E. R. NIGHTINGALE, JR.
894
If - 0.74 and - 1.1 v. are taken as approximate values for the standard potentials of reactions 20 and 21, the standard free energies of formation of Tez-- and Te-- are 34.13 and 50.7 kcal., respec-
Vol. 66
tively. From these values, the standard potential of reaction 22 was estimated to be - 0.92 v., which is quite close t o the value observed experimentally.
VISCOSITY OF AQUEOUS SOLUTIONS. 111. TETRAMETHYLARl~ilONIURiZ BROMIDE AYD THE ROLE OF T H E TETRAALKYLAMMONIUM IONS Esso Research
BY E. R. SIGHTINGALE, JR.~ & Engineering Co., Linden, .V. J., and University of Nebraska, Lincoln 8, Neb. Recezued November 19, 1961
The viscosities of aqueous tetramethylammonium bromide solutions have been measured a t 20, 25, and 30" in the concentration range 0.0005 to 1 ?n. The viscosity data have been interpreted in terms of the Jones-Dole equation for strong electrolytes. Gsing this relation, the viscosity B-coefficients for the salt and for the tetramethylammonium ion a t 25" are calculated to be +0.1014 and 0.1434 l./mole, respective1 . Unlike that for the larger tetraalkylammonium ions, the B-coefficient for (CH3)4NBr increases with temperature yiebing a negative activation energy for viscous flow. This behavior is interpreted and corroborates a previous conclusion that the (CH,)?N + ion is weakly hydrated a t the ionic surface, much in ions. The energies and entropies of activation for viscous flow for the the same manner as are the Ba+2,IO3-, and R4N+ions are demonstrated t o be congruous with those for the common inorganic ions if corrected (a) to the molal scale to compensate for the varying amounts of solvent in a molar solution and (b) for the excess activation free energy which rewlts from the large molar volume of the R&+ ions.
Recent discussions from these Laboratories2.3 have emphasized that transport processes can provide significant information concerning t,he nature of ion-solvent interactions and the effective size of the hydrated entities. The infrared spectra of aqueous solutions4 and the influence of ionic charge on the viscosity5 indicate, however, t,hat the ionic interactions with water are highly specific and greatly dependent upon the charge, size, and shape of the ions. One class of ions whose role has not been adequately characterized is that of the tetraalkylammonium ions. Recently, Frank6,' has suggested t'hat the tetraalkylammonium ions increase the "ice-like" structure in water away from the ionic surface because the non-polar a,lkyl group participates only very weakly in the "flickering icelike clusters." This concept accounts not only for properties such as viscosity in which the tet'raalkylammonium ions behave as if appreciably hydrated, but also for the excessive molal heat capacity and increased dielectric relaxation time of their solut'ions. However, the behavior of the smaller ions in this series, particularly the tetramethylammonium ion, has remained less certain. I n the previous discussion on the effect'ive size of hydrated ions,2 t'he tet,ramethylammonium ion was assumed to be hydrat,ed at the surface much like t,he sodium or iodate ion. Because accurate viscosity data are not available in t'he literature, the viscosit'y of tetramethylammonium bromide has been re-examined. The viscosity coefficients for the (CH3)4N+ ion have been calculated and compared wit'h those for t'he other tetraalkylammonium ions. (1) Esio Research 8: Engineering Co., Linden, N. J. ( 2 ) E. R. Kightingale, Jr., J . Phys. Chem.. 63, 1381 (1939). (3) E. R. Nightingale, Jr., and R. F. Benck, ibid,63, 1777 (19.59). ( 4 ) E. R. Nightingale, Jr., and H. S. Frank, unpublished work. ( 5 ) E. R. Nightingale, ,Jr., and J. F.Kuecker, to be published. (6) TI. S. Frank, Proc. Rou. Sac. (London), A247, 481 (1958). (7) H . 6 . €rank and K . Y. Wen, Discussions Faraday Soc., 24, 133 1957).
Experimental Eastman Kodak white label tetramethylammonium bromide was purified by twice recrystallizing the salt from conductivity water and drying at 110" for 4 hr. The salt sohtions were prepared on the molal basis with conductivity water. The densities of the solutions were measured a t 20, 25, and 30 i.0.05" with 25-m1. specific gravity bottles and are precise within &0.0001 g./ml. As described previously, a the viscosities were measured within d=0.02" of the specified temperatures using an Ostwald viscometer which was calibrated with water by means of eq. 1 s / p = Kt L/t (1) where 7 is the absolute viscosity, p is the density, and t is the flow time. The characteristic viscometer constants K and L were 0.00005251 and 0.00011, respectively. The absolute viscosity of water a t 20, 25, and 30" is 0.01002, 0.008903, and 0.007976 poise, respectively.~ The densities are 0.99823, 0.99707, and 0.99568 g./ml., respecti~ely.~
-
Results The viscosities of the salt solutions were computed by means of eq. 1. The absolute viscosities a t 20, 25, and 30" for ten tetramethylammonium bromide solutions in the concentration range 0.0005 to 1.0 molal are presented in Table I. The data TABLE I ABSOLUTEVISCOSITIESOF AQUEOUSTETRAMETHYLAMIaoP;ru%rBROMIDES o ~ u ~ r o lAT v s 20, 25, AXD 30" m,
moles/1000 g.
0 0005137 ,0009992 002997 .009939 , 0 1685 ,03384 .06015 ,1013 ,4068
1.043
-----Absolute 200
0.010021 ,010023 ,010027 .010032 ,010038 .010053 ,010073 ,010102
viscosity, poise--250
0.008905 .008906 ,008909 ,008918 .008926 ,008944 .008971 ,009012 ,009289 ,009847
30'
0.007978 ,007979 .007982 .007992 .008001 ,008022 ,008054 .008103
( 8 ) J. R. Coe and T. B . Godfrey, J . A p p l . Phus., 16, 625 (1944). (9) L. W.Tilton and J. K. Taylor, J . Research .VatZ. Bur. Standards, 18,205 (1937).
VISCOSITYCOEFFICIENTS OF TETRAALKYLAMMONIUM IONS
May, 1962
have been analyzed using the Jones-Dole equation.10 7,ir)O
=1
+ A d 5 4-BC
(2)
where v/vo is the viscosity of the salt solution relative to that of the solvent water, C is the molar concentration, and A and B are constants characteristic of the electrolyte. The A-coefficient represents the contribution from interionic electrostatic f0rces.l' The B-coefficient is a measure of the effective hydrodynamic volume of the solvat'ed ions and is proportional to the entropy of hydration of a gaseous i o a 2 This coefficient denotes the order or disorder introduced by the ions into the solvent structurie, and is a specific and approximately additive property of the ions of a strong electrolyte a t a given temperature,12 although no satisfactory theoretical treatment has yet been given. Plotting (v/vo - l)/.\/C us. the A-coefficient is the ordinate intercept, and the B-coefficient is given by the slope of the resulting straight line. The experimental values for the Acoefficient for tetramethylammonium bromide solut,ions a t 20, 25, and 30' are 0.0062, 0.0066, and 0.0064, respectively. The experimental value at 25 O compares fairly well with t'he theoret'ical va,lue of 0.00623 calculat'ed according to theory of Falkenhagen and Vernon.ll The B-coefficients are observed to be $0.0627, 0,1014, and 0.137 at, 20, 25, and 30". Taking the value of the B-coefficient for the bromide ion to be -0.049,13 -0.042,14 and -0.0355,13 respectively, we calculate the magnitude of the B-coefficient for the tetramethylammonium ion as $0.112, 0.1434, and 0.172 a t these three temperatures. Discussion Previously, it has been demonstrated t'hat the theory of absolute reaction rat~esas applied by Eyring, et al., to viscositylj may be adapted to aqueous salt solutions to calculate ionic activat,ion energies and entropies for viscous Table I1 records the energies and entropies of activat,ion for viscous flow for the tetraalkylammonium ions calculated from this work and data available in the literature.16 The positive activation energies for the tetraa.lkylammonium ions other than (CH3)&+ are consistent wit,h the interpretation of Frank6,' that large R&+ ions increase the viscosity of water by increasing the ice-like structure apo-surface. l7 A s the temperature is increased, t,he already ordered struct,ure of the solution is
895
TABLE I1 FREEESERGY, ENERGY, A S D EKTROPY O F ACTIVATION FOR VISCOUSFLOW AT 25' (C = 1 YOLE/L.)
dc,
B?
Salt
(HzO) NaBr (CHd4NBr (CzHd4NBr (C3H7)4NC1 (C4H&NBr
+O 0443" 1014b
.343" 1 O8jd 1 354" (Be).
Ion
AF*, kcal
(2 2 2 2 2 2
19) 21 30 44
75 88
AB*, kcal
AS*, e.u
( 4 01) 3 79 2 82
( 6 1) 5 3 1.7 5 0 5 6 7 1
3 93 4 41 5 00
A E P , cal.
AS%*,e.u.
Br-
-0 042 -240 -0 85 (CH3)4K+ $0 1434 -950 -3 55 (CZHS)~X 0 385 +160 -0 4 ( C3H714X 1 092 620 +o 25 1 396 1230 +I 85 (C4Hs)d b This a Ref. 14; dB/dT estimated from C1- and I-. work. c V . D. Laurence and J. H. Wolfenden, J . Chem. Soc., 1144 (1934). d "International Critical Tables," Vol. V, McGraw-Hill Book Go., New York, X.Y., p. 13. e P. Goldberg and R. M. Fuoss, Proc. LVutl.Acud Sci. US., 38, 758 (1952);. dB/dT from W. Y. Wen, Ph.D. Thesis, University of Pittsburgh, 1957. +
+
+
+ +
diminished more than is that of the pure solvent, and the relative viscosity and hence the B-coefficient decreases. The negative activation energy for (CH3)4N+ is congruous with our previous conclusion that this ion, unlike the other tetraalkylammonium ions, is weakly peri-surface hydrated.2 The ion-dipole interaction energy for a univalent ion the size of (CH&T\T+ is approximately 10kT and is sufficiently large compared with that for hydrogen bond formation to orient some of the water dipoles at the ionic surface more strongly than in bulk water itself. The effective hydrated radius of (CH&X+ closely approximates that of the iodate ion (3.67 lis. 3.74 A.) although the latter is somewhat more extensively hydrated by virtue of charge delocalization in the iodine-oxygen bond. l 8 It is clear that there cannot be appreciable aposurface hydration as with the larger R4N+ ions since this type of structure making always is accompanied by a negative temperature dependence for the B-coefficient. It may be emphasized that the conclusion that (CH3)4?;+ is weakly perisurface hydrated is not inconsistent with the data of Haggis, Hasted, and Buchananlg on the change of the dielectric relaxation wave length in aqueous solutions. These workers have demonstrated that "hydrogen bond-forming" molecules and ions increase the dielectric relaxation time in water, but it is not possible to diff erentiate between apo(10) G. Jones and IkI. Dole, J. Am. Chem. SOC.,61, 2950 (1929). surface and peri-surface hydration by these meas(11) H. Falkenhagen and E. L. Vernon, Physik. Z.,85, 140 (1932). (12) W. 1vI. Cox and J. H. Wolfenden, Proc. Roy. SOC.(London), urements. For instance, both structure-making 8145, 475 (1934). salts such as LiCl and structure-breaking salts like (13) Estimated froin known temperature dependence of C1- and I -. RbCl decrease the relaxation time while the struc(14) M. Kaminsky, Discussions Faraday SOC., 24, 171 (1957). ture-ordering ions F-, (CF13)4X+,and (C2H5)4X+ (15) S. Glasstone, K. J. Laidler, a n d H. Eyring, "The Theory of R a t e Processes," McGraw-Hill Book Co., New York, N. Y., 1941. all increase the relaxation time. It appears that, the (16) A plot of Bq 11s.m3(see ref. 2) suggests t h a t Bv for (CaH7)dNCl major difference between the structure-breaking I is t o o large by ea. 0.18 unit. The literature value for dB/dT is apion and the structure-making (CH3)eN+ ion proximately correct, however, and thus yields consistent values for AEi* and A&*. is one of size: the normal water structure about an (17) Literally-away from the surface of the ion. Ions for which iodide ion collapses because the first-layer water the force field is sufficient to order water molecules at the ionic surface about the ion behaves as a disturbing center and maybe said t o be hydmted peri-surface-meaning a t and round-about
the ionic surface. The latter class includes, however. both structure makers such a s Li+ and F - and structure breakers such a s R b f and GI-.
(18) E. R Nightingale, Jr J P h y s Chsm 64, 162 (1960) (19) G H. Haggis, J . B Hasted, and T. J Buchanan, J . Chwn. Phys., 20, 1452 (1962).
896
E. R. NIGHTINGALE, JR.
previous paper.3 I n Fig. 1, these data are compared for a wide variety of ions. Curves A and C appear to infer that the energy-entropy relation for the RdN+ ions does not in general conform to that for the more common ions. However, it must be recognized that these calculations all have been based on the molar concentration scale. For common ions, this scale is satisfactory since the density of most common inorganic salt solutions is such that one liter of a molar solution contains very close to 54 moles of water. For (CH3)4NBr, (C2H&NBr, (C3H&NCl, and (C4H9)4NBr,however, one liter of a molar solution contains only 49, 46, 43, and 39 moles of water, respectively. Thus for these latter species, the viscosity and the apparent B-coefficient of a molar solution are appreciably greater than for a molal solution. The appropriate corrections in AE" and AS" may be made as follows. Assuming20that
+25oc
-'20oc
+1500
w i
Vol. 66
+loo0
8\ -I
Q. V
it may be shown3that
.-
-1uoo
I -4
&===Me;4NC -2
I
I
0
+2
,
+4
AS:, E.U. Fig. 1.-Activation energy us. activation entropy: A, RrN+ ions on molar scale; B, R4NC ions corrected to molal scde; C, common ions on molar scale.
interferes with the ice-like water structure,6 whereas the weakly oriented water about the larger (CH3)4N+ ion participates more readily in the fluctuations of the water structure. I n the previous discussion on activation energies and entropies for viscous A O W ~it was shown that the apparently anomalous relation of positive Bcoefficients accompanying negative activation energies occurs for ions such as Ba+2, IO3-, SOr=, and now (CH&N+, which are minimally peri-surface hydrated. Furthermore this relation is temperature-dependent, for if a higher reference temperature, say 40°,is chosen in place of 25", "normal" ions such as K+ and C1- likewise appear anomalous. This behavior is characteristic of ions for which extensive hydration beyond the primary solvent sheath is not significant and for which the temperature independent ion-dipole solvation forces predominate. Thus the viscosity temperature coefficient of aqueous solutions containing (CH3)4N+ is like that described previously: as the temperature increases, the normal ordering of the water structure is destroyed, and the water molecules become more susceptible to peri-surface ordering in the relatively weak field of the ion. It is instructive to compare the activation energies and entropies for viscous flow of the tetraalkylammonium ions with those calculated in the
where the fractionf is given by f = ncln, 5 1 where n, and n, are the number of moles of water in a molar and molal solution, respectively. Table I11 lists the corrected values for AE" and AS* for both the salts and the cations calculated using eq. 4. I n correcting these values, AF" was TABLE rrI CORRECTED ACTIVATION ENERGIESAND ENTROPI~S FOR VISCOUSFLOW AT 25" (CONCN. = 1 IXOLE/~OOO 0.) AE*,
Salt
(&)+
kcal.
AE+*, cal.
AS*, e.u.
A&*, e.u.
(CH&NBr
0.131 2.85 -920 +1.85 -3.40 (C2H&NBr .327 4-11 $350 5.61 +0.35 (C&7)*NCl ,882 5.00 $1230 7.54 +2.25 (CJXB)4NBr ,987" 6.05 +2280 10.6 +5.35 For internal consistency, this value has been used instead of that measured by Wen (Table 11, ref. e), although Wen's value for dB/dT has been used to calculate AE* and AE+*. Using Wen'svalueforB?, AE*is decreased about 10%.
assumed to remain constant since the change in the logarithm of the particle volume is negligibly sma11.3 Curve B in Fig. 1 demonstrates that when corrected to the molal scale,21the behavior of the activation energies and entropies for the tetraalkylammonium ion closely parallels that of the common ions. The apparent deviation between curves B and C in Fig. 1 stems directly from the large activation free energy of the tetraalkylammonium ions (Table 111, which in turn results from their abnormally large molar volume (ref. 3, eq. 6). If allowance is made for this difference in AF", (20) The error introduced by this assumption is proportional to ( b m / b C ) c I and is negligibly small. (21) The Jones-Dole equation originally was used with both the molal a n d molar concentration scales (ref. 10) but virtually all recent viscosity data havo been interpreted on the baais of the molar scale (ref. 14). Curve C in Fig. 1is based on the molar scale (ca. 54 moles of water per liter of solution).
-
May, 1962
HIGHSPEEDSTIRRING TECHNIQUES
it may be seen that the activation energies and entropies of the tetraalkylamrnonium ions are in fact consistent with those of the common ions.
IN
SOLUBILITY STUDIES
897
Acknowledgment.-The assistance of Mr. R. F. Benck in determining the viscosities of some of the solutions is gratefully acknowledged.
HIGH SPIEED STIRRING TECHKIQUES IN SOLUBILITY STUDIES : A CRITICAL APPRAISAL1 AND APPLICATION TO HIPPURIC ACID ESTERS’ 13Y R. J. LARESI3, D. A. ROBINSOS, w.F.BRASSINE,A N D W. J. CASADY~ West Virginia University Medical Center, Department of Biochemistry, Morgantown, West Virginia Received November 16, 1901
Since a possible relationship between the variation of rate of hydrolysis with ionic strength and the variation of solubility with ionic strength has been suggested, it was considered desirable to determine the effects of ionic strength upon the solubility of a serieci of hippuric acid eaters. Some difficulties involving hydrolysis before reaching equilibrium were encountered. A method is outlined using very rapid stirring a t approximately 30,000 r.p.m. Equilibrium was rpached within less than one hour. I n order to test the high-speed technique, the temperature dependence of the solubility of free hippuric acid was determined, and the thermodynamical values obtained were compared to the results of an earlier work which made use of conventional agitation. The agreement was found to be entirely satisfactory.
Introduction
It has been suggested by Miles, Robinson, and Canady3 that the variation with ionic strength of certain kinetic constants associated with some enzyme catalyzed reactions may be related to the variation of the solubility of the substrate with ionic strength. Since it has been shown that a homologous series of hippuric acid esters, up to and including butyl hippurate, are hydrolyzed in the presence of ol-chymotrypsin,* it was deemed advisable to study the effect of ionic strength on the solubility of those substrates. One problem which might be anticipated in regard t o such a study of these esters in aqueous solvents would be the possibility of hydrolysis while equilibrium was being reached. This problem was indeed encountered, the apparent solubility slowly increasing with time. Even after 4-6 days of equilibration with the mild agitation used iii a previous study of the solubility of free hippuric the readings still mere rising. This continuous rise was accompanied by a corresponding drop in p H . The decision was reached that a much more rapid method was required in order to study the solubilities of such esters. It was judged that the most likely way to keep the ester in contact with water for the minimum length of time was to employ extremely high-speed agitation in order to reach equilibrium very rapidly. After examination of available equipment, it was decided that tlhe Virtis Model 23 homogenizer supplied the necessary features. Four blades are used, and according to the manufacturer, the speed attained with solutions of the visocosities encountered in this study is approximately 30,000 r.p.m. No material change in reading could be detected (1) Supported by Grant No. NSF-G-7587 from the National Science Foundation and by Grant No. RG-8122 from the National Institutes of Health. (2) Reprint requests t o this author. (3) J. L Miles, D A. Robinson, and W. J Canady, Federation Proc., 20, 231 (1961). (4) G . H. Nelson, J. L. Miles, and W. J. Canady, Arch. Biochem. Baophys., in press. (5) R . J. Larese and W. J. Canady, J . Phyr. Chem., 66, 1240 (1961).
with any of the substances investigated here after treatment for 30 min., and it was assumed that equilibrium had been reached in this time. It still remained necessary to demonstrate the validity of the high-speed technique before it could be applied with any certitude to the st’udy of the hippuric acid esters. A suitable test was considered to be a study of the temperature dependence of the solubility of hippuric acid itself, which already has been investigated using conventional stirring technique^.^ Agreement of the thermodynamical quantities for the solutions of hippuric acid obtained by both methods could be taken to constitute a good test of the method employed. For this reason, the work presented consists of the study of the temperature dependence of hippuric acid in water, and the effect of potassium chloride on the solubility of methyl, ethyl, propyl, isopropyl, and butyl hippurates a t 25”. Experimental Materials.-The materials for the temperature depcndence studies on hippuric acid were the same as those previously d e ~ c r i b e d . ~The esters were prepared by the method of Nelson, Miles, and can ad^.^ The potassium chloride mas Fisher’s “Certified A.C.S.,” and was used without further treatment. Equipment.-Constant temperature was maintained by means of a Sargent thermistor controlled water-bath, whic) is capable of maintaining the temperature within =kO.Ol . The temperature was measured with two EXAX solidpoint thermometers having temperoature ranges of 0 to 30 and 20 to 50” in increments of 0.1 . These thermometers were calibrated against a Leeds and Northrup platinum resistance thermometer over the entire experimental range. The platipum resistance thermometer had been calibrated previously by the U. S. Bureau of Standards. A Beckman DUV spectrophotometer waa used for the photometric determinations. As mentioned earlier, the Virtis Model 23 homogenizer was used to provide agitation. Procedure.-The homogenizer was placed near the waterbath and the head of the instrument swung around to extend out over the bath. The flask supplied with the homogenizer was supported in the bath by means of a tripod, and the clamp supplied with the instrument tightened down to make it secure. Thus the temperature within the homogenizer flask was maintained by the mater-bath. Agitation for protracted periods of time was found to appreciably warm the solution in the homogenizer flask, hence intermittent agitation was used. Three-tenths of B gram of hippuric acid or ester of hippuric
