1695
ACTIVITY COEFFICIENTS OF NONELECTROLYTES
Acid-Base Equilibria in Concentrated Salt Solutions. V.
Activity
Coefficients of Nonelectrolytes and Equilibria Involving Some Uncharged Bases in Lithium Chloride Solutions1 by William Proudlock and Donald Rosenthal Department of Chemistry, Clarkson College of Technology, Potsdam, New York 1,9676
(Received November 4,1968)
The activity coefficients of some aniline derivatives and naphthalene were determined in 0-10 M LiCl by solubility measurements. I n several instances smrtll but significant deviations from the equation logf = BM were observed. The significance of these deviations was discussed. Also, other equations were used t o fit the data. The acid dissociation constant, KBH,and the activity coefficients quotient, & B E , were determined in 0-8 M LiCl for the unsubstituted, N-methyl-, and N,N-dimethyl-p-nitrosnilines by spectrophotometric measurements. Values for log &BE - log ~ B were H calculated, and various equations were used to fit the log &BH and log &BE - bgfBH results. With appropriate assumptions the differencesbetween the log &BE and log Q B K - log SBH results for the primary, secondary, and tertiary nitroanilines can be explained in terms of differences in solvation of the anilinium ions.
Introduction In explaining the effect of concentrated strong acid or salt solutions upon acid-base equilibria, it has been assumed in previous s t ~ d i e s ~that - ~ the activity COefficient of nonelectrolytes can satisfactorily be represented by the expression logf, = BM
(1)
where fi is the molar activity coefficient of the nonelectrolyte i in a solution M molar in strong acid or salt, and B is a constant for a particular base in a particular acid or salt. Other workers have made the same assumpt i o m 6,’ Many of the data on the activity coefficients of nonelectrolytes in strong electrolyte solutions are known to conform to cq 1.8 However, in most of the studies the total concentration of electrolyte never exceeded 2 or 3 M . Some results have been reportedg-12 which do not conform to this simple relation. Several other expressions for the activity coefficient of nonelectrolytes have been proposed. It has been suggested that the activity coefficient is directly proportional to the molality of added e l e ~ t r o l y t e , ~ -the l ~ logarithm of the activity of water,14 the hydration number and a polynomial in the molarmolality of ele~trolyte,’~ of electrolyte, e t ~ . ~ , l ’ ity8,l2or molality12~1~ The purpose of this study was to determine the activity coefficients of some nonelectrolytes in 0-10 M LiCl and to consider the extent to which these results conform to eq 1 and some of the other expressions. Further, the effect of concentrated lithium chloride solutions upon acid-base equilibria involving some of the nonelectrolytes which are bases was determined, and the activity coeficient results were used in attempt-
ing to understand tjheequilibrium results. The possible role of hydration in explaining some of the differences between primary, secondary, and tertiary amines was considered. 2-7
Experimental Section Reagents. Baker Analyzed reagent grade LiCl, formic acid, and HC1 were used. The nitroanilines were Eastman Kodak White Label compounds recrystallized twice from 95% ethanol and dried in vacuo. The pbromoaniline was an Eastman Kodak White Label com(1) This investigation was supported by U. S. Public Health Service Research Grants GM-09583 and GM-12086. A portion of this work was presented at the 150th National Meeting of the American Chemical Society, Atlantic City, N. J., Sept 17, 1965. (2) D. Rosenthal and 3. €3. Dwyer, J . Phys. Chem., 66, 2687 (1962). (3) D. Rosenthal and J. S. Dwyer, Can. J . Chem., 41, 80 (1963). (4) D. Rosenthal, I. T. Oiwa, A. D. Saxton, and L. R. Lieto, J . Phys.
Chew., 69, 1588 (1965). (5) D. Rosenthal, to be published. (6) K. N. Bascombe and R. P. Bell, Discussions Faraday SOC.,24, 158 (1957); R. P. Bell, “The Proton in Chemistry,” Cornel1 University Press, Ithaca, N. Y., 1959, p 82. (7) M. Ojeda and P. A. H. Wyatt, J . Phys. Chem., 68, 1857 (1964). (8) F. A. Long and W. F. McDevit, Chem. Rev., 51, 119 (1952). (9) L. P. Hammett and R. P. Chapman, J . Amer. Chem. SOC.,56,1281 (1934). (10) R. H. Boyd, ibid., 85,1655 (1963). (11) D. R. Robinson and W. P. Jencks, ibid., 87, 2470 (1965). (12) E. J. Cohn and J. T. Edsall, “Proteins, Amino Acids and P e p tides,” Reinhold Publishing Corp., New York, N. Y., 1943. (13) H. 8. Harned and B. B. Owen, “The Physical Chemistry of Electrolyte Solutions,” Reinhold Publishing Corp., New York, N. Y., 1958, p 531. (14) J. T. Edward and I. C. Wang, Can. J . Chem., 40,404 (1962). (15) D. G. Miller, J . Phys. Chem., 60, 1296 (1956). (16) H. L. Friedman, ibid., 59,161 (1955). (17) E. Hogfeldt and L. Leifer, Ark. Kemi, 21,285 (1963). Volume 79,Number 6 June 1969
1696 pound recrystallized twice from water and dried in vacuo. The naphthaline was a zone-refined Fisher Scientific Co. Certified reagent which was finely ground before use. The uncorrected melting points obtained after the above treatment were 148" for p-nitroaniline, 151" for N-methyl-p-nitroaniline, 163" for N,N-dimethyl-pnitroaniline, 66" for p-bromoaniline, and 81" for naphthalene. These are in good agreement with the literature values. Solutions. A ca. 11 M LiCl solution was prepared and allowed to stand for 4 to 7 days until the insoluble impurities had settled out. The clear supernatant liquid was siphoned off and standardized with a silver nitrate solution. The titer was adjusted to 10.00 M within 2 ppt. Stock solutions of the other reagents were prepared when required. Calibrated volumetric glassware was used in the preparation of all solutions. Solubility Measurements. If the saturated solutions of a sparingly soluble nonelectrolyte in water and in LiCl solution are in equilibrium with solid nonelectrolyte having the same composition and crystalline form, the chemical potential of the solid phase is a constant and the activity of the nonelectrolyte in the two solutions will be the same, i.e., OB) So = f B S where S is the molar solubility of a nonelectrolyte B in salt solution and So refers to the solubility in water. The reference state is a dilute solution of nonelectrolyte in water, i.e., f"B = 1. Thus, f~ = S o / S . Because of the limited solubility of B, the assumption that f~ is independent of the concentration of B is reasonableas Kaphthalene, p-bromoaniline, p-nitroaniline, Nmethyl-p-nitroaniline, and N,N-dimethyl-p-nitroaniline were equilibrated with 50 to 100 ml of 0-10 M LiCl solution in test tubes with screw caps using a tumbling device which kept the test tubes completely immersed in a thermostated water bath. Solutions were tumbled for about 48 hr at 25 f 0.02". A fritted glass filter tube was inserted into the test tubes, and a suitable aliquot was removed for analysis by pipet. The samples were heated t o 50" and tumbled for 12 hr at this temperature. The temperature of the thermostat was then returned to 25", and the tubes were tumbled for 24 hr before removing an aliquot. In those instances where the two equilibrations did not yield consistent results, additional equilibrations were performed until reproducible results were obtained. To ensure the absence of the protonated form of the substituted anilines, solutions used in the equilibration experiments and for the spectrophotometric soluM in NaOH. bility measurements were The solubilities in water at 25" were 3.97 X low3M for p-nitroaniline, 5.26 X 10-4 M for N-methyl-pnitroaniline, 8.27 x 10-6 M for N,N-dimethyl-p-nitroaniline, 1.69 X M for p-bromoaniline, and 2.70 X 10-4 M for naphthalene. Values of 4.10 X M for p-nitroaniline18 and 2.62 X M for naphthalenel9 The Journal of Physical Chemistry
WILLIAM PROUDLOCK AND DONALD ROSEKTHAL have been reported. A solubility of 2.62 X M can be computed for naphthalene using the absorbance data of Paulzoand molar absorptivities determined in this study. The differences between the values reported for p-nitroaniline and naphthalene and the present values are no greater than the experimental uncertainties in the present measurements. The principal source of error in those solubility determinations was the error in the preparation of solutions of known concentration for use in the measurement of molar absorptivity. BecausefB is a ratio of solubilities (or absorbances), an error in molar absorptivity is not reflected as an error in log f ~ .An error of more than 0.013 in log f~ seems unlikely . Spectrophotonaetric Measurements. Measurements were made using a Beckman DU and a Cary R!bdel 14 spectrophotometer with 10-cm fused silica cells. The solutions and cells were thermostated at 25 0.1". The reference solution in all spectrophotometric measurements was identical with the sample solution except for the absence of the absorbing substance of interest. To obtain suitable absorbance values in the solubility measurements the saturated solutions were diluted with water. The resulting solutions were sufficiently dilute in LiCl concentration that no appreciable band shifts were observed. The wavelengths used in the solubility measurements corresponded to absorption maxima and were obtained in preliminary studies using solutions of known concentrations. These solutions conformed to Beer's law in the concentration ranges employed. The analytical wavelengths and molar absorptivities were 380 mp and 1.35 X lo4 1. mol-I cm-I for p-nitroaniline (in 0.001 M NaOH), 408 mp and 1.66 X lo4 for Nmethyl-p-nitroaniline (in 0,001 M NaOH), 424 mp and 1.85 X lo4for N,N-dimethyl-p-nitroaniline (in 0.001 M NaOH), 290 mp and 1.38 X lo4for p-bromoaniline (in 0.001 M NaOH), and 219.5 mp and 8.75 X lo4 for naphthalene. The effect of concentrated salt solutions upon acidbase equilibrium was studied using the nitroanilines in 0, 2, 4, 6, and 8 M LiCl solutions. The wavelength corresponding to the absorption maximum of the basic form was determined a t each concentration of LiC1. In 2, 4, 6, and 8 M LiCl the maximum occurred a t 380, 382, 384, and 386 mp for p-nitroaniline; 411, 414, 417, and 422 mp for N-methyl-p-nitroaniline; and 428, 432.5,437, and 442 mp for N,N-dimethyl-p-nitroaniline. The molar absorptivity of the appropriate acid form was zero a t these wavelengths. A fixed concentration of nitroaniline was used at each salt concentration. In each LiCl solution for each nitroaniline the absorbance, AB, was measured with the
*
(18) A, R. Collett and J. Johnston, J . Phys. Chem., 30, 70 (1926). (19) J. E.Gordon and R. L. Thorne, ibid., 71,4390 (1987). (20) M.A.Paul, J. Amer. Chem. Soc., 74, 6274 (1952).
1697
ACTIVITY COEFFICIENTS OF NONELECTROLYTES
Table I: Experimental LogfB Values for Some Nonelectrolytes in LiCl Solution molarity
molalitya
Activity’ of water
1 2 3 4 5 6 7 8 9 10
1,022 2.086 3.197 4.360 5.579 6.860 8.205 9.620 11,110 12.682
0.9631 0,9169 0.8590 0.7888 0.7078 0.6190 0,5253 0.4345 0.3502 0.2787
7 -
LiCI----
___----_____-
-----____logfBb p-NAC
0.076 0.162 0.262 0.334 0.409 0.464 0.533 0.606 0.665 0.730
N-Me-p-NAC
N,N-DiMe-p-NAC
0,085 0.200 0.293 0.404 0,503 0.583 0.676 0.766 0.857 0.933
0.102 0.232 0.327 0.434 0. 538 0.668 0.752 0.876 0,990 1.102
p-BrAC
Naphthalene
0.098 0.173 0.274 0.400 0.474 0.562 0.664 0.732 0.830 0.930
0.188 0.376 0.536 0.724 0.898 1.056 1,236 1.426 1.594 1.781
See ref 3. * Calculated from f~ = So/S (see Experimental Section). p-NA is pnitroaniline, N-Me-pNA is N-methyl-p-nitroaniline, N,N-DiMe-p-NA is N,N-dimethyl-p-nitroaniline, and p-BrA is p-bromoaniline.
nitroaniline completely in the basic form and the absorbance, A , was measured a t three to six different HC1 or buffer concentrations. In each instance the ratio of the concentration of protonated to unprotonated form of the nitroaniline is given by [BH+]/[B] = (AB - A ) / A
Potentiometric Measurements. PHGE is the pH as determined with a pH meter using a glass electrode (GE) and a saturated calomel reference electrode. pR4H is minus the logarithm of the total molar concentration of strong acid. ~ H G measurements E were made with a Beclrman Model GS pH meter as described p r e v i o ~ s l y . ~In ! ~ acidic solution pMH - PHGE has previously been shown2to be a constant for a particular LiCl concentration. The tabulated values of pR4H P H G Ewere ~ used to calculate ph4H from PHGEvalues obtained with the formic acid buffers. PKBH and log QBH Values. It has previously been shown that the quantitative aspects of acid-base equilibria in concentrated salt solutions can be satisfactorily explained in terms of the expression2t4 K B H = ([B][H+]/[BH+])&’BH where KBHis the thermodynamic acid dissociation constant and QBH is a constant for a particular base in a particular salt solution. This can be written in the logarithmic form
data points) = 6, SD,, (standard deviation of pK) = 0.00321 and N,N-dimethyl-p-nitroaniline (0.652, np = 6, SD,, = 0.0071) were in good agreement with some of the literature v a l u e ~ . ~ l -The ~ ~ PKBHvalue for Nmethyl-p-nitronniline was 0.525 (np = 6, SD,, = 0.0038). These PKBHvalues were used in eq 2 to calculate log QBHvalues in 2 , 4 , 6, and 8 M LiCl s ~ l u t i o n . ~ * ~
Results The activity coefficients were calculated from the solubility data for each of the five nonelectrolytes and are presented in Table I. Least-squares calculations were performed to fit the data with eq 1 and the following equations which have been proposed2-17 log f B = n log a,
+ n log a, = BM + C M 2
b g f B = BM log f B
+
(4)”4
(5)8,12
log f B = Bm
(6) l 3
+ n log a, = Bm + Cm2
log f B = Bm log f B
(7)
(8)l6 where M is the LiCl molarity, m its molality, a, the activity of water and n, B, and C are least-squares parameters. Calculations were made with an IBM 1620 computer. The least-squares parameters and mean-squared deviation from regression, (SDy)2, are given in Table 11. N
The PKBHvalues for the three nitroanilines used in this study were determined in water a t 25” in the following way. [BH+]/[B] values were determined spectrophotometrically in solutions of known HC1 concentration; ( ~ K B H log &BE) was calculated using eq 2 and plotted against acid concentration. These plots were linear and were extrapolated to infinite dilution (log QBH = 0) by a least-squares treatment. The PKBH values obtained for p-nitroaniline [0.988, np (number of
(3Y4
(SDy)’
[IogfB (ca1cd)i i= 1
-
log f ~ ( e x p t l ) i ] ~ / (N LSP)
(9)
(21) M. A. Paul and F. A. Long, Chem. Rev., 57, 1 (1967). (22) E. M. Arnett and G. W. Mach, J . Amer. Chem. SOC.,86, 2671 (1964). (23) A. I. Biggs and R . A. Robinson, J . Chem. Soc., 388 (1961). (24) D. D. Perrin, “Dissociation Constants of Organic Bases in Aqueous Solutions,” Butterworth and Co. Ltd., London, 1965,pp 65, 91.
Volume 78, Number 6
June 1069
1698
WILLIAMPROUDLOCK A N D DONALD ROSENTHAL
Table I1 : Least-Squares Fits of Log f~ Dataa Nonelectrolyteb
Equation
p-NA
1 3 4 5 6 7 8 1 3
N-Me-p-NA
4 5 6 7 8 1 3 4
N ,N-DiMe-p-NA
0
6 7 8 1 3 4 5 6 7 8 1 3 4 5 6 7 8
p-Br-A
Naphthalene
a
n
B
...
0.0788
- 1.6009
C I
...
0.2965
0.0890 0,0873 0.0628 0.0953 0.0831 0.0958
...
... 0.8672
-2.0322 0.1959
-0
...
...
-0.000953 ... ..,
-0.002077 ...
... ...
...
-2.3366 - 0.0375
0,1079 0.1082 0.0910 0.1155 0.1063 0,0932
...
... 0.6535
...
...
- 1.9825
0.000175
... ...
- 0.001560
0.0967 0.0961 0.0774 0.1035 0.0937 0.1779
... 0.6976
...
...
- 0.00365 ... ...
- 0.001659 . . ~ ...
...
-3.7878 -5.6415
...
0.1804 0.1803 0.1477 0.1931 0.1761
... 1.2116
...
I
... ... ...
...
0.0775
001466
... ... ... ...
0.1046 0.1033 0.0795 0.8656 0,0999 0.1096
...
0.000422 0.016196 0.000052 * 0.000053 * 0.001978 0.000046 * 0.000076* 0.000223 0.022328 0.000067 * 0.000073* 0.001989 0.000066 * 0.000064* 0.000082 * 0.023787 0.000076 * 0.000086* 0.001177 0.000076 * 0 000098* 0.000162* 0.019171 0.000153* 0.000156* 0.001376 0.000137 * 0.000161* 0.000114* 0.066389 0.000113* 0.000109* 0.003887 0.0001 19* 0.000175*
.
... ...
-0.002066
. I .
0.1119
.
(SDY)~~
-0.000312
... ...
- 0.002887
Values which are not significantly poorer than the best fit (as determined by F test, 90% level) are indicated with an asterisk. See eq 9.
’ See Table I, footnote c.
Table 111: Log &BE Values for Nitroanilines LiCl, M
2 4 6 8
___-
---p-NA
log Q B H ~
0.478 0.977 1.593 2.390
_-____-SDxb 0.0012 0.0038 0.0038 0.0035
__-_-_0.641 1.311 2.039 2.956
------N,N-DiMe-p-N.4-------.
N-Me-p-NA----
log Q B H ~
SDXb
0.0027 0,0019 0.0095 0.0144
log Q B H ~
0.775 1.558 2.420 3.366
SDXb
0.0009 0.0034 0.0076 0.0092
Calculated using eq 2 and the following PKBRvalues: 0.988 for p-NA, 0.525 for N-Me-p-NA, and 0.652 for N,N-Di-Me-p-NA. is the standard deviation of the mean log &BE. The mean value is based on determinations in three different acid or buffer soluH pMH - p H a ~ values. tions. These standard deviations do not reflect the uncertainty in ~ K Baiid a
* SD,
where N , the number of data points, is 10 and LSP is the number of least-squares parameters. 26 Values of (SDy)2 marked with an asterisk are not significantly different from the ones corresponding t o a best fit. In each of the least-squares calculations designated with an asterisk the magnitude of the difference between the calculated and experimental log f~ values is probably The Journal of Physical Chemistry
no greater than the uncertainty in the experimental values. The results of the study of the effect of LiCl concentration upon acid-base equilibria involving the three
w, Snedecor, ,,statistical Methods,,, Iowa state College (25) Press, Ames, Iowa, 1956,
1699
ACTIVITY COEFFICIENTS OF KONELECTROLYTES nitroaniline bases are summarized in Table 111. Values for log QBH were calculated from eq 2 using the PKBH values obtained in this study, spectrophotometric measurements to obtain [BH+]/ [B] and the stoichiometric HC1 concentration or pHcE measurements to calculate pMH. The differences between log QBH (Table 111) and log f B (Table I) are given in Table IV.
Table IV: Log QBH
[B]awyf B [B.QHz~]~B.~H,o
needs to be considered. Where only one equilibrium is involved
- logfs Values for Nitroanilines
LiCI, M
p-NA
N-Me-p-NA
N,N-DiMe-p-NA
2 4 6 8
0.316 0.643 1.129 1.784
0.441 0,905 1.456 2.191
0.543 1.124 1.752 2.490
Discussion Activity Coeficients of Nonelectrolytes in LiC1. From the results of the least-squares calculations, which are summarized in Table 11, it appears that the log f B values of naphthalene, p-bromoaniline, and N,Ndimethyl-p-nitroaniline are linearly related to the molarity of LiCl (eq 1) in 0-10 M LiC1.8 N-R4ethyl-pnitroaniline and p-nitroaniline do not conform to this simple relationship. Note the curvature apparent in the plot of the experimental points for these latter two compounds (Figure 1). The addition of an n log a, termzd4or a C M 2 term8s12 to the BM term results in an equation (4 or 5 ) which gives a good fit to all the data. A polynominal in M of degree higher than two8p12does not lead to a significantly better fit. Equation 6 which is linear in molality13 does not give a good least-squares fit to the data of Table I. The addition of an n log a, term (eq 7) or a Cm2term (eq 8) to the Bm term does give a good fit. A polynomial in m of degree higher than two does not appreciably improve the fit. Equation 3 which is linear in log a, does not fit the data very well. Most of the theoretical lead to dilute solution expressions for logfB which are linear in molarity or molality. The results of this study indicate such a "limiting law" is applicable to all of the nonelectrolytes studied in LiCl. Deviations from this simple expression in more concentrated LiCl solutions can be considered to be due to electrostatic or chemical interactions between the nonelectrolyte ions and water which can be neglected in a narrow range of dilute solutions or do not become important except at large salt concentrations. One possible chemical interaction is variable hydration of the nonelectrolyte,26 so that one or more equilibria of the type
B-QHZO and
K B ~
B
+ qHzO
where (j'& is the experimentally determined activity coefficient. Provided KBpfB.pH~O/fBuwq is comparable
0
2
4 6 8 Concn of LiCI, M.
IO
Figure 1. Plot of log f~ for nonelectrolytes w. molarity of LiCl : 0, pnitroaniline; 0, N-methyl-pnitroaniline; d , N,N-dimethyl-pnitroaniline; 0, p-bromoaniline (points and line displaced by 0.3 unit on y axis to avoid overlap with N-methyl-pnitroaniline) ; (3, naphthalene. The lines represent a least-squares fit using eq 1. (26) G. Briegleb, Z . Elektrochem., 53, 350 (1949); D. Pressman and M. Siegel, J . Amer. Chem. Soc., 79,994 (1967).
Volume 75,h'umber 6
June 1969
1700
WILLIAMPROUDLOCK A X D DONALD I~OSENTHAL ~
Table V : Least-Squares Fits of Log & R H and Log & B H
_________
QBH data
-----------Log
n
p-NA N-Me-p-NA N,N-DiMe-p-NA
-2.719 -2.194 -1.518
(SDY)*
B
0,1745 0.2687 0.3516
6.08 x 10-4 8.01 X 1 . 4 2 x 10-4
to or larger than one, the value of log (fB)E will be significantly affected by the activity of water. The sharpness of the absorption peaks in the naphthalene absorption spectrum and the relatively weak x electron-water interaction are consistent with the expectation that naphthalene should be relatively free of strong solvation and specific interactions in water. The absence of the nitro group in p-bromoanilineg and the insertion of two methyl groups for amine protons in N,N-dimethyl-p-nitroanilines would be expected to weaken solvation and specific interactions. This is consistent with the observed conformity to the “limiting law” behavior for these compounds. Alternatively, the deviations from eq 1 or 6 might also be explained in terms of the “nonideality” of the solutions. The n log a, term in eq 4, the C M 2 term in eq 5, or the Cm2 term in eq 8 may be regarded as a reflection of this “nonideality.” The constant C may be considered as analogous to the second virial coefficient of a gas.27 As the deviations from 1 and 6 are relatively small, it is not possible to distinguish between specific chemical interactions and LLn~nideality.”27~28 Much larger deviations have been observed in other salt systems.p Q Activity Coeficients Quotient for Weak Bases, QBH. For any particular lithium chloride solution the log QBH values are different for the primary, secondary, and tertiary nitroanilines (see Table 111). This indicates that a single acidity function cannot be defined in terms of these three compounds which differ from each other in respect to N substitution. The results previously obtained for aniline and 2-aminopyrimidine differ significantly from the log QBH values for any of these nitroanilines.2~4 Similar differences have been reported for concentrated strong acid s o l ~ t i o n s . The ~ ~ ~log ~~ &BH values for p-nitroaniline differ somewhat from those previously reported for p-nitroaniline and other indicators. 2 , 3 In explaining the effect of concentrated salt solutions upon acid-base equilibria (log QM)~--Sit has been assumed that for nonelectrolytes log f B is linearly related to the molar salt concentration as in eq 1. The results of the present study indicate that a simple linear relationship does not provide a best fit of the experimental data for some compounds in LiCl. However, even for p-nitroaniline the standard deviation of the linear fit was less than 0.021, The uncertainty in most log &BH values is frequently greater than this. SOthat The Journal of Physical Chemistry
~~~~
- bg,fB Data for Nitroanilines -------Log
QBH
- log /B data--------
n
B
-3.014 -2,428 -1.593
0,08.57 0.1626 0.2386
(SDYP
6.47 x 10-4 6 . 9 1 x 10-4 1 . 0 7 x 10-4
in considering log QBH results in LiCl, the error introduced in assuming log fn is linear with lithium chloride concentration may be negligible compared to the errors in the log QBH results. Equations like log Q B H = B M
+
YL
log U,
+C
(11)
and log Q B H - log f B
=
BM
+ n log a, + C
(12)
with B , n, and C as least-squares parameters have successfully fitted log QBH data.2-6 Least-squares fits were obtained for the data of Tables I11 and IV. The results for the equation without a constant term, i.e., where C is zero, are summarized in Table V. The standard deviation from regression, SDy, is between 0.01 and 0.03; 0.03 is probably somewhat greater than the experimental uncertainty in the log QBH or log QBH - log f B results. The inclusion of a constant term in some instances leads to fits within the experimental uncertainty. In no instance were any of these threeparameter fits significantly better (F test, 90% level) than the fits presented in Table V. The fits obtained in Table V were significantly better than any oneparameter fit obtained with B, n, or C as the leastsquares parameter and the other parameters equal to zero. In general, the B, n, with C equal to zero fit was significantly better than any of the other twoparameter fits. The two exceptions to this were the n,C log & - log f B p-NA calculation and the B,C log Q N-Me-p-NA calculation, where the (SDY)~values were comparable to those of the corresponding B,n fit. QBH can be represented as a quotient of activity coefficients,2-6i8 i.e.
c
For any two indicator acids in a given LiCl solution
and (27) E. A. Guggenheim, Trans. Faraday Soc., 56, 1159 (1960). (28) G. R. Haugen and H. L. Friedman, J. Phya. Chem., 67, 1757 (1963). (29) D.Rosenthal and A. D. Saxton, to bepublished. (30) M. J. Jorgenson and D. R. Hartter, J . Amer. Chem. Soc., 85, 878 (1963).
ACTIVITY COEFFIC~ENTS OF NONELECTROLYTES
1701
bh’ refer to N-Me-p-NA and n“, b“, and bh” refer to N,N-DiMe-p-NA, then n’ can be evaluated from the data in Tables 111and IV Alternatel~~-~ a8
8 3
-n
=
6‘
- b + bh - bh’
and n r f - n = b”
- b + bh - bh“
The calculated n’ - n and n” - n values are presented in Table VI. If it is assumed that the uncharged bases aTe not solvated or are solvated to the same extent b = b’ = b”
If it is assumed that and equal to one.31 A = (log Q’B”
f’BH/f’BlH
i s medium independent
- 10gfBt) - (log & B H
- 1ogfB) =
( n - n’)log a,
(18)
Table VI presents the differences between the log QBH - log f B results of each of the other two indicators and
Table VI: Values of A, n’
-
n, and n’’ N-Me-p-Na and N,N-DiMe-p-NA LiC1, M
2 4 6 8 a
----N-M+p-NA-A(eq 19)= (n’ - n)
0.125 0.262 0.327 0.407
3.32 2.54 1.57 1.12
- n for --N,N-DiMe-p-NA-A(eq 18)a
0.227 0.481 0.623 0.706
(R”
- n)
6.03 4.67 2.99 1.95
p N A is the reference base B.
p-nitroaniline, A, Le., the left side of eq 15, 17, and 18 where B is p-XA. If A is divided by -log a,, n’ - n is obtained (eq 18)- If the average hydration numbers of the proton, H+, the base, B, and its conjugate acid, BHf, are h, b, and bh, respectively, presumably n = h b - bh. If n, b, and bh refer to p-NA; n’, b’, and
+
n’ n”
- n = bh - bh‘ - n = bh - bh“
If further it is assumed that the hydration of the anilinium ion is proportional to the number of hydrogen atoms bonded to the nitrogen, bh : bh’ : bh” : : 3 :2 : 1 and (n’ - n)/(n” - n ) = 0.5. The results presented in Table VI are in reasonable agreement with this prediction. Further, a value of n’ - n of about 1 and n’’ - n of about 2 is obtained in 8 M LiC1. This is consistent with three, two, and one water molecules being bonded to the primary, secondary, and tertiary anilinium ion in 8 M LiC1. In 2 M LiCl n’ - n is about 3 and n” - n is about 6. This implies that there are rather large differences in the hydration numbers for primary, secondary, or tertiary anilinium ions. This would be explained in terms of several solvation layers of water about the anilinium ion. It should be remembered that these conclusions follow from several assumptions implicit in the derivation and interpretation of eq 18. One or more of these assumptions may not be valid, and A may not be directly proportional to (n’ - n) or (n” - n). Acknowledgment. The authors are indebted to Dr. G. R. Haugen of the Stanford Research Institute for his comments upon an early draft of this paper. (31) J . F . Bunnett, J . Amer. Chem. Soc., 83,4975 (1961).
Volume 75,Number 6
June 1969
