STANDARD PARTIAL MOLALHEATCAPACITIES OF SODIUM TETRAPHENYLBORON difficultie~.'~However, it seems likely that only one water molecule is involved in this reaction. This conclusion is based on the fact that when reaction 4 involves trimethylamine and its conjugate acid, only one solvent molecule is involved when the solvent is either water5&or methanol.12 I n view of this evidence, it seems reasonable to assume that one water molecule is involved for the methyl-substituted pyridines, since in methanol it was found' that one methanol molecule is involved for these compounds. Thus the transition state for this reaction is probably similar to the one suggested in the methanol artic1e.l In the transition state, the nonbonded p electrons of the oxygen of the water are probably involved and the oxygen is probably pyramidal as shown in Figure 1. Whether this transition state is symmetric (a) or unsymmetric (b) cannot
2525
be decided on the basis of the present information. As a result, both possibilities are illustrated in this figure. The number of solvent molecules involved in the acid dissociation step given in eq 5 is not known. However, the fact that reaction 5 occurs indicates that at least two water molecules must be involved. Thus the transition state for the acid dissociation step may be identical with the one shown in Figure 1, with the exception that one B molecule is replaced by a water molecule which may or may not be hydrogen-bonded to other water molecules. (14) The experiment which would indicate the number of solvent molecules involved in this reaction requires that [BH+]/[B] 2 100. Because the methyl-substituted pyridines are not sufficiently strong bases, it was not possible to determine accurately by potentiometric titration the value of [B] in solutions containing this buffer ratio.
Standard Partial Molal Heat Capacities of Sodium Tetraphenylboron in Aqueous Solution from 0 to 90°. Effect of Water Structure and Hydrophobic Hydration by S. Subramanian and J. C. Ahluwalial Department of Chemistry, Indian Institute of Technology,Kanpur, India
(Received January 5, 1568)
The standard partial molal heat capacities of sodium tetraphenylboron in aqueous solution from 0 to 90' have been determined by measuring the integral heats of solution as a function of temperature over the range 5-85', AC,o and Zp1p20 values at all temperatures studied are positive and larger than those reported for any other solute. The plots of A C and ~ cP: against temperature show two discontinuities which correspond to a minimum around 50' (ACpo = 154 cal deg-' mol-l) and a maximum around 70' (AC; = 245 cal deg-1 mol-l). The minimum is explained in terms of "hydrophobic interactions" and the maximum is presumed to be due to a reduction in the structure-making capacity of the solute above 70'. No quantitative interpretation for the discontinuities is available at present. This is the first instance that such pronounced discontinuities are observed in the temperature dependence of partial molal heat capacities of solutes (containing a large amphiphilic ion) in aqueous solution. This work suggests the need of more experimental data on the temperature dependence of thermodynamic properties of aqueous solutions of nonpolar solutes or solutes containing nonpolar groups in order to have a better understanding of the structure of aqueous solutions. Introduction The structural aspects of ion-solvent interactions in aqueous solutions have been discussed in great detail by Frank and Wen.2 Relatively small and multivalent ions have a net structure-making effect, while most anions and large monovalent cations have a net structure-breaking effect on the water structure. That normal 1 : 1 electrolytes cause the disruption of water structure has been confirmed by various experimental
meansn2 Such electrolytes increase the viscosity of water and give rise to negative partial molal heat capacities in aqueous solutions. As the temperature is increased, the net structure-breaking influence of such electrolytes decreases, thereby causing a diminishing of the viscosity enhancementa and the negative (1) T o whom all correspondence should be addressed. (2) H. 8. Frank and W. Y. Wen, Discussions Faraday Soc., 2 4 , 133
(1967). Volume 72, Number 7
July 1568
S. SUBRAMANIAN AND J. C. AHLUWALIA
2526 partial molal heat capacities. However, nonpolar solutes or solutes containing nonpolar groups in aqueous solutions display a behavior unlike those of normal electrolyte solutions. For example, the aqueous solutions of tetraalkylammonium halides have been found to give positive viscosity B coefficients4 which are highly dependent on temperature, large apparent molal heat capacitieslZ peculiar activity coeficients,s anomalous concentration dependence oi the partial molal volumes,6 and characteristic mobilities for the ionsS7 These observations are in conformity with the view that nonpolar solutes and ions with large nonpolar groups promote the water structure by increasing its "icelikeness" through the formation of Frank-Evans "icebergs."* It would be interesting to compare the structure-making capacity of sodium tetraphenylboron in aqueous solution with that of tetraalkylammonium halides. The former has a large nonpolar aromatic substituent in the symmetrical anion, while in the latter the substituents in the symmetrical cation are large nonpolar aliphatic hydrocarbon residues. This comparison would at once indicate the similarity and also variance, if any, in the two classes of compounds. The partial molal heat capacities of solutes in aqueous solutions is a convenient property for studying the influence of the solutes on the structure of water. Since very little precise data are available on the temperature dependence of properties in aqueous solutions, the present work was undertaken to obtain accurate partial molal heat capacities of aqueous solutions of NaBPh4 as a function of temperature over a large range of temperature. The results obtained from such an investigation are expected to be of great help toward a better understanding of the structure of aqueous solutions. An easy and accurate method of determining the partial molal heat capacities of electrolytes at infinite dilution is the "integral-heat methodJ1s which has specific and distinct advantages over the specific heat method, since in the latter the reliability of extrapolation from concentrated solutions to infinite dilution is subject to question. The integral-heat method involves measurements of the heat of solution at several temperatures. The heat involved in the dissolution of a solute in water is expressed as
AHa = nlR1
+ nzRZ+ nJ?lo
- nzH2
(1)
where Bl and R2are the partial molal heat contents of water and the solute, respectively, is the heat content of pure water, Hz is the heat content of pure solute, and nl and n2 represent the number of moles of water and solute, respectively. At infinite dilution
AH2 = n2Hzo- nzHz
(2)
Over sufficiently small temperature intervals, the temperature coefficient of the above expression is T h e Journal of Physical Chemistry
where ACpois the change in the heat capacity for the dissolution, C,, is the heat capacity of the pure solute, , is the partial molal heat capacity of the solute and CO in solution at infinite dilution. So an accurate determination of AH,O at various temperatures leads to values of partial molal heat capacities as a function of temperature. Experimental Section Apparatus. The submarine calorimeter used in this study was essentially similar to that used by Cobble, et al.9r10 A 550-ml glass dewar-type flask was fitted to a standard 71/60 taper joint and an evacuated stopper. The stopper contained four 10-mm exit tubes extending to a height of 5 cm above the top of the stopper. One of the tubes was fused to a standard joint to which a precision-bore tubing was attached to house the stirrer shaft. The other three tubes were meant for introducing a heater, a thermistor, and an ordinary Pyrex tubing closed a t one end to which the sample bulbs were attached. The stirrer was driven by an ac-dc motor at -500 rpm. The sample bulbs could be broken by moving the tube vertically downward and by hitting the bulbs against the anvil at the bottom of the calorimeter. The calorimeter was immersed in a thermostat whose temperature was kept constant to d=0.002" at lower temperatures and to i0.005" at higher temperatures using a Sargent Thermonitor. Extra heaters were used when working at higher temperatures. The heating element was made by winding 2 ft of no. 36 manganin wire noninductively around 4-mm Pyrex tubing which was painted with Araldite and which was baked for several hours at 60". Copper leads (no. 18) were used to carry the current. The potential leads for measwing the potential across the heater were attached to the midportion of the currentcarrying leads. The lead wires of the precision thermistor (Yellow Springs Instruments, Yellow Springs, Ohio) were soldered to copper leads, which in turn were soldered to a two-core shielded cable connected to an amphenol in order to be fed into the Wheatstonebridge circuit. The Wheatstone bridge was constructed from precision decade resistors (Electro Scientific Industries, Portland, Ore.) and precision resistors. Three legs of (3) M.Kaminsky, Discussions Faraday Soc., 24, 171 (1957). (4) R.L. Kay, T. Vituccio, C. Zawoyski, and D. F. Evans, J . P h y s . Chem., 70, 2336 (1966). (5) S. Lindenbaum and G. E. Boyd, ibid., 68, 911 (1964). (6) W. Y. Wen and 9. Saito, ibid., 68, 2639 (1964). (7) R. L. Ray and D. F. Evans, ibid., 70, 2325 (1966). (8) H.S. Frank and ,M.W. Evans, J . Chem. Phys., 13, 507 (1945). (9) C. M. Criss and J. W. Cobble, J . Amer. Chem. SOC.,83, 3223 (1961). (10) J. C.Ahluwalia and J. W. Cobble, ibid., 86, 5377 (1964).
STANDARD PARTIAL LIOLAL
HEATCAPACITIES O F SODIUM TETRAPHENYLBORON
the Wheatstone bridge consisted of the thermistor (3 kilohms for low temperatures and 10 kilohms for higher temperatures), and the 1.2-liilohm dekastat (in 0.1-ohm steps) in series with a fixed 49.9-kilohm resistor. The fourth leg consisted of a 12-kilohm dekastat in (1-ohm steps). The 12-kilohm dekastat was used to match the thermistor at all temperatures for a rough balance, and finer manipulations were always done with the 1.2kilohm dekastat. A mercury activator (1.35V) was connected between the thermistor-dekastat junction and its opposite 49.9-kilohm resistor. The remaining junction points were connected to a Leeds and Northrup amplifier. The amplifier, in turn, drove a Sargent Model T R 0-2.5-mV recorder. The power source for the manganin-wire calibration heater was a Sargent coulometric current source Model W with a built-in electronic timer which can be read with an accuracy of 0.02 sec. The current passed through the calibration heater was measured by measuring the voltage across a 10-ohm standard resistor (NBS Certified) using a precision K-3 potentiometer (Leeds and Northrup). The temperature sensitivity that could be detected over the whole range was -2 X Materials. All water used in the measurements was conductivity water obtained by passing distilled water through a Barnsted mixed-bed ion-exchangeresin column. Sodium tetraphenylboron was purchased from Fisher Scientific Co. (assay, 99.7%) and was purified by the method of Skinner and Fuoss.ll Procedure. The operating procedure was similar to that used p r e v i o ~ s l y . ~ Thin-walled ~~~ sample bulbs having a diameter of 8 mm made from 6-mm Pyrex tubing were cleaned, dried, weighed, and filled with pure dry sodium tetraphenylboron and were weighed again. The bulbs with the sample were dried and were sealed with a very thin flame a t the neck. Sample sizes ranged from 150 to 750 mg, resulting in calorimetric solutions of to 5 X lod3 m. The exact temperature of the water in the calorimeter at each operating temperature (at midpoints of the runs) was measured with the help of platinum resistance thermometer and a Mueller bridge. The runs were started when a linear time-temperature drift curve with a small slope was observed. Two electrical calibrations were made for each run, one before breaking the sample bulb and another after. A "best" straight line was drawn for each of the time-temperature curves and was extrapolated to the time at which either the sample bulb was broken or the calibration made. Several measurements of the heat of bulb breaking showed that the heat was negligible. The resistance of the calibration heater was measured at every temperature by measuring the voltage across a 10-ohm standard resistor connected in parallel to the calibration heater. The calorimeter was calibrated by measuring heats of solution of KCI. The values obtained were in good agreement (within 0.2%) with those reported by Gunn.12
-5500
2527
I
25
I
3s
,
!
45 $5 66 TENPLRANRL( Y )
, 75
I
or
, 95
I
I
Figure 1. Heat of solution of NaBPha at different temperatures.
Calculations and Results The heats of solution a t infinite dilution were obtained by extrapolating the plot of heat of solution as a function of molality at each temperature. The integral heats of solution, AH,, a t different molalities as well as the integral heats of solution at infinite dilution, AH$, for SaBPhd at the various temperatures studied are listed in Table I. The standard deviations of AHs values are also indicated in Table I. AHsovalues as a function of temperature over the range 5-85" are plotted in Figure 1. The dotted straight line in Figure 1 indicates the otherwise anticipated linear situation. The AC,O values were calculated from AHsovalues a t two adjacent temperatures; the temperature intervals were chosen such that there was no significant difference between dAHso/dT and A(AHso)/AT. The AC,O values were taken to represent the mean of the two adjacent temperatures. The heat capacity of solid sodium tetraphenylboron, C,,, a t each temperature was estimated by extrapolating linearly the values reported13 for KBPh4 up to 300°K and by making suitable correction for the difference between the K and IYa salts. The extrapolation was justified on two grounds. The variation of C,, with temperature for the I< salt was linear from 200 to 300°K. Also the differential thermal analysis on NaPBh4 showed that there seems to be no break in the C,, us. temperature curve for NaBPh4 from room temperature up to more than 200". The C,, values of NaBPh4 at different temperatures were obtained from those of KBPh, by assuming that the difference would be constant between the two salts a t all temperatures and further that the difference would be the same in (11) J. F. Skinner and R . M. Fuoss, J . Phgs. Chem., 68, 1882 (1964). (12) S. R. Gunn, ibid., 69, 2902 (1965). (13) T. Davies and L. A . Staveley, Trans. Faraday Soc., 53, 19 (1957).
Volume 72, Number 7 Julg 1968
2528
S. SUBRAMANIAN AND J. C. AHLUWALIA ~-
Table I : Heats of Solution of NaBPha in Conon, x 103
-AH&, oal mol-1
nt
Concn, m X 10s
-AH%, cal mol-1
Temp, 5.04' 7992 1.215 8033 i 5a 1.473 8023 f 5 1.614 7968 f 5 1.760 7978 f 5 1.850 8031 i: 13 2.090 8005 f 13 2.546 7998 AH2 = -8000 f 16 cal mol-'
Temp, 15.10' 0.8072 6289 f 11 0.8851 6325 f 11 0,9854 6310 f 11 1.1860 6308 2.1370 6306 2.4400 6247 i 12 2.6190 6223 f 12 3,1031 6197 f 31 3.1870 6135 f 31 AH2 = -6380 f 15 cal mol-"
Temp, 25.12" 1.490 4786 1.615 4744 =k 13 1.650 4717 i 13 1.964 4744 f 14 2.059 4758 f 14 2.064 4712 f 14 2.252 4693 =k 11 2.360 4676 i 11 2.463 4715 f 11 2 580 4675 f 10 2.586 4696 i 10 2.676 4720 2.980 4683 AH2 = -4805 f 15 cal mol-'
Temp, 34.91' 1.148 3091 1.370 3060 f 21 1.378 3103 f 21 1.533 3041 rt 24 1.793 3089 f 24 1.975 3016 f 1 1.975 3014 f 1 2.058 3073 2.465 3061 2.808 3009 3.234 3002 4.021 3007 AH2 = -3110 rt 20 cal mol-'
Temp, 44.73 O 1.736 1122 =k 2 1.927 1119 f 2 2.442 1097 f 3 2.533 1103 f 3 2.802 1103 Jr 12 2.902 1127 i 12 3.023 1123 f 8 3.150 1108 f 8 3.366 1076 3.694 1075 AH2 = -1150 f 8 cal mol-'
Temp, 55.01' 2.104 -399 f 7 2.250 -412 f 7 2,752 -419 f 7 3.184 -405 i7 3.400 -414 =k 2 3.408 -418 =k 2 3.641 -417 4.293 -411 AH2 = 410 f 4 cal mol-'
0 897 I
I
Temp, 1,165 1.522 1.764 2.008 2.410 2.883 2.984 3.139 3.485 AH2 = -2235
64.92 ' - 2198 -2077 f 24 -2130 f 24 -2150 i 24 2052 -2116 f 30 -2056 i 30 -2003 i 20 -2041 Jr 20 f 30 cal mol-'
-
Temp, 75.17' 1.021 -4620 f 15 1.230 -4650 f 15 1.471 -4660 f 4 1.713 -4667 f 4 2.210 -4652 2.743 -4598 f 6 3.046 -4610 f 6 3.395 -4661 AH2 = 4670 rt 17 cal mol-1
0'
a Standard deviation of individual measurements from the average value of determinations a t a close range of molalities.
I
I
,
I
I
IO
20
39
40
SO
60
TtMP6RA7UeL
1
I
,
70
do
PO
Y
("c)
Figure 2. Standard partial molal heat capacities of NaBPha in aqueous solutions a t different temperatures.
various complex salts of Na and K. The estimated C,, values of NaBPhr are subject to correction whenever actual determinations are made. However, we believe that the uncertainty in the estimated value is probably not more than 2 cal deg-l mol-l and would not, in any significant manner, affect the trend of our results and the discussion in view of the large value observed for ACPo. The partial molal heat capacities at infinite dilution, were obtained by adding Cp, and ACpo values. Table I1 gives the values of ACpo, C,,, and c,O a t various temperatures from 0 to 90". The values at 0 and 90" are extrapolated ones. ACpoand are plotted as functions of temperature from 0 to 90" in Figure 2. The accuracy of ACPo and is better than f 3 cal deg-I mol-l at all temperatures except at 70°, where the uncertainty is rt4.5 cal deg-' mol-'. The estimated uncertainties in the heat capacity values follow from those in the AH,O values indicated in Table I. Smoothed-out values of standard partial molal heat capacities of NaPBh4 in aqueous solution from 0 to 90" are given in Table 111.
cp,O,
cppaO
cppaO
Table 11: Heat Capacity D a t a for Crystalline and Aqueous NaBPhP Temp, OC
ACpQ
CPZ
GPZO
0.0 10.1 20.1 30.0 39.8 49.9 60.0 70.0 90.0
162.Ob 162.0 Jr 3 . 1 157.5 f 3 . 0 169.5 f 3 . 5 196.0 f 2 . 8 156.0 rt 1 . 2 182.5 f 3 . 4 244.0 f 4 . 7 85. Ob
94.6 97.6 100.8 104.1 107.4 109.7 113.7 117.3 124.0
256.6* 259.6 =k 3 . 1 258.3 Jr 3 . 0 275.6 f 3 . 5 303.4 i:2 . 8 265.7 i 1 . 2 296.2 f 3 . 4 361.3 rt 4 . 7 209. Ob
Temp, 84.71O 1.150 -5920 -I: 10 1.425 -5900 -i: 10 1.750 -5840 f 35 2.050 -5910 f 35 - 5870 2.925 - 5880 3.550 AH2 = 5950 f 14 cal molF1
The Journal of Physical Chemistry
I
'06
Water from 5 to 85'
a
Units in cal deg-1 mol-'.
* Extrapolated values.
STANDARD PARTIAL MOLALHEATCAPACITIES OF SODIUM TETRAPHENYLBORON
Table I11 : Smoothed-Out Values of ACpo and for Aqueous NaBPhra
0 10 20 30 40 50 60 70 80 90
162' 160 160 168 196 154 182 245 130 83
cp2
257' 257 260 272 303 264 295 360 248 209"
'
a Units in cal deg-1 mol-'. The estimated error in AC: and values is less than & 3 cal deg-1 mol-' a t all temperatures except 90°, where the uncertainty could be three times as large, Extrapolated values.
cp:plo
Discussion Figure 1shows the variation of AH2 of XaPBh4 with temperature. The value of AHSO at 25" is -4805 f 15 cal mol-', which agrees perfectly well with that obtained by Wu and Friedman14 and fairly closely with that of Arnett and M ~ K e l v e y . ' ~It may be seen from Figure 1that AHSO becomes more and more endothermic with increasing temperature. The increase in endothermicity is quite significant for AHso increases as much as by about 14 kcal on going from 5 to 85", the values being -8000 cal at 5" and $5950 cal a t 85". The variation of AHsowith temperature is linear only up to 50". These results find some similarity in the temperature dependence of heats of solution of benzene in water as determined from solubility studies.16 The AHSO value of benzene in the aqueous medium increases linearly with temperature from a small exothermic value at subroom temperatures to +2 kcal mol-' around 60". The recent experimental data on the heats of solution of alkylhexoxyethylene glycol monoethers" at 25 and 40" show that the heats of solution and ACpobecome more positive with increase in temperature and also with increasing carbon chain length. To explain the increase in endothermicity of heat of solution of NaBPhc with temperature as observed in the present investigation, we shall center all our discussions on the "flickering-cluster" model2 for water structure to which a statistical treatment has been afforded by NBmethy and Scheraga.l8 According to the flickeringcluster model, we have "icelike" (hydrogen-bonded) and "free" (unbonded) water molecules, the icelike patches enclosing within themselves void spaces. There is considerable support for the Frank-Evans hypothesis* that nonpolar solutes promote water structure through the formation of icebergs in aqueous solutionsS2 Like benzene and alkyl chain compounds, the
2529
tetraphenylboride ion, being significantly nonpolar, seeks the icelike regions in water, gets enclosed in partial cages,19 and interacts with the surrounding water molecules in such a way as to shift the equilibrium toward more icelikeness or more structuredness. That the nonpolar solute gets enclosed in cavities is known from the fact that the partial molal volumes of hydrocarbons are much less in water than in nonpolar solvents.20 Now the enforcement of water structure by the formation of more hydrogen bonds should make the enthalpy of introduction of the solute in water negative. I n addition there is a positive enthalpy contribution for the dissolution process arising from the formation of a tensile cavity around the nonpolar solute. The relative magnitudes of the two effects decide the sign and magnitude of AHso at any temperature. At low temperatures, since more structure will be present in water, there will also be more solvent cavities, which indicates that the enthalpy of solution will be predominantly controlled by structure promotion, whereas a t higher temperatures, as the solvent structure is being broken down, the solvent cavitation energy takes precedence over the structure-making enthalpy making AHso more positive. Around 50" AHso is zero, implying a balance of positive and negative-enthalpy contributions. At still higher temperatures, solvent cavitation energy exceeds the negative-enthalpy term and hence AHSO continues to be increasingly endothermic. ACpo and vs. Temperature Curve. The temperature dependence of ACpo and of NaBPh4 in aqueous solution over the temperature range 0-90" is shown in Figure 2. One finds large positive values of ACpoand a t all temperatures. ACpoas well as cpt increases with temperature, exhibiting a minimum around 50" and a maximum around 70". values of various common electrolytes in aqueous solutions reported in the l i t e r a t ~ r e ~ all ~ ~have ~ ' ~ negative ~~~,~~ values. These electrolytes have all been classed as structure breakers, leaving the solution less structured than waters2 The large positive values of ACpoand of NaBPhc
cp',2"
cp',2"
cppjzO
cppO
cp',2"
(14) Y.C. Wu and H. L. Friedman, J . Phya. Chem., 70, 501 (1966). (15) E. M.Arnett and D. R. McKelvey, J. Amer. Chem. SOC.,88, 5031 (1966). (16) R.L. Bohon and W. E'. Claussen, ibid., 73, 1571 (1951). (17) J. M.Corkill, J. F. Goodman, S. P. Harrold, and J. R. Tate, Trans. Faraday SOC.,63, 773 (1967). (18) G. NQmethy and H. A. Scheraga, J . Chem. Phys., 36, 3382 (1962). (19) G. NQmethy and H. A. Scheraga, ibid., 36, 3401 (1962). (20) W. L. Masterton, ibid., 22, 1830 (1954). (21) Thermal Properties of Aqueous Uni-univalent Electrolytes, National Bureau of Standards Annual Report NS RDS-NBS-2, U. S. Government Printing Office, Washington, D. C., 1965. (22) (a) J. C. Ahluwalia and J. W. Cobble, J . Amer. Chem. Soc., 86, 6381 (1964); (b) R. E. Mitchell and J. W. Cobble, ibid., 86, 6401 (1964); (c) E. C. Jekel, C. M. Criss, and J. W. Cobble, ibid., 8 6 , 5404 (1964). Volume 72,Number 7
July 1988
S. SUBRAMANIAN AND J. C. AHLUWALIA
2530 in aqueous solution are in conformity with the earlier observation that nonpolar solutes or solutes with nonpolar groups like tetrabutylammonium bromide are structure makers and hence give rise to positive AC,O values. It is interesting to compare the AC, values of NaBPh4 and n-Bu4NBr in aqueous solution. ACPo of NaBPh4 a t 25" is 164 f 3 cal mol-l deg-', while that reported2 for n-BuaKBr is 120-150 cal deg-I mol-' at the same temperature. On the basis of the larger size as compared to that of of n-Bu4N+ ( r = 4.94 BPh4- (T = 4.2 and the fact that the nonpolar part in n-Bu*N+ is aliphatic while in BPh4- it is aromatic, one would expect larger AC, values for the n-BuaN+ ion, but actually n-Bu4NBr has a less positive AC, than NaBPh4. This could be because of the Br- ion which, being a structure breaker, might have reduced the effect due to the structure-making capacity of R4n'+, while in NaBPha, Ka* ion may enhance the structure-making capacity of BPh4-. It is also possible that the sign of the large ion and the aromatic substituent may have some influence. The temperature dependence of AC," and (Figure 2) of NaBPha in aqueous solution is quite puzzling. ACPo values continue to increase in the temperature range 0-40" , the increase being negligible from 0 to Z O O , while from 20 to 40" it is as much as 38 cal deg-l mol-'. After 40" ACPo and hence c,,O begin to drop, giving rise to a minimum at about 50" followed by further increase resulting in a maximum a t 70". Above 70" the values drop again. The ACPo values corresponding to the minimum and maximum are 155 and 245 cal deg-l mol-l, respectively. The increase in ACPo and C?,; from 0 to 40" is in accord with the view2 that more and more water structure promoted by the nonpolar solute is broken down with increasing temperature, thereby causing more heat to be absorbed, which enhances the heat capacity. A similar temperature behavior of AC,O over the temperature range of 25-55" has been observed for potassium 0 ~ t a n o a t . e . ~ ~ As for the temperature dependence of ACPoand of the compound above 40" we have little doubt about the occurrence of the minimum and the maximum, because the uncertainty in the AC,O values ( k 3 cal deg-1 mol-l) is too small compared with the large drop (40 cal deg-1 mol-') in AC,O from 40 to 50" and the large rise (88 cal deg-' mol-l) from 50 to 70". Also it is very unlikely that any uncertainty in the estimated value of C,, obtained by extrapolation of known values between 200 and 300°K would rule out such pronounced discontinuities in the C?,;-T curve. Any discontinuity in the C,,-T curve is also ruled out from differential thermal analysis results. The minimum around 50" suggests a drastic reduction in the structure around this temperature. Although there are feeble evidences for discontinuities26in the properties of water as a function of temperature,
e,;
The Journal
of Physical Chemistry
the drop in AC, is too much to be supported by the thermal anomalies. Formation of ion pairs is also ruled out from the conductometric and spectroscopic of aqueous solutions of NaBPh4. The possibility of water-structure-enforced ion pairingz8 causing any change does not arise, since the Na+ ion is too small to cause a huge disturbance to water structure. Although precise data on the temperature dependence of partial molal heat capacities in the higher temperature range are available for a few aqueous electrolyte solut i o n ~ , we ~ , are ~ ~not , ~ aware ~ of any such data existing for aqueous solutions of electrolytes which contain nonpolar groups in the ions. We propose the following tentative qualitative explanation for the unusual behavior witnessed in the temperature range 40-70". There is ample evidence in the literature for the incidence of "hydrophobic interactions" and their consequential effects on the conformations of macromolecules. Advances in theoretical and experimental studies of hydrophobic interactions have been recently reviewed.29 Hydrophobic interactions describe the tendency of nonpolar groups to associate in aqueous solution, thereby reducing the extent of contact with neighboring water molecules. Hydrophobic bonding is frequently invoked in the interpretation of various anomalies in protein structure and reactivity. The positive free energies of transfer of amino acid side chains from H2O to D2O indicates more extensive hydrophobic bonding in D2O than in H 2 0 which is appropriate since D2O is known to be a more structured solvent than water.30 Similarly the transfer of hydrocarbons and tetraalkylammonium iodides from water to aqueous urea is accompanied by a negative free energy change, while AHo and ASo are positive, indicative of disruption of hydrophobic bonding by urea which means an increased solubility of hydrocarbonsai and tetraalkylammonium iodidesea2 If these examples are considered, it seems very likely that in order to reduce the interaction with water, the tetraphenylboride ions might associate, giving rise to hydrophobic interaction which would help minimize the solute-water contact to a considerable extent. The (23) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," Butterworth and Co. Ltd., London, 1959, p 125. (24) E. Grunwald, G. Baughman, and G. Kohnstam, J . Amer. Chem. SOC.,82, 5801 (1960). (25) P. White and G. C. Benson, J . Phys. Chem., 64, 599 (1960). (26) W. Drost-Hansen, presented a t the First International Symposium on Water Desalination, Washington, D. C., Oct 1965. (27) (a) A. K. Covington and M. J. Tait, Electrochim. Acta, 12, 113 (1967); (b) A. K. Covington and M.J. Tait, (bid.,12, 123 (1967). (28) R. M. Diamond, J . Phw. Chem., 67, 2513 (1963). (29) G. NQmethy, Angew. Chem. Int. Ed. En&, 6, 196 (1967). (30) G. C. Kresheck, H. Schneider, and H. A. Scheraga, J . Phys. Chem., 69, 3132 (1965). (31) D. B. Wetlaufer, S. K. Malik, L. Stoller, and R. L. Coffin, J . Amer. Chem. SOC.,86, 508 (1964). (32) F. Franks and D. L. Clarke, J. Phys. Chem., 7 1 , 1155 (1967).
STANDARD PARTIAL MOLALHEATCAPACITIES OF SODIUM TETRAPHENYLBORON enthalpy of hydrophobic interaction is slightly positive3a a t room temperature for amino acids involving aromatic and aliphatic side chains. It has been described in great that although hydrophobic interaction is significantly maximal a t low temperatures in view of the maximal structure of water, the endothermicity would make the of hydrophobic bonding itself, A",: interactions stronger with an increase of temperature. calculation^^^ show that for the interaction of a pair of phenylalanine side chains, which resemble the substituent in BPh4- ion, the hydrophobic interaction gains maximal strength around 42". Since hydrophobic interaction is accompanied by a decrease in the heat capa~ity,33,3~ the temperature of maximum hydrophobic interactions would correspond to a maximum decrease in the AC, value. For the tetraphenylboride ion, the temperature of maximum hydrophobic interactions might be anywhere between 45 and 5 5 " , in which case the minimum in the ACp0-T curve around 50" would be explained. The foregoing evidence suggests convincingly, but not conclusively, the existence of hydrophobic interactions in NaBPh4 aqueous solutions. With increase of temperature, AC, increases owing to the thermal melting of icebergs but at the same time there is a concomitant decrease because of the increased strength of hydrophobic interactions. At temperatures below 40", the temperature effect might be the predominating effect, giving rise to a positive slope to the curve. At T > 40", hydrophobic interactions might supercede and submerge the temperature effect, thereby causing a net decrease in AC,. This decrease is maximum around 50", where the hydrophobic interactions are strongest. Above 50" while the temperature effect in increasing AC, continues, the hydrophobic interactions might have withered away, either because of the changes setting in the molecular conformation of the tetraphenylboride
2531
ion or because of natural attenuation, resulting from the lack of entropy-favored driving force, causing AC, to rise once again till it reaches a maximum value a t 70". The decrease in AC, above 70" may be due to the decrease in the structure-making ability of the solute a t the highest temperatures where the solvent structure is nearing total collapse. It might be that this factor is values responsible for the maxima observed in the for various e l e c t r ~ l y t e s ~ ~in" the J - ~region ~ 50-70". The Cp,eO values of NaBPh4 follow the same trend of ACPo with regard to the temperature variation, although the temperature coefficient of C,, of solid NaBPh4 is positive in the temperature range covered. The temperature coefficient is small enough (0.3 cal deg-l mol-') to get submerged in the large changes in ACPo. The opposing forces of temperature effect and hydrophobic interactions in determining the ACp0-T curve finds a parallelism in the factors determining the thermal stability of proteins.35 The interplay of hydrophobic interaction in the aqueous solutions of solutes containing nonpolar groups in determining the temperature dependence of the partial molal heat capacity of the solute is a plausible interpretation of the results obtained in this investigation but is by no means a certainty. We believe much more work needs to be done with solutes of the type of NaBPh4 on the temperature dependence of thermodynamic properties of aqueous solutions before anything could be said conclusively about the factors contributing to the structural changes in aqueous solutions with the change in temperature. We are presently continuing to investigate the same solute in aqueous solution by other studies which are in progress.
e,?
(33) G. NQmethyand H. A . Scheraga, J . Phys. Chem., 66, 1773 (1962). (34) G. C. Kresheck and L. Benjamin, ibid., 68,2476 (1964). (35) H. A. Scheraga, G. NQmethy, and I. Z. Steinberg, J . Biol. Chem., 237, 2506 (1962).
Volume 72,Number 7 July 1968
