MARTINB. SMITH
364
The Monomer-Dimer Equilibria of Liquid Aluminum Alkyls. I.
Triethylaluminum
by Martin B. Smith Chemical Research and Development, Ethzll Corporation, Baton Rouge, Louisiana
(Received July $9,1966)
Experiments are described demonstrating the feasibility of determining the position of the monomer-dimer equilibrium of a liquid aluminum alkyl as a function of temperature by measuring its heat of dilution. Using a calorimeter developed especially for the purpose, the heat of dilution of a small quantity of triethylaluminum (TEA) with a relatively large quantity of n-hexadecane was measured at four temperatures from 60 to 150’. Equations were derived expressing the heat of dilution in terms of four parameters, two pertaining to the heat absorbed due to dissociation and two to the heat of physical mixing. A computer program determined values of the parameters which minimized the rms difference between calculated and observed heats of dilution. The values obtained for the heat and entropy of dissociation of 1 mole of TEA dimer are 16.93 i: 0.23 kcal and 32.19 i: 0.63 cal/deg. Degrees of dissociation of TEA in the pure liquid state and at various mole fractions in hydrocarbon solution are tabulated over a wide temperature range. The results obtained show satisfactory agreement with literature values. The AH of physical mixing of TEA with n-hexadecane is small and positive and decreases with rising temperature.
Introduction Trimethylaluminum (TMA), triethylaluminum (TEA), and at least the next few aluminum tri-nalkyls are primarily dimeric in dilute hydrocarbon s~lution.l-~In addition, TMA and TEA are partially dimerized in the vapor state.4 It is therefore appropriate to regard these compounds as dimeric according to the formula RGAl2 with partial dissociation to monomeric units, R3A1. A bridge structure has been established for the dimems Monomeric molecuIes, because of the electron deficiency of the aluminum atom, would be expected to be far more reactive than their dimeric counterparts. Indeed, kinetic studiese of the addition of ethylene to TEA, the commercially important “growth reaction,” have confirmed a suggestion by Ziegler5 that the monomeric form of the alkyl is the active species in the reaction. Dissociation to monomer and recombination provides a mechanism, perhaps the principal one under certain conditions, for the rapid exchange of alkyl groups which occurs when two aIuminum alkyls are mixed. Monomeric molecules may undergo thermal
decomposition much more readily than dimeric molecules. In this case, it may be possible to correlate thermal decomposition rates with degrees of dissociation. A knowledge of the degrees of dissociation of liquid aluminum trialkyls a t various temperatures and dilutions is therefore important. Literature data on the degrees of dissociation of aluminum trialkyls are meager. Molecular weight measurements on tri-n-butylaluminum and tri-n-hexylaluminum2 have indicated that these compounds are appreciably dissociated in dilute hydrocarbon solution (1) K. S. Pitzer and H. S. Gutowsky, J. Am. Chem. Soc., 68, 2204 (1946). (2) K. Ziegler, Special Publication No. 13, The Chemical Society, London, 1959. (3) E. G. Hoffman, Ann. Chem., 629, 104 (1960). (4) A. W. Laubengayer and W. F. Gilliam, J. Am. Chem. SOC.,63, 477 (1941). (5) K. Ziegler in “Organometallic Chemistry,” H. Zeiss, Ed., Reinhold Publishing Gorp., New York, N. Y., 1960. (6) C. 5. Smith, Ph.D. Thesis, Chemicd Engineering Department, Purdue University, Lafayette, Ind. : Dissertation Abstr., 26, 1540 (1965).
MONOMER-DIMER EQUILIBRIA OF LIQUIDALUMINUM ALKYLS
a t 5". The values obtained could be used to calculate equilibrium constants at this one temperature. However, similar measurements on TRIA and TEA1+ have shown only that their degrees of dissociation under these conditions are too small for satisfactory evaluation by this method. The monomer-dimer equilibrium existing in TAIA vapor has been determined from 100 to 160" by vapor density measurement~,~ the heat of dissociation of 1 mole of dimer being evaluated as 20.2 kcal. This investigation is the first of a series conducted to determine the degrees of dissociation of liquid aluminum trialkyls as functions of concentration and temperature. The experimental method selected consists of measuring the heat of dilution of a small quantity of alkyl with a relatively large quantity of saturated hydrocarbon. The heat of dilution, after subtracting the heat due to "physical mixing," is used to calculate the degree of dissociation of the pure alkyl.
Experimental Section Materials. To avoid exposure to oxygen and moisture, all materials were stored in a nitrogen drybox, and transfers to other containers were conducted there. TEA was prepared by sodium reduction of ethylaluminum sesquichloride followed by distillation. Chemical analysis showed it to contain 97.42% (CzH5)3Al, 0.41% (C2H&A1H, and 2.17% (CzHJzAlOC2Hj. Thus the TEA contained 2.98 ethyl groups per aluminum atom. Normal hexadecane was ASTM grade (99% minimum) supplied by the Humphrey Chemical Co. It was deoxygenated by bubbling dry nitrogen through it for 2 hr and was stored over molecular sieves. Triply distilled mercury was deoxygenated similarly. Apparatus. The calorimeter consisted of a 300-ml, 7-cm i.d. silvered borosilicate glass dewar (H. S. Martin & Son) provided with a Teflon cover (Figure 1). Temperatures were read to the nearest 0.0002" with a platinum resistance thermometer used in conjunction with a G-2 nfueller bridge and a Leeds and Northrup dc null detector. The stainless steel turbine stirrer, 19 mm in diameter a t the base, was driven at 1800 rpm by a constant-speed electric motor. A rubber band 3 mm wide served as a belt. It passed around a Teflon pulley attached to the top of the 3/16in. stirrer shaft and around a section of Tygon tubing slipped over the motor shaft. The liquids were brought to the test temperature and maintained there by means of a 165-w Chromalox cartridge heater controlled with two powerstats connected in series, one of which was plugged into a Sola constant-voltage transformer. The
365
TEFLON SLEEVES TEFLON COVER WRAPPED HERE
SOLVENT LEVE
THERMOMETER
SILVERED DEWAR GLASS DUMMY
GLASS SAMPLE VESSEL WITH
STAINLESS-STEEL TURBINE STIRRER
1
I
Figure 1. Calorimeter.
heater fit loosely inside a 10-mm i.d. glass well containing just enough silicone oil (Dow-Corning No. 200) to cover the heater. Auxiliary heating was provided by a 24 X 0.5-in. heating tape (Electrothermal HT340, 0.5 amp). The tape was wrapped around the top of the dewar and the adjacent portion of the cover and was controlled by a powerstat. The aluminum alkyl sample was contained in the 23mm 0.d. bulb of a glass vessel made from 3-mm i.d. tubing. The alkyl was held in the bulb by a small quantity of mercury in the side arm of the vessel. The neck of the vessel, which projected several centimeters above the Teflon cover, was connected by gum rubber tubing to a three-way valve (Becton, Dickinson & Co., MS08) attached to a 10-ml hypodermic syringe containing an appropriate volume (about 4 ml) of dry nitrogen. A second glass vessel, termed the 'Ldummy" vessel, was rigged identically except that (1) it contained dry nitrogen instead of sample and (2) the plunger of its syringe was fully inserted. The sample and dummy syringes were mounted in a line, back to back, with the plungers touching. When the plungers were manipulated simultaneously, the alkyl was forced out the side arm of its vessel into the solvent. At the same time, an equal volume of solvent was drawn into the dummy vessel, thereby maintaining a constant liquid level in the calorimeter (this was found to be essential in order to obtain small, reproducible blanks). Volume 71, Number 3
January 1067
MARTINB. SMITH
366
A small vertical vent hole through the cover ensured equalization of pressure inside and outside the calorimeter. The calorimeter, syringes, and the electric motor were enclosed in a Plexiglas nitrogen drybox which provided full visibility. Procedure. The hexadecane (184 ml) was added to the dewar and its weight was determined to 0.01 g. An appropriate volume of TEA ( 2 ml for "A" experiments and 10 ml for "B" experiments) was added to the hexadecane by syringe and its weight was measured to 0.0001 g (from the loss in weight of the syringe). The purpose of this preaddition was to destroy any traces of reactive materials still present in the solvent. I n the case of the "B" experiments, an additional purpose was to reduce the magnitude of the heat absorbed due to dissociation relative to the heat of physical mixing and thereby provide a more accurate evaluation of the latter. The dewar was closed tightly with a rubber stopper. Mercury was added to the side arms of both the sample vessel and the dummy vessel and the side arms were closed with small rubber plugs. TEA (4 ml) was added to the sample vessel by syringe and its weight was determined to 0.0001 g. The necks of both vessels were plugged. The dewar and the vessels were transferred to the Plexiglas drybox The calorimeter syringes and their rubber tubes were flushed with nitrogen and the ends of the rubber tubes were plugged. The drybox was closed and thoroughly flushed with nitrogen. The calorimeter was assembled and the heating tape was tied in place. The syringe valves werc: set at the proper positions to open the rubber tubes to the box (to keep pressures equalized during the heating period). The calorimeter and contents were heated rapidly toward the desired test temperature (60, 90, 120, or 150") using high settings of the cartridge heater powerstats. The powerstat for the tape heater was given an appropriate setting which varied with the test temperature. As the temperature approached the test temperature, the cartridge heater powerstats were cut back. They were adjusted until the temperature leveled out a t the desired value (f0.2"). The syringe valves were then set at the proper positions to connect the syringes t o the vessels. Temperatures were read a t regular intervals for several minutes until the rate of change became constant at 0.002" or less per minute. The TEA was forced from the sample vessel into the solvent by moving the syringe plungers to the second position. The plungers were moved back to the first position, causing solution to be drawn into the sample vessel (and discharged from the dummy vessel), and then returned to the second position. This rinsing of the sample The Journal of Physical Chemistry
40.4811
v)
40.452 W
-----03176 ohms
c
3
6 a
40.451
40.45
4
40.446
I 2
1
I
4 6 TIME, MINUTES
I
8
Figure 2. Typical temperature-time curve; experiment 150A1; time a t which mixing occured: 4.0 min.
vessel was repeated twice. Temperature readings were resumed and continued until a steady trend was again established. A blank experiment was performed by manipulating the plungers through the same sequence as before. The temperature change was determined from a temperature-time plot, an example of which is given in Figure 2, and the blank correction applied (blank corrections varied from -0.0030 f 0.0003" a t 60" to 0.0040 0.0006" a t 150"). The heat of dilution (QT)was calculated from the temperature change, the total heat capacity, and the weight of alkyl (corrected for buoyancy, as were all weights of materials). The heat of dilution was corrected to the target temperature (60, 90, 120, or 150"). These small corrections, which did not exceed 0.50j0, were made with the aid of a plot of log QTus. temperature. Numerical Constants. The energy measurements were expressed in terms of the thermochemical calorie (1 cal = 4.1840 absolute joules). Temperature conversions were based on the relation 0°C = 273.15"K. The 1961 International Atomic Weights were used, the gram formula weight of triethylaluminum being 114.168. Heat Capacity Data. The specific heat of n-hexadecane was read from a plot obtained by extrapolating the measurements of Finke and others.' The specific heat of triethylaluminum was determined over a wide
+
MONOMER-DIMER EQUILIBRIA OF LIQUIDALUMINUM ALKYLS
367
to dissociation,
is heat due to physical mixing, and
temperature range in this laboratory (data not published). The heat capacity of the calorimeter (with mercury in the vessel side arms) was evaluated by draining a measured quantity (about 130 ml) of n-hexadecane a t a known temperature near ambient into the calorimeter, which already contained some n-hexadecane (about 54 ml) and had been preheated to a somewhat higher, known temperature. The value obtained for the heat capacity at 25' (30.85 f 0.25 cal/deg) was extended to higher temperatures using known temperature coefficients of heat capacity for the various materials present . Discussion of Errors. Besides the 0.41% (CZHJZA1H and 2.17% (C2H6)2A10C2H6 already present in the TEA, small additional amounts of impurities (estimated as less than 0.27;) were formed owing to contact with traces of moisture and oxygen in the nitrogen blanket. The amount of TEA decomposed thermally during an experiment was also insignificant (less than 0.2% at 150'). The heat, of addition at 120" was not changed measurably upon substituting a sample of TEA containing about twice as much impurity, mostly (C2H5)2A10C2H5.Therefore, no corrections were applied. The amount of TEA reacted in destroying traces of reactive materials in the solvent used in an experiment was calculated from calorimetric data as 0.033 g. When this amount was subtracted from each of the TEA preaddition weights, the calculated values of the heat and entropy of dissociation were increased by only 0.22 and 0.09%, respectively. Accordingly, no corrections were made. If all of the TEA vapor in the sample vessel (about 5 cc) were condensed immediately upon mixing at 150°, the observed heat absorbed would be lowered by 1.1%. The actual error is much less since (1) only a portion of the vapor is condensed and (2) the condensation presumably occurs over a period of several minutes so that the error is partially eliminated by plotting and extrapolating the temperature readings. Again, no corrections were applied.
AQD =
Derivation of Equations
Amoles of monomer
The heat of dilution of an aluminum alkyl with a hydrocarbon (already containing some of the alkyl in solution) has two components: the heat due to dissociation of the alkyl and the heat due to physical mixing. This is expressed by the equation QT
= QD
+
QP
(1)
where each Q is heat absorbed in calories per gram formula weight of alkyl added. QD denotes heat due
QP
QTis total (experimental) heat of dilution. Heat Due to Dissociation. The following assumptions are made. (1) Triethylaluminum, either as the pure liquid or in hydrocarbon solution, consists of an ideal mixture of monomer and dimer. The equilibrium constant for the dissociation of the dimer into the monomer is therefore given by the expression KD
= X'monomer/Xdimer
(2)
where X is mole fraction. (2) KD does not vary with the concentration of the alkyl in the solvent, its value being the same as in the pure alkyl. (3) The variation of the molar heat of dissociation with temperature is small and can be taken as zero. Consider the addition of fo gfw of TEA to a solution containing fl gfw of TEA dissolved in n h moles of nhexadecane. Let fi = gram formula weight of TEA in final solution = fo f1; rl = nh/fl; r2 = nh/f2; P = weight fraction of alkyl dissociated; Po = /3 for pure alkyl; P1 = P for initial solution; /32 = for final solution; and AHD' = heat of dissociation, cal/mole of dimer dissociated. For either solution (or the pure alkyl), moles of monomer = Pf, moles of dimer = (1 - P)f/2, and
+
total moles =
Pf
+ (1 - P)f/2 +
@/(I + P + 2r); + + 2 ~ ) ;and
Xmonomer (1 P
=
For the pure alkyl r
=
nh
=
(f/2)(1
+ P + 2r)
=
(1 - P)/
Xdimer
0 and the expression becomes
Solution of the latter equation gives
P / P ~= d W r 2
+ 2r + 1 - Por
(4)
Heat absorbed in experiment (due to dissociation) = (Amoles of monomer)(AHDo/2).
~ O Q D=
QD
p2r2 - (pofo+ pf,) = f O ( P 2 - Po) - fl(P1 - P d [fo(Pz - 60)- fl(Pi - Pz)]AHD'/~ =
-
= (PoAHD"/~)[(Pz/Po)
1 -
Substitution of values of gives
(fl/fO>((Pl/PO)
P2/P0
- (PZ/PO))l
and Pl/Po from eq 4
(7) H. L.Finke, M. E. Gross, G. Waddington, J. Am. Chem. SOC.,76, 333 (1954).
and H. M. Huffman,
Volume 71, Number @. JanWTy 1067
MARTINB. SMITH
368
Table I: Heats of Dilution of Liquid Triethylaluminum with n-Hexadecane Temp, OC
Expt no.
60.00
60A1 60A2 60B1 60B2 9OAl 90A2 90B1 90B2 120A1 120A2 120B1 120B2 150A1 160A2 l5OBl l5OB2
90.00
120* 00
150.00
-Initial solutionGrams of Grams of hexadecane TEA
142.41 142.00 141.82 141.82 142.37 141.59 141.75 142.08 141.35 141.50 141.80 142.08 141.65 141.53 141.42 141.75
Pori - d P O 2 T 2
1.7088 1.7823 8.7667 8.3375 1.6899 1.6942 8.1642 8.4600 1.7694 1.7999 8.3718 8.2547 1.7266 1.7875 8.3126 8.3363
Grams of TEA added
-At,
OC
Exptl
3.3750 3.3550 3.4656 3.4774 3.4186 3.4015 3.4790 3.3281 3.4996 3.4762 3.4664 3.4369 3.4521 3.4892 3.4947 3.5071
0.0395 0.0430 0.0257 0.0236 0.0826 0.0826 0.0403 0.0394 0.1650 0.1647 0.0736 0.0751 0.3229 0.3227 0.1438 0.1412
153 156 97 91 320 320 163 166 672 673 313 321 1387 1371 634 624
+ 2rz + 1 + P0rz)l
(5)
=
(na -I- nh)(A
Bt)XaXh = ( A f Bt)nanh/(%
+
The J
O U T of ~
+ Bt)nh2/(?ta+
Physical Chemistry
nh)’
=
(A
Qp
QD
60.5 60.4 55.1 55.4 41.4 41.4 37.9 37.8 22.2 22.2 20.3 20.4 3.1 3.1 2.8 2.8
96.4 93.3 40.8 42.2 277.0 276.1 122.9 121.0 654.0 651.4 295.2 298.7 1385.3 1363.4 628.4 628.1
+Bt)z2
where r h is the average xh in the solution before and after the addition. Since Ana = I/&, it follows that Q
-_____
P -
fo
2Ana
(7)
Results and Discussion The endothermic process accompanying each dilution was completed within 1 min (and probably much sooner) as shown by the temperaturetime curves (see Figure 2). The experimental results are listed in the first seven columns of Table I. At each temperature the total heat absorbed (QT)is roughly half as great for a “B” experiment (in which the initial solution contained about 10 ml of TEA) as it is for an “A” experiment (in which the initial solution contained about 2 ml of TEA). The net dissociation occurring in a “By’ experiment is therefore much less than that occurring in an “A” experiment a t the same temperature. This would be predicted from the monomer-dimer equilibrium; the presence of additional monomer molecules in the initial solution should have an inhibiting effect on the dissociation of added TEA. Within
nh)
where A and B are constants to be determined and t is temperature. Differentiating with respect to n,
dQ/iha = ( A
-csl/gfw-
156.9 153.7 95.9 97.6 318.4 317.5 160.8 158.8 676.2 673.6 315.5 319.1 1388.4 1366.5 631.2 630.9
AQ/Ana = ( A
(6)
where A S O ~= entropy of dissociation, cal/mole of dimer deg and T = temperature, OK. Heat of Physical Mixing. The molar heat of mixing of two hydrocarbons a t a particular temperature is given approximately by the relation AH, = CXIX2, where X is mole fraction. The measurements of McGlashan and other^^^^ indicate that for pairs of hydrocarbons the proportionality constant C is linear with temperature to a first approximation. The physical mixing of ‘TEA with n-hexadecane may be expected to resemble the mixing of two hydrocarbons. Since TEA is primarily dimeric, even in dilute solution (except at high temperatures where the heat of physical mixing is small), it is treated here as though it were all dimeric. It is therefore assumed that the heat of physical mixing of na moles of (C2H&A12 with nh moles of hexadecane is given by the expression
Q
cal/gfwCalcd
For a small addition of alkyl (An,), as in the present experiments, the expression becomes, to a good degree of approximation
Application of basic thermodynamic formulas leads to the equation
hi KD = (ASD’/R) - ( A H D ” / R T )
Calcd values, -QT,
+ Bt)Xh2
(8) M. L. McGlashan in “Experimental Thermochemistry,” Vol. 11, H. A. Skinner, Ed., Interscience Publishers Ltd., London, 1962, Chapter 15, pp 337-339. (9) J. A. Friend, J. A. Larkin, A. Maroudas, and M. L. McGlashsn, Nature, 198, 683 (1963).
MONOMER-DIMER EQUILIBRIA OF LIQUIDALUMINUM ALKYLS
either the “A” series or the ((B” series QT and therefore the net amount of dissociation occurring increase exponentially with temperature. This result would also be expected from the monomer-dimer equilibrium. Values of the parameters A H D O , ASDO, A , and B were determined using a nonlinear least-squares computer program based on eq 1, 3, 5, 6, and 7. This routine solves for the values of the parameters for which the sum of the squares of the differences between calculated and observed heats of dilution (QT)is a minimum. The values obtained using a Scientific Data System 910 computer are listed in Table I1 with their Table 11: Values of Parameters Derived by Computer Program AHDO, cal/mole of dimer A S D O , cal/mole of dimer deg A, cal/mole B, cal/mole deg
8 8 a
a
?
i i g la.
9 d
3 69
400
t t
oo = or =
300300
OT 0 5
*
‘CHEMICAL HEAT’’ “PHYSICAL HEAT” TOTAL HEAT
200200
100-
0 -
*
16,930 230 3 2 . l g i 0.63 207 i 14 -1.34f0.12
estimated accuracy limits. Calculated values of QT based on the above numbers are given in column 8 of Table I where they are compared with experimental values (column 7). The rms difference between experimental and calculated values is 3.9 cal/gfw. Calculated values of the heat of physical mixing (QP)and the heat due to dissociation (QD) given in the last two columns are all positive in sign. With increasing temperature, QD increases exponentially while QP decreases. A t each temperature QP is larger relative to QD for a “B” experiment than for an “A” experiment. For two of the experiments (60B1 and 60B2), the heat of physical mixing exceeds the heat due to dissociation. The contributions of “chemical heat” (QD) and “physical heat” (QP)to the total heat absorbed (QT) a t 90” are shown graphically for the entire composition range in Figure 3. At this temperature, QP exceeds QD a t hexadecane mole fractions up to 0.6. When the program was performed without the parameters A and B describing the heat of physical mixing, a much poorer fit of the experimental data was obtained. An analysis of variance of the fits of the data with and without parameters A and B indicated that the inclusion of the parameters is significant a t better than the 97.5% level. The molar heat of mixing of (CzH&412 with n-hexadecane a t X = 0.5, calculated as AH, == 45.1 cal a t 25”, decreases with increasing temperature. This small positive heat of mixing decreasing with rising temperature is typical for pairs of similar hydrocarbons.* The assumption made in deriving the equations that the physical
I
0
I
I
I
0.4 0.6 0.8 MOLE FRACTION HEXADECANE
0.2
I .o
Figure 3. Contributions of chemical and physical heat to total heat absorbed a t 90” as functions of composition. These calculated values are for the addition of 4 ml of TEA to various TEA-hexadecane mixtures, each containing 184 ml of hexadecane. Compositions designated as A and B are those employed in the “A” and “B” experiments, respectively. TEA was taken as the monomer in computing mole fractions.
mixing of TEA with n-hexadecane resembles the mixing of two hydrocarbons therefore appears to have been justified. On substituting the values obtained for AHDO and A S D O in eq 6, the expression for the equilibrium constant becomes log K D = 7.0344
- 37@,4/T
(8)
Values of K D calculated from this equation a t 10” intervals are given in column 1 of Table 111. The degree of dissociation of pure TEA a t each of these temperatures was calculated from the equilibrium constant K D ) which is using the equation PO = d & / ( 4 derived from eq 3. These values, expressed as per cent of TEA dissociated, are given in column 3 of Table 111. Degrees of dissociation at various mole fractions in hydrocarbon solution, calculated from eq 4, are listed in the remaining columns of the table. From their vapor density measurements, Laubengayer and Gilliam4 calculated the heat of dissociation of TMA vapor as 20.2 f 1.0 kcal/mole of dimer. The corresponding value for the heat of dissociation of liquid TEA obtained in this investigation (16.93 f 0.17 kcal/mole of dimer) is lower by 3.3 kcal. This seems reasonable since TEA is known to be less strongly associated than TMA.4~s~10
+
MARTIN B.SMITH
~~
~~~~
Table I11 : Equilibrium Constant and Degree of Dissociation of Liquid Triethylaluminuma % of TEA dissociated in hydrocarbon aolution at TEA mole fraction* of
,
Temp, OC
KD
1
0.5
0.2
0.1
0.01
0.001
0.0001
0.00001
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210
3,072 x 10-7 9.243 X 2 580 X 10-6 6 729 X 1 651 X 3.832 X 10-6 8.456 x 1,782 x 10-4 3.599 x 10-4 6.994 X 0.001312 0.002380 0,004190 0.007173 0.01196 0.01948 0.03101 0.04833 0.07387 0.1109 0.1636 0.2374
0.02771 0.04807 0.08031 0.1297 0.2032 0.3095 0.4598 0.6674 0.9485 1.322 1.810 2.439 3.235 4.231 5.461 6.961 8.770 10.93 13.47 16.42 19.82 23.67
0.04799 0.08324 0.1390 0.2245 0.3515 0.5351 0.7942 1.152 1.634 2.273 3.103 4.165 5.500 7.151 9.165 11.58 14.44 17.77 21.58 25.87 30.62 35.78
0.083 10 0.1441 0.2407 0.3884 0.6079 0.9247 1.371 1.984 2.810 3.897 5.302 7.082 9.295 12.00 15.23 19.04 23.41 28.35 33.79 39.65 45.79 52.05
0.1207 0.2093 0.3495 0.5639 0.8819 1.341 1.985 2.869 4.054 5.608 7.602 10.11 13.19 16.90 21.27 26.29 31.93 38.08 44.60 51.31 57.99 64.41
0.3901 0.6758 1.127 1.813 2.825 4.272 6.280 8.984 12.52 17.00 22.50 29.01 36.44 44.54 52.98 61.32 69.13 76.04 81.85 86.49 90.07 92.75
1.231 2.126 3.527 5.634 8.681 12.91 18.55 25.72 34.36 44.18 54.57 64.76 73.92 81.49 87.27 91.42 94.27 96.17 97.43 98.26 98.81 99.17
3.843 6.571 10.73 16.74 24.90 35.23 47.23 59.82 71.55 81.16 88.15 92.77 95.63 97.36 98.38 98.99 99.36 99.59 99.73 99.82 99.88 99.92
11.65 19.31 30.04 43 I57 58.52 72.54 83.51 90.75 94.99 97.29 98.52 99.17 99.53 99.72 99.83 99.90 99.94 99.96 99.97 99.98 99.99 99.99
a
I
Values at 0-50" and 160-210° are extrapolated.
* TEA was taken m the monomer in computing mole fractions.
Smith6 conducted kinetic studies on the addition of ethylene to TEA in hydrocarbon solution. Assuming the monomeric form of TEA to be the only active species in the reaction, he derived dissociation constants for TEA at three temperatures. These constants are compared in Table IV with corresponding values ob-
Table IV : Comparison of Dissociation Constants with Literature Values -
K
Temp,
This
o c
work
Lit."
120 140 160
0,00419 0.0120 0.0310
O.OO60 0.021 0.062
a Calculated from related equilibrium constants given in ref 6.
tained in the present investigation. Considering the indirectness of Smith's method and the assumptions involved, the agreement is rather good.
The Journal of PhysicaZ Chem6try
Extrapolated values of the degree of dissociation of TEA at 5" range from 0.36 to 1.15% as the TEA mole fraction (computed with TEA as the monomer) is decreased from 0.02 to 0.002. Such lorn degrees of dissociation could scarcely be detected with certainty by cryoscopic molecular weight measurements. The (extrapolated) results of the present investigation therefore agree with the results of cryoscopic measurements reported in the l i t e r a t ~ r e . ~ , ~ Similar studies are planned of the monomer-dimer equilibria of other aluminum alkyls including triisobut ylaluminum.
Acknowledgments. The author wishes to thank Mr. G. E. Bass for assistance in the design and construction of the apparatus and in the performance of preliminary experiments, Dr. G. J. Brendel for preparation of the TEA sample, Mr. G. A. Daniels for computational assistance and helpful discussions, and Mr. A. E. Harkins for programming the equations for the computer. (10) The mixing of TMA and TEA is exothermic presumably because of the replacement of ethyl bridges with methyl bridges (unpublished data, Ethyl Corp).
