June, 1963
1343
ELECTliOSTRICTIOS IN P O L A R SOLVEXTS
molecule of benzopiiiacol is produced, and two benzophenone molecules are released by hemiacetal cleavagethis would correspond to a quantum yield of one for benzophenone disappearance. The existence of species I is reasonable, since by this scheme, two ketyl radicals dimerize and hemiacetal cleavage of species I leads to another molecule of benzopinacol, thereby resulting in a quantum yield of two for benzophenone
disappearance or unity for the formation of benzopinacol. Conclusion The quantum yield for the photochemical disappearance of benzophenone in isopropyl alcohol a t 313 m p has been shown to be dependant on the inverse square root of the light intensity. This relationship indicates the importance of recombination processes, second order with respect to the radicals concerned. Results obtained indicate that the quantum yield can exceed one and approach a value close to two as the light intensilty is lowered. A reaction scheme is proposed which is coiisistent with experimental results and attributes the variation in quantum yield to t\yo competing processes. A hemiacetal radical, (C,H&COC(CH,),OH, is presumed to contribute more to tlie over-all disappearance of benzophenone a6 the intensity is lowered. At high light intensities, the quantum yield of unity is attributed to the direct coupling of ketyl radicals. At low light intensities, the quantum yield is larger than one and is attributed to the disappearance {of benzophenone by two concomitant processes; (1) dimerization of ketyl radicals and ( 2 ) hemiacetal cleavage Of (C6H,)zC(OH)C(CGHS)SC(CR~)~OH.
ELECTROSTRICTIOS I N POLAR SOLVENTS. I1 BY DEBBIEFu-TAITTAN~ AND RAYMOND ni.
P’UOSS
Contrzbutzon hTo.1727 froin the Sterlzng Chemistry Laboratory of Yale Cnzversaty, S e w Haven, Connectzcut Recezved January ZS, 1963 Viscosities and densities of a series of quaternary salts have been measured in acetonitrile and several other solvents; some electro-neutral solutes were also investigated. Up t o about 0.2 mole/l., viscosities satisfy the AC‘/Z Bc and the densities are given by p / p ~ = 1 (Mc/1000)(~0- v,) where v9 is equation 7/70 = 1 the specific volume of the solute in solution and the other symbols have their usual meanings. Assuming the Einstein viscosity mechanism (spheres in a continuum), B = Mv,/400. It was found that B and V = IO-31Wo8 are additive in contributions from the constituent ions. For large ions (e.g., Bu*N+, Ph4B-), the radii calculated from B and B agree, confirming the theory and model. But, for small ionn, the B-values are larger than the values computed from V , and the more so, the smaller the ion. Neutral molecules, on the other hand, give smaller B’s than expected from the V’s. Electrostriction in the first case and slipping in the second are proposed as explanations. This suggestion is confirmed by the behavior of dipolar solutea.
+
+
The properties of aqueous solutions of inorganic electrolytes are in general highly specific to the individual ions, and generalizations are difficult to find. The B-coefficients in the viscosity equation (concentration, moles/l.) q/qO
1
+ Acli2 + BC
(1) are, however, approximately additive3+ in contribu-. tions from the ttvo ions of a given salt for aqueous systems. Very few data are available for non-aqueous systems, where, by and large, the situation should be simpler because complications due to water structure are excluded. In particular, one would hope to find good additivity and a good correlation between struc=:
(1) This paper is based on a thesis presented by Debbie Fu-Fai Tuan. t o the Graduate School of Yale University in partial fulfillment of t h e requirements for t h e Degree of Doctor of Philosophy, June, 1961. ( 2 ) Hey1 Research Fellowship, 1960-1961. (3) W.M. Cox and J. H. Wolfenden, Proc. Roy. SOC.(London), A146, 476 (1934). (4) H. S. Harned a n d B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” Third Edition, Reinhold Publ. Corp., Kew York, S . Y . , 1958, pp. 236-242. ( 5 ) R. W. Gurney, “Ionic Processes in Solution,” McGraw-Hill Book Company, Inc., New York, N. Y., 1953, Chapter 9.
+
ture and the value of B , because in the case of the idealized model of spheres in a continuum B should be given by tlie Einstein relation
B
== 54/2c
+
== ( N ~ / 3 0 0 ) ( R + ~ R-3) (2) where 4 is volume fraction of solute, N is Avogadro’s number and R+ and R- are, respectively, the radii of the spheres representing cation and anion. (We are neglecting the contribution to B from higher electrostatic terms arising from tlie same source as tlie Ac’” term.) Furthermore, we expect a correlation between viscosity and density data for lion-aqueous systems, which is masked in water by the marked effect of ions on the structure of water. Suppose we take z g. of solute of niolecular weight M and (1 - z) g. of solvent of specific volume uo (density pO = l/oo) to make one gram of solution at concentration c moles/l. with specific volume u = I / p . Clearly
2’ =
llJc/1ooop
(3)
DEBBIEFc-TAI TUANAND RSYMOXD IT.Fuoss
1344
Let us assume that the solute has a specific volume
v, in s o l u t i o n and that v, is independent of concentration. Then
v
=
p/po =
1
(1
- X ) V ~+ x v a
(4)
whence
+ (fl/!c/1ooo)(vo -
0,)
(5)
Again representing the ions by spheres, we have Ua =
+
( ~ T N / ~ J I ) ( R R-3) +~
(6) Elimination of the radii between (6) and (2) then gives
B
i'Uv,/'400
=
2.5V
(7) The purpose of this paper is to present viscosity and density data for a variety of electrolytes (and several related noli-electrolytes) in acetonitrile (and for a few compounds, in several other solvents). Good additivity is found for both B and Mu,, and eq. 7 is satisfied in the limiting case of large ions such as those of the quaternary tetraphenylborides. Furthermore, the values of radii calculated from (2) and (6) are quite reasonable in magnitude and agree fairly well with each other and with ionic radii derived from conductance data. Experimental 2
Materials.-Acetonitrile (Matheson 2726) was refluxed overnight with Drierite and fractionated; b.p. 80.0-80.8". Fisher A412 certified methanol or hfallinckrodt 3016 analytical reagent methanol was used as received. Nitromethane (Matheson 124) was refluxed overnight with Ilrierite and fractionated; b .p. 1 0 0 . 5 101.5". Methyl ethyl ketone (IIIatheson 2609) was refluxed over activated alumina for 24 hr. and distilled; b.p. 7S.5-79.5'; another lot was refluxed for 4 hr. over a mixture of potassium hydroxide and permanganate; b.p. 78.3-79 .O". The second batch gave about 0.27, lower viscosity. Fisher carbon tetrachloride (certified reagent C187) was used as received. The above were used as solvents, and also to calibrate the viscometers. Additional calibrating liquids were water, Fisher certified reagent benzene and toluene, dioxane6 and ethylene chloride (b.p., 83.7'; central cut from a Todd still), and Cannon Instrument Company n-hexane, n-decane, and methylcyclohexane. Tetra-n-butylammonium bromide (Eastman) ?vas recrystallized from benzene and n-hexane7; m.p. 117.0-117.5". Tetraethylammonium bromide (Eastman) was recrystallized from absolute ethanol. Tetramethylammonium bromide (Eastman) was recrystallized from a 50:50 ethanol-methanol mixture (5 g. of salt/100 ml. of solvent). Tetra-n-butylammonium iodide was from laboratory stock: m p . 145.5-146.3'. Tetra-n-propylammonium iodide (Fisher) was purified bi- dissolving 4 g. in 8 ml. of 95% ethanol at 80°, adding 45 ml. of n-hexane, and allowing to cool. The product (45% first crop) was pure white. Tetraphenylborides were prepared from tetraalkylammonium halides and sodium tetraphenylboride" and recrystallized from 3 : 1 acetone-water mixtures; tetrabutylammonium tetraphenylboride, m.p. 230-235"; tetrapropylammonium tetraphenylboride, m.p. 206-207". Picrates were prepared by neutralizing tetraalkylammoniurn hydroxide solutions by picric acid and were recrystallized from ethanol; tetra-n-butylammonium picrate, m.p; 91.6-91 .go; tetra-n-propylammonium picrate, m.p. 117.1-118.1"; tetraethylammonium picrate, m.p. 255-256"; tetramethylammonium picrate, m.p. 319-322". Amine picrates were prepared by addition: tripropylammonium picrate, m.p. 115'; tri-nbutylammonium picrate, m.p. 108.3". Picric acid was recrystallized from water. Diphenylmethane and diphenyl ether were fractionally crystallized. Diphenylamine (Matheson) was iised as received, after allowing the ammonium carbonate stabilizer to evaporate. (6) J. E. Lind, Jr., and R. PI. Ruoss, .I. Phgs. Chrm., 66, 999 (1961). (7) F. Acoasoina, 6 . Petrucci, and R. M. Fuoss, J . A m . Chern. Soc., 81, 1301 (1959). (8) D. S. Berm a n d R. M. Fuosa, ihid., 82, 5585 (1960).
Vol. 67
Viscometer.-The viscometer is shown in Fig. 1. The instrument is designed so that a series of dilutions can be made on a sample of solute without opening the viscometer between check runs a t a given concentration. I n this way, evaporation errors are eliminated, and contamination of the viscometer contents by dust or moisture are minimized. The viscometers fit into spring clips in racks in the thermostat (25.00 i 0.02') which position them accurately vertical, and which permit rapid removal and remounting. The working volume is refilled by taking the viscometer out of the thermostat for about 10 sec. in order to tip it and run liquid thrcugh the side tube C from the dilutionchamber A to the top chamber B. The viscometer is then placed back in the thermostat at about 30" from vertical on the side of tube C while the bulb D fills through the tube E. For acetonitrile, this operation takes about 2 min. Then the viscometer is taken out of the bath for a few seconds and tipped to run most of the excess liquid in B backinto A through C; it is then immediately clamped in its vertical position. I t will be noted that tube E projects 6-8 mm. above the floor of B; the liquid hold-up in E above the mark P gives the operator ample time to position the viscometer and focus the telescope on P before the meniscus passes it, when the electric timer is started. The working volume (bulb D ) is 20-25 ml. The lowx capillary is 8.0 cm. long and 00356 cm. in diamete-. The filling capillary E and the ones above and below D are 2 mm. in internal diamcter; liquid flows from B through E into D much f ster than it can drain out through the 0.0356 cm. capillary under D. The 5 mm. spherical cavity a t the T-juncture of the capillaries is important; if constant 2 mm. bore is maintained, an air bubble is usually trapped. With the sphere, the bubble escapes through D and H. Two viscometers were used, with flow times of 3175 and 2635 sec. for water a t 25'. A11 solut ons and solvents were filtered into the viscometers through a coarse frit. When eventually dust did get into the viscometer, the latter was cleaned by filling with filtered concentrated nitric acid and heating for 8 hr . in a water bath a t 80-90". The viscometers were calibrated, using waterg (7 = 0.008903), dioxaneLs( 4 = 0.011937), n-hexane" (7 = 0.002952), n-decane" (4 = 0.008555), and methylcyclohexanell (7 = 0.006824). Literature values, if not based on the standard value of 0.010020 for waterg a t 20", were recomputed to this standard before use. Eight other liquids were used as secondary standards. The Poiseuille equation Q =
rpghr4t/81V - m p 1 7 / 8 n l t
was put into the familiar form qiipt = C
- D'tZ
The values of D (0.140 and 0.126 for viscometers I and 11, respectively) were computed from viscometer dimensions, using nz = 1.2. Then D/t2 was added to the average values of v / p t for each calibrating liquid. The final results are 106C = 2.831 0.004 for viscometer I and 3.399 + 0.005 for 11. Since we are primarily concerned with relatzve viscosities of dzlute solutions, this precision in calibration is adequate. The flow times for a given liquid gave a standard deviation of 0.02% or less. Methods.-M solutions were prepared by weight. Viscosities were measured a t a series of concentrations, the lowest concentration being about 0.01 mole/l. Usually the highest concentration was about 0.2, which was found empirically to he the practical limit of the linear equations 1 and 5. At higher concentrations, the viscosity plots usually became concave-up. Densities were measured over the same range of concentrations, using a Sprengel pycnometer ( V o = 21.5743 ml.) which was calibrated with distilled water at 25". Results.-Since both the viscosity and the density data can be reduced to linear functions of c up to about 0.2 mole/l. for the systems studied, a compact summary of the results can be presented by giving the numerical values of the constants of eq. 1 and 5 . Back-calculation showed that the constants reproduce the densities and viscosities to about +O.O27,, averaged over all the systems. Table I gives the solute-solvent pairs investigated, together with an identification code. (The symbol "Pi" stands for the picrate ion; the other symbols are familiar. The last (9) J. F. Swindella, J. R. Coe, Jr., and T. R. Godfrey, J. f l e e . S u t l . Bur. Std., 48, 1 (1952). (10) J. A. Geddes, J. A m . Chem. Soc., 65, 3832 (1833). (11) >I. R. Cannon, A n d . Chem., 32, 355 (1960).
ELECTROSTRICTIUN 1.K P O L A R
June, 1963
1345
SOLVESTS
three compounds, disubstituted benzenes, are all para.) Table I 1 describea the solvents. 'Table 111 gives the constants vs, M v ~ , and B which were derived from the data. In order to obtain B , [ ( a - ~ o ) / y a C 1 / ~was ] plotted against the square root of concentration; the slope gives B , and the intercept a t c = 0 gives the Falkenhagen coefficient A when the system is electrolytic. The Ac'/z term was quite small for our systems in the range 0.01 < c 5 0.2; within experimental error, the coefficient A agreed with the theoretical value.12 For the non-electrolytic solutes, A is, of course, zero; in these cases, B was obtained as the weighted average of [(qo - qo)/qac]. The values of lOOA for the electrolytes are: A , 1.6; B, 2.1; C, 1.9; D, 3.0; E, 1.7; F, 1.5; G, 2.1; H , 1.9; I , 2.5; J, 2.2; K, 2.0; L, 1.9; M, 1.7; N , 1.6.
TABLE I DESCI~IPTIOS OF SYSTEMS Sol\ent
Solute
Kel
A
Key
MeOH MeOH MelWOz MeCOEt MeCK E MeCS F MeCS G MeCS H PrJI I Bu4NBPh4 MeCN J PrrSBPh, MeCN MeCN K BuJPi L P T ~ X P I RIeCN RfeCN ?VI Et4NPi
S
MerNBr BuaNBr Bu4NBr BudNBr Bu4NBr EtrNBr BuaN
B C D
0 P
Q R S T C V W X Y Z
Solute
C
Solvent
Me4NPi MeCN Bu3NHPi RleCN PnSHPi NeCK MeCS HPi BulN MeCN RIeCN PhZCHz PhzO MeCK PhzSH MeCN PhzCH2 CC14 CCI, PhzSH MeCGH4Me RleCN 02SC6H4r\;02 MeCN H2NC6H,?iO2 MeCS
TABLE I1
Fig. l.-Viscomet8er.
Solvent
lOO?lo
PO
MeOH MeSOz MeCOEt MeCN CC14
0.5417 ,6175 ,3820 ,3425 ,904
0.7870 1.1262 0.8010 0,7777 1 ,5846
TABLE I11 CONSTANTS FOR DEXSITY AND VISCOSITY EQLATIONS Key
A B C D E F G H I J K L M N 0 P
Q R S T U V W
X Y Z
US
0.643 ,912 ,931 ,885 ,894 ,714 ,834 ,764 1.010 0.985 ,854 ,801 ,721 ,662 .821 ,768 .563 1.301 1.001 0.946 ,913 ,981 ,900 1.173 0.694 0.721
IO-SMv,
B
4
0.099 ,294 ,300 ,285 ,288 ,150 ,308 ,239 ,567 ,498 ,402 ,332 ,278 ,200 ,340 ,286 ,129 ,241 .168 ,161 ,155 ,165 ,152 ,125 .117
0.42 .84 .i5 1.01 0.93 .69 .87 .71 1.35 1.24 1.13 0.90 .85 .78 .99 .88 .48 ,157 .207 ,205 .274 ,196 .30 .042 .169 .294
4.25 2.85 2.50 3.54 3.23 4.60 2.83 2.96 2.38 2.49 2.81 2.71 3.06 3.90 2.91 3.08 3.72 0.65 1.23 1.27 1.77 1.19 1.97 0.34 1.44 2.94
.loo
Discussion We first consider the coefficients B and V = 10-3. M u , l./mole with respect to each other. In the last (12) Reference 4, eq. 4-2-28, p. 104.
column of Table I11 is given q , the ratio B / V . Accorcling to eq. 7 , this ratio should be 2.5, if (I) the linear term in the viscosity is due to the Einstein volume effect and if ( 2 ) the ~ o l u m edetermined via the density is a true measure of the volume occupied by the solute. Two salts, Bu4NBPh4 and Pr4SBPh4 in acetonitrile, satisfy the ratio test for the validity of the model. These are the two salts among those studied both of whose ions are large and centrally symmetric; if an.y of the salts should agree with the working hypotheses, it should be these two. Since Bu&+ and Ph4B- have nearly the same mobility,13 we sliall diyide B and V for BuJN.BPh4 equally in order to obtain single ion values for these two ions. Then, if the coefficients 13 and I' are additive properties of the constituent ions, me can assign single ion values to the ions of the other salts studied. There are six cases among the systems of Table I which permit a test of additivity; they are summarized in Table IV. TABLEIV ADDITIVE PROPERTIES OF B
AKD
V
B PhaB'
PI'
I'
1 20
0 96 1.10
0 71 0.87
0 33 0.40
0.24 0 31
Pr4K B u ~ +S
1.35
Pr& Bu~N
0.50 0 57
+
V +
+
It is seen that pair-&e differences are constant, thereby establishing additivity for these six cazes at least. We shall assume that it is general, i.e. B
=
B+
+ B-,
I; =
v+ + v-
(8) Kext, we note that the other salts of Table I11 (wit1,L (13) R. IV. Kunae and R. AI. Fuoss, J . Phys. Chem.. 67, 385 (1963).
1346
Fig. 2.-Comparison
DEBBIEFu-TAITcA4xAND RAYMOSD AI. Fuoss
of viscosity and density coefficients; key in Table I.
the single exception of Bu4SBr in nitromethane) all give q-values larger than 2.5. This is shown best in Fig. 2, where B is plotted against V ; the solid line is drawn in accordance with eq. 7 . The systems are identified by the code given in the first and fourth columns of Table I. All the electrolyte points lie above the line, except the two tetraphenylborides and the nitromethane point. For the tetrapheiiylborides, we found that v,, as determined from the slopes of the density curves, is nearly equal to the reciprocal of the density pe of the dry salt: Bu4S.BPh4,us = 1.01, 0.98; PrqK.BPh4, 21, = 0.98, l / p , = 0.95. s required a little more space in solution than in the rigid crystal lattice. Let us assume that, for all the salts, v, is a valid measure of the static volume occupied by the ions in solution. (It should be mentioned that conductance measurements show that association is negligible in acetonitrile, due to the high dielectric constant; for -lIecX.S O , , where both ions are sma11,I4 Ka, the association constant, is only 23, and still smaller values of K.4 are to be expected for the salts of Table I, with the exception of Me4KBr.) Then the fact that the points lie above the solid line of Fig. 2 can have only one interpretation: most of the salts produce a viscosity increment greater than that corresponding to their volumes. In other words, if we assume that the V-values are physically correct, then the B-values are “too large.” One explanation would be failure of the ion to coliform to the spherical model which leads to the Einstein coefficient of 5/2; cylindrical ions, for example, would give much larger viscosity increments than spherical at the same volume fraction.16 But 111e4‘NBr, Et4XBr, Bu4SBr, Pr4n-1, and BudSI have spherical anions, and yet their q values are, respectively, 4.25, 4.60, 3.23, 2.96, and 2.83, all significantly larger than 2.5. The discrepancy can be rationalized as follows. The Einstein model is spheres in a continuum. Real liquids contain a certain aniount of unoccupied space (“holes” of one sort or another) and transport by slip without paying the price in friction is possible. Hence in general we would expect real solutes in real solvents to gir-e a smaller contribution to viscosity than corresponds to their volumes. This is precisely what is observed for the non-electrolytic solutes BuaN, PhnCH,, Ph,O, and Ph,NH (systems R, S, T, U) in either the highly polar acetonitrile, or in the non-polar car(14) D. s. Berns and R. 11.Fuoss, J . A m Chem. Soc., 83, 1321 (1961). (15) F.Prrrin, J. p h y s . radaum, 7, 1 (1936).
Vol. 67
bon tetrachloride (V, W). We therefore conclude that the small ions in acetonitrile pull solvent dipoles to themselves (electrostriction) and thereby produce two effects which increase viscosity: (1) the holes in the vicinity of the ions are squeezed shut and (2) the kinetic entity which corresponds to a moving ion effectively is the ion plus a certain number of solvent dipoles which, on a time average, accompany it (“solvation”). If we use the spherical model, and split the B and V coefficients equally for Bu4T\‘BPh4,then radii can be computed for the various ions of Table I. The results of these calculations are shown in Table V, where T B is (300B,/N~r)‘/~ and TV is ( 7 5 0 V j / N ~ r ) ’ and / ~ , Bj and Vj are the appropriate single ion values obtained on the assuniption of additivity, assuming also, as already mentioned, equal division for Bu4N BPh4. (Parentheses indicate which value of a pair was assumed.) TABLE V RADIIFROM
i71SCOSITY ASD
Salt
l O 8 r +B
108, -B
BuaNBPh4 PrlNBPh4 Bu4iYPi PraiYPi EtrNPi MedSPi Bu,XHPi Pr,NHPi Bu~XI Pr,W BurXBr EtJBr
(4.74) 4.37 (4.74) 4.39 4.22 3.96 4.49 4.17 (4.74) 4.34 (4.74) 4.14
(4.74) (4.74) 4.06 (4.06) (4.06) (4.06) (4.06) (4.06) 3.15 (3.15) 3.35 (3.35)
DEKSITY l o b +v (4.81) 4.40 (4.81) 4.39 3.81 3.18 4.44 4.05 (4.51) 4.34 (4.81) 3.84
108,-v
(4.81) (4.81) 3.61 (3.61) (3.61) (3.61) (3.61) (3.61) 2.37 (2.37) 1.44 (1.44)
In a general way, the radii of Table T’ are quite satisfactory: they are of the right order of magnitude, and sequences are in the expected direction (Bu > Pr, etc.). The TV values for the first four quaternary ions, Ale4N+, . , BUN+ are oiily a little smaller than the values 3.47,4.00,4.52, 4.92 calculated by Robinson and Stokes16 from the molar volumes of the corresponding paraffins. These values are larger than the Stokes radii calculated from limiting conductances in waterL6 (2.04, 2.81, 3.92, 4.71) and strikingly different froin the values (2.83, 3.94, 5.55, 6.05) calculated from the B coefficients determined from the viscosity of aqueous solutions of the quaternary salts.17 As mentioned in the introduction, aqueous solutions do not belong to the general class of solutions, and we merely say that we are not surprised a t the lack of agreement between constants derived from measurements in water and in acetonitrile. Study of the table reveals some significant details. For the larger ions (Bu4N+, Pr4K+, Ph4B-, Bu8HY+, Pr,HS+), the agreement between TV and T B is excellent, and confirms our feeling that the model ought to be satisfactory in these cases. But as the size of the ion decreases, TB decreases much more s l o ~ l ythan one would expect on the basis of the siniple model; see values for Et4K+ and 31e4N+, for example. This point is best demonstrated by the halide ions; for bromide, rV, which by hypothesis is a measure of the actual ionic size, is 1.44 l., while T B is 3.35, over twice
.
(16) R. 2. Roblnson and R. H. Stokes, “Electrolyte Solutions." 2nd Ed., Academic Pres,. New York, N Y , 1959, Table 6.2, p. 124. (17) E. R. Nightlngale, Jr., J . Phgs. Chem., 66, 894 (1962).
MCDEVIT-LONG EQUATION FOR SALTEFFECTS OR'
June, 1963
as large. That is, t,he bromide ion affects a volume about ten times its own in tlie flow process. The discrepancy between TV aiid 1 * ~thus supports our suggestion of electrostriction. The lion-electrolytic solutes also show evidence of electrostatic interaction with the solvent. The nonpolar or slightly polar solutes give B-values which are considerably smaller than one would expect from tlie corresponding volumes. The sequence of the last three compounds of Table I11 is especially informative; the three molecules have roughly the same shape and size, so the geometrical contributions to B should be not greatly different. The p-values, however, increase by nearly an order of magnitude in the sequence MeC6HJle, 02SCsH4S02, 02SCaH4n"2. The first two components have zero dipole moments, the first due to absence of electrical asymmetry and the second by compensation of vectorially opposed moments. The value of B for the diiiitro compound is, however,
Y OX-ELECTROLYTES L
1347
over four times that for p-xylene; strong local interaction between the individual nitro-dipoles and solvent molecules is clearly indicated. The value for p-iiitroaniline neatly confirms the argument; the net dipole moment is very large ( = 7 Debyes) and has an intense field at both ends. The value of B (2.94) is greater than the ideal 2.5, which shows the strong dipoles can also produce electrostriction in their vicinity. Finally, a comparison of tributylammonium picrate with tributylamine and picric acid also leads to the conclusion that electrostatic interaction, in addition to purely geometrical. effects, determines viscosity. The sum of V's for picric acid and the amine is 0.37, which is in fair agreement with 0.34, the value of V for the amine picrate. But the sum of the B's is only 0.64 as compared with 0.99 for the amine picrate. The field a t the nitrogen end of the Bu&H+ ion is of course much stronger than that a t the Bu3N nitrogen, and a large B is expected and found for the amine picrate.
THE: MCDEVIT-LONG EQCATIOK FOR SALT EFFECTS ON SON-ELECTROLYTES1 BY K. C. DENO, ~ N DCHARLESH. SPIKK~ College of Chemist?y and Physics, the Pennsyltanaa State Universaty, Universrty Park, Penna. Receaved January 31, 1963 Evidence is presented supporting the theory that the salting-out and salting-in of non-electrolytes depends on the molecular volume of solute and on the changes in internal pressure of the solvent which take place on addit,ion of salt.
The familiar salting-in or salting-out of non-electrolytes is correlated by the equation log f = kscs (1) where j' is the activity coefficieiit of the noli-electrolyte, lis is the Setschenow constant, and c, is the concentra,tion of salt in rn~les/liter.~ Based on the concept of volume energies, Long and RIcDevit4 derived the equation IC, =
vlyvs-
I',")/2.3RT@o
(2) Equation 2 requires that salt effects are determined by the molecular volume of the solute molecule and the extent of electrostriction, (V, - T:), of the solvent by the salt. Long aiid XcDevit used the compressibility data of Gibson5 t o evaluate the electrostriction. The resulting evaluation of k, for salt effect on the solubility of benzene in water ga,ve the correct salt order and correct sign of k , for a variety of salts. The concept of volume energies also has been used to correlate solubility and distribution data for a large number of hydrocarbons in mater,6 sulfur dioxide,{ and ammonia.' In these systems, the activity coefficient of the non-electrolyte is again related to the volume energies (1) This q o i k was supported in p a r t b y t h e Petroleum Research Fund administered by t h e American Chemical Society. Grateful acknovledgment is hereby made of this support. (2) Recipient of a d u Pont Fellomship. (3) F. A Long and T. F. AfcDe\it, Chem. Rev.,61, 119 (1952). (4) I-. A Lona and W. F. hIcI)e\,it, J . A m Chem. Soc., 74, 1773 (1952). (5) R. E. Gibson, zbsd., 66, 4, 865 (1934); 67, 284 (1935). (6) J. C. McGowan, J . A p p l . Chem., 2, 323 (19521, 4, 41 (1954). (7) N. Deno a n d H. Berkbeimer, J . Chem. Eng. Data. 4, 1 (1959).
RT In f
=
VAP,
(3)
In eq. 3, V is the molecular volume of the solute arid A p e is an empirical parameter that depends only on the two liquid phases and js iiiterpret,ed to be the difference in internal pressures.* If eq. 3 is differentiated with respect to salt concentration for solutions of non-electrolyt'es in varying salt concentrations, eq. 4 results. d logf/'dc,
=
k,
=
(V/2.3RT)(dAPe/dcS)
(4) Since V is approximately equal to Vifl for non-electrolytes, eq. 2 and 4 are equivalent. The change in iiiternal pressure with salt concentration, d APe/dcs in eq. 4,is equal to the internal pressure factor, ( V , - Vi0)JPD,, +sf the McDevit-Long eq. The success of eq. 3, independent of eq. 2, supports the McDevit-Long eq. (eq. 2 ) and suggests that eq. 2 or 4 deserves more experimentaJ testing than has previously been given. 3 * 4 , 9 Experimental The solubilities of tetralin, diphenylmethane, and 2,4-dipheny.l2-methyl-2-pentene were measured in sodium sulfate solutionn. Concentrat)ions of the hydrocarbons in solution were determinesd by conventional spectrophotometric methods using a Beckman DU spectrophotometer. All hydrocarbons were distilled and., ( 8 ) The original notation of McGowan (ref. 6 a n d 7) has been changed in order t o be more consistent with t h e underlying concepts a n d with t h e noteltions of Gibson (ref. 5 ) a n d Long a n d 'lcDevit (ref. 4). T h e original expression of McGowan was (log f = k k l f ' ) , where k~ is a constant for a given solvent pair a n d P is t h e Parechor, a measure of molecular volume. AfcGowan's expression f o r t h e molecular volume near t h e m.p., 0.42 P (J. C. bloGowan, Rec. trav. chim., 76, 199 (1956)), is t h e most convenient way t o estimate V in eq. 3 in view of t h e availability of Tables of Paiaclior increments (0. R. Quayle, Chem. Reo., 63,484 (1958)). (9) XI. A. Paul, J . Am. ('hem. Soc., 74, 5274 (1952).
