,076
1.113 1.225 1.326 1.431 1.482
0.049 0,049 0.054 0.056 0.076 0.086 0.121 0 168
0.824 0,925 1,023 1.117 1.228 1.328 1.441 1.495
B
I:b)
(a) (CHs)~NH-n-Hexane $20 10 0 10 -20 - 30 - 40 - 50
+ -
+20 +100 - 10 - 20 - 30 -40 - 50 LOB
0.794 0.892 0.989 1.085 1.187 1.294 1,404 1.474
$0 .042 +0.045 +0.048 $0.035 $0.027 +o * 002 $0. 002 -0.059
0.888 0.984 1.078 1.189 1.287 1.396 1.452
$0.063 4-0.061 $0.054 + O . 047 + O , 033 $0.014 -0.010 -0.029
(CHs)zND-n-Hexane 4-0.057 +o .os3 +0.047 +0.033 $0.016 +o. 002 -0.029 -0.081
0.920
1.021
0.061 0.068 0.066 0.066 0,090 0.111 0.139 0.119
(d) (CD3)zND-n-Hexane
(c) (CDs)zNH-n-Hexane 0.792
C
r
a
+0.046 +0.050 +0.045 f0.038 $0.021 f0.006 -0.016 -0.078
0.063 0.067 0.073 0,077 0.097 0.109 0.151 0.137
B. Results and Discussion 1. The measured pressures are given in Tables I-IV. The constants from which the activity coefficients are to be obtained with eq 3 are listed in Table V. Figure 1 shows the p / p ’ values of the undiluted compounds (solid lines) and for comparison the p / p ’ values of methylamine (dotted lines) as a function of temperature. The p / p ’ values of pairs with equal amino but different methyl groups (curves 1 and 2 in Figure 1) correspond to an inverse isotope effect on the vapor pressure ( p > p’), The deviations from unity are 0.070.05, i.e., 1.5-1.7 times the deviations in the case of methylamine. They decrease with increasing temperature, the amounts being approximately twice those of methylamine. For the interpretation we used the equation
L
Figure 1. p / p ’ values of undiluted isotopic dimethylamines (-) and methylamines (- - - - -), respectively, as a function of temperature. 1, P(CDa)aNH/P(CHa)aNH and PCDaNHz/PCHaNHz; 2, P(CDa)aND/P(CHs)aND and PCDaNDz/PCH8NDa; 3, P(CHa)zND/P(CHa)aNH and PCHaNDz/PCHaNHa; 4, P(CDs)aND/P(CDa)zNH and P C D ~ N D ~ / PCDaNHz; 5, P(CDa)aND/P(CHs)zNH and PCDaNDz/PCHaNHa; 6, P(CHa)aND/P(CDa)zNH and PCHaND$/PCDsNHz). I n ref 2 curves 1 and 2 as well as curves 3 and 4 should be interchanged. In the case of curve 6, p is the pressure of the light and p’ the pressure of the heavy compound.
entire range of measurements had to be the same within *0.2 Torr. (CD&NH2CI (Merck, Darmstadt) was starting compound for the deuteriomethylated compounds. n-Hexane was research grade (Phillips Petroleum company, Bartlesville, Okla.).
E
i=7
0 ‘ieondeigas -~ ekonde’igas
sinh
ellgas ~
2 1’
eioond sinh 2T
etgas
(4)
e’ioond
sinh - sinh _ _ 2T 2T
(0,is the characteristic temperature of vibrations, with i ranging from 1 to 3 of the translations, with i ranging from 4 to 6 of the librations, and with i ranging from 7 to 3N of the intramolecular vibrations in the gaseous and in the condensed state; prime refers to the lighter isotopic compound) which gives p / p ‘ as a function of the difference between the inter- and the intramolecular (9) J. Bigeleisen, J. Chem. l‘hys., 34, 1485 (1961).
Volume 74, Number 7 April 8, 1970
1604
H. WOLFFAND R. W.L;RTZ
vibrations of the compounds of a pair. As could be shornn,lo,l1the factor of the intramolecular vibrations (i = 7-3N) generally decreases with increasing temperature, whereas the factor of the intermolecular vibrations (i = 1-6) increases. Obviously, the intermolecular vibrations of the amino groups cancel each other in eq 4, because the amino groups are the same. Thus the p / p ' values are determined primarily by the differences between the methyl group vibrations. The factor of these vibrations is contained twice in eq 4. Therefore the deviations of p / p ' values from unity as well as the decrease of these deviations with increase of temperature are crudely twice those of methylamine (taking into account that (1 y)z = 1 2y is valid for low values of y). The p / p ' values of pairs with equal methyl groups but different amino groups (curves 3 and 4 in Figure 1) correspond to a normal isotope effect ( p < p ' ) . The difference between the p / p ' values of 0.94-0.98 and unity is, however, smaller than in the case of methylamine. The same is true for the increase of p / p ' with temperature. As the intermolecular vibrations are responsible for this increase, we have to assume that the methyl group vibrations cancel each other in eq 4 and that p / p ' is a function of the influence of the intermolecular vibrations which is reduced by the counteracting influence of the intramolecular amino group vibrations. Thus the smaller normal effect (compared with methylamine) and the somewhat weaker increase with temperature are explained by the weaker association of dimethylamine or by the lower frequency of the intermolecular vibrations and the smaller change of the intramolecular amino group vibrations generated by the weaker The p / p ' values of pairs with different amino groups and with different methyl groups represent combinations of the values already considered. Curve 5 in Figure 1, representing p / p ' when both groups of the same compound are deuterated, follows from multiplication of the values in curves 1 and 4. Both, curves 1 and 4, are higher than in the case of methylamine, therefore curve 5 for dimethylamine is also higher than that for methylamine. It lies in the region of the inverse effect, and its slope is less than that of curve 4. I n contrast, curve 5 of methylamine lies completely in the region of the normal effect. Curvc 6 represents the p / p ' values for pairs in which the deuterated amino group is in one compound, and the deuteromethylated groups are in the other compound. Curve 6 follows from the division of the values of curve 3 by the values of curve 1. I n this case, too, both 1 and 3 are higher than the corresponding curves for methylamine. The differences, however, cancel out in division. Therefore, curve 6 is nearly the same for dimethylamine and methylamine. Its slope is again less than the slope of curve 3, because of the decrease of curve l.
+
The Journal of Physical Chemistry
"06 v - 20oc ooc
t20oc
1.04
1.02
1
y y 1
+
,
~
1.04 -
1.02 -
l*OO
in solutioii Figure 3. p / p ' values of (CD3)2XDand (CHS)~KD with n-hexane between +20 and -40' as a function of mole fraction 21 of dimethylamine.
2. Figures 2-7 represent the plp'values as a function of the mole fraction of dimethylamine for given temperatures. The approximate independence of the values on dilution (Figures 2 and 3 ) coiifirms the statement that the p / p ' values for pairs with equal amino groups and different methyl groups are nearly independent from association and are determined essentially by methyl group vibrations alone. (The deviations of the curves a t lorn mole fractions from the horizontal may be due to errors.) The p/p' values depend heavily upon concentration for pairs with equal methyl groups but unequal amino groups (Figures 4 and 5). This observation corresponds to the expectation that the normal effect of the hydro(10) H. Wolff in "Physics of Ice," N. Riehl, B. Bullemer, and H. Engelhardt, Ed., Plenum Publishing Corp., Kew York, N. Y . , 1969, p 305. (11) H. Wolff and E. Wolff, Ber. Bzinsenges. Phys. Chem., 7 3 , 393 (1969).
T7APOR PRESSURE ISOTOPE
1605
EFFECT O F DIMETHYLAMINE
-p -P'
(z i-1
qd)l-x
bonded
n:
Qt
( 3i N s1
x) free
(5)
equilibrium between dimethylamine molecules with free amino groups (mole fraction 5 ) and molecules with hydrogen or deuterium bonded groups (mole fraction 1 2)-Since ( l k , ) f r e z > 1and ( n q t ) b o n d e d 1 - ' > ( n q i ) b o n d e d , it follows that p / p ' of the undiluted compounds, which are
0.g
t
Figure 4. p/p' values of (CH,),ND and (CHa)zNH in solution with n-hexane between $20 and -40" as a function of mole fraction 21 of dimethylamine.
1.06
1.04
1.04 r
O .' o
' 0:2
Ox
Xl 0:6
018
1.b
Figure 6. p / p ' values of (CDa)zND and (CHa)zNH in solution with n-hexane between $20 and -40" as a function of mole fraction 21 of dimethylamine.
0.98 0.94 L
b
Figure 5 . p / p ' values of (CDa)2NDand (CD3)2NHin solution with n-hexane between +20 and -40" as a function of mole fraction 21 of dimethylamine.
gen-bonded molecules is replaced by the inverse effect of ~ ' ~inverse ~ effect monomers. As could be ~ h o w n ,this results primarily from the solvent shift of intramolecular vibrations. The intermolecular vibrations of monomers are low in frequency or rotationlike and approximate the classical behavior of vibrations, therefore their factor in eq 4 being nearly 1. The same explanation holds true for the concentration dependence of p / p ' for pairs with unequal groups (Figures 6 and 7). However, the effects of methyl and of amino group vibrations are to be multiplied in one case and divided in the othep, as with curves 5 and 6 of Figure 1. Equation4 has to be replaced by the two-state function" (eq 5) if one takes into account the association
+20°c
ooc -2OOC
Figure 7. p / p ' values of (CH3)zND and (CD&NH in solution with n-hexane between +20 and -40" as a function of mole fraction z1 of dimethylamine. As in the case of curve 6 of Figure 1 p is the pressure of the light and p' the pressure of the heavy compound. (12) H. Wolff, BeT. Bunaengea. Phy8. C h m . , 73, 399 (1969).
Volume 74, Number 7 April 8 , lQ7O
1606 partly associated, is greater than p / p ' of the compounds associated perfectly. Furthermore it follows that p / p ' increases with temperature due to the temperature dependence according to eq 4 as well as due to the increase in the number of monomers. Neglecting the presence of the solvent and the small difference of the association degree of corresponding NH and N D compounds, eq 5 may be assumed t o be valid also for the dissolved molecules. (As has been shown for methylamine in ref 6 and as will be shown for dimethylamine in a forthcoming paper,l8 the N D compound is somewhat more associated.) The values of (n[ql)fr,:ehave then to be calculated from the frequencies of gaseous compounds and the solventshifted frequencies of monomers. Inserting the values of p / p ' and IL: for two mole fractions results in two equations, the solution of which yields (IIqi)fre and ( n q l ) b o n d o d . Reinserting these values and inserting the value of the vapor pressure ratio of the pure compounds permits one to calculate the fraction z of free groups in the undiluted state. Tentatively, the p / p ' values of (CH&NH- and (CH3)zND-n-hexane at mole fractions of 0.1 and 0.2 (Figure 4) have been used for calculation. It could be assumed that these values are determined more exactly than those of (CD3)&H- and (CD&ND-n-hexane, for they correspond to the expectation that the vapor pressure ratio of NH and N D compounds at the state of monomers amounts to 1.01-1.02. (The p / p ' values of monomers or values not influenced by association amount to 1.01-1.02 for CH,OH-CH,OD, 1.02-1.03 for CHINH2-CH3ND2, and 1.04-1.06 for CH3NH2-CDsNH2.12) x resulted from the fractions of monomers, dimers, trimers, and tetramers, determined as in ref 14, under the assumption that each of the different forms contains one free group (Table VI). The values of 1.013 and 1.015 at f20 and -20" for (IIql)rree resulting in this way are in reasonable agreement with those of 1.017, obtained from Figure 4 where z1 approaches zero. Values of 0.92 are obtained for ( n q l ) b o n d e d . The value of 0.92 presumes
The Journal of Physical Chemistry
H. WOLFFASD R. WURTZ Table VI: Fractions x of Free G ~ O L of I ~ (CH3)2?SH S in n-Hexane Solution, Determined from Fraction pi of Monomers, PZof Dimers, p3 of Trimers, aiid P4 of Tetramers" Fraction x of free groups
Mole fraction ZI of (CHa)zNH in CsHu
+ llzP2 + '/spa +
(81
soln
PI
0.1 0.2
0.841 0.717
PI
'lapa)
Pa
Pa
0.008 0.021
0.002 0.007
0.017 0.035
0.005
0.859
0.017
0.738
+200 0.065 0.096
0.916 0.841
-20" 0.1 0.2
0.749 0.578
0.088 0.108
' The assumption is made that each of these forms contains one free group. PI, Pz, p3, and 04 are calculated from the data of Table V as in ref 14, assuming validity of the theory of ideal associated solutions.
that all molecules of dimethylamine are hydrogen bonded. If one inserts it in eq 5 and thereby relates it to the values of 0.978 or 0.962, measured at +20 and -20" for the undiluted compounds (Figure 4), one obtains the fractions 0.64 and 0.44, which are due to the free groups. Values of 0.59-0.33 in the same temperature range have been obtained from infrared measurements in the first harmonics. l5 Thus, even the simplified calculations with eq 5 give reasonable results.
Acknowledgment. We gratefully acknowledge support of this work by the Fonds der Chemischen Industrie, Frankfurt, and by the Badische Anilin und Soda-Fabrik, Ludwigshafen. (13) H. Wolff arid R. TVurtz, 2.Phys. Chem. (Frankfurt am Main), in press. (14) H. Wolff and A . Hopfner, Ber. Bzmsenges. Phys. Chem., 66, 149 (1962). (15) H. Wolff and G . Gamer, in preparation.
