JOURNAL O F T H E AMERICAN CHEMICAL SOCIETY Registered in U.S . Palent O&C.
@ Copyright, 1963, by the American Chemical Society
VOLUME85, NUMBER 11
JUNE
5, 1963
PHYSICAL AND INORGANIC CHEMISTRY [CONTRIBUTION FROM THE
DEPARTMENT OF CHEMISTRY,
UTAH STATE UNIVERSITY,
LOGAN,UTAH]
The Activity Coefficients of Indicators in Sulfuric Acid Solutions. The Relationships between Indicator Acidity Functions BY RICHARD H. BOYD RECEIVED DECEMBER 20, 1962 The variation of activity coefficient with acid concentration in aqueous sulfuric acid solutions has been measured for a number of indicators appropriate to the Ho, H R and H- indicator acidity functions. All ionic indicator activity coefficients have been referred to a common standard ion, the tetraethylammonium ion. The variations of activity coefficients with acid concentration are discussed and the differences between the above acidity functions interpreted in terms of these variations. It is found that from any one of the acidity functions and activity coefficient data the other two may be calculated over a considerable range of concentration. Protonation equilibrium data for some HO indicators are also reported.
Introduction The acidity function approach to the study of concentrated acids since its introduction by Hammett and Deyrup over thirty years ago’ has proved to be very u s e f ~ l . ~ -The ~ basic method of using indicators as a means of measuring the protonating ability of acids is simple and direct. However, the interpretation of acidity functions has been the subject of much discussion since the inception of the concept. The general acidity function, H z , based on the equilibrium
is the question of the invariance of the ratio f B H Z f l / f B Z , to indicator structure among the class of indicators used to establish the acidity function. This point can be tested t o some extent by the measurements used to establish Hz.5 Second, HZ is often applied as a measure of hydrogen ion activity in equilibria (or rates6,’) other than of the type used t o establish Hz. When this is done the ratio f B H z + I / f B z ) always appears relative to another such ratio appropriate to the new equilibrium (or rate). As an illustration, the equilibrium constant for the reaction A21
+ H+
AHz’+I
is defined by
can be expressed in terms of Hz. Thus
from which
and substituting for log aH+from eq. 3
(4)
where C refers to concentration, f is an activity coefficient and aH+ is the hydrogen ion activity. Equation 3 demonstrates that H Z is a measure of the hydrogen ion activity, but when regarded so, involves a t least one single ion activity coefficient. These latter two quantities, of course, are not in principle measurable separately. Equation 4 shows explicitly that HZ actually involves combinations of activity coefficients that are determinable in principle. The use of a function such as HZ in a given medium is complicated by two types of difficulties. First, there (1) L. P. H a m m e t t and A. J. Deyrup, J . A m . Chem. SOL.,64,2721 (1932). (2) Nearly every textbook on physical organic chemistry contains a section on acidity furctions. See, for instance, J. E, Hine, “Physical Organic Chemistry,” McGraw-Hili Book Co., Inc., New York, N . Y., 1956; E. S. Gould, “Mechanism and Structure in Organic Chemistry,” Holt, Rinehart and Winston, New York, K. Y., 1959. (3) For t h e inorganic-analytical point of view see H A. Laitinen, “Chemi1960. cal Analysis,’’ McGraw-Hili Book Co., Inc., New York, N. Y., (4) For t h e biochemical point of view see E. Kosower, “Molecular Bio b w , ” McGraw-Hill Book Co., Inc., New York, N. Y., 1962. (5) A comprehensive general review is given by M. A. Paul and F. A. Long, Chem. Reu., 57, 1 (1957).
(5)
Thus it is apparent that, although ( ~ B H Z +l!fBz> involves one or more single ion activity coefficients,. Its appearance in eq. 7 along with the ratio appropriate to the new equilibrium (fAz’/fAHz’+ 1) always involves combinations of activity coefficients which are, in principle, determinable. However, there is, a t present, almost no experimental information regarding the actual values of these determinable combinations. I n fact, when 2 = 2’ the last term in eq. 7 is often taken t o be zero for lack of better information. Clearly, a more satisfactory, yet economical, procedure would be to measure the activity coqfficients of the charged species appropriate t o Hz relative-to a standard ion. Similar measurements of ionic activity coefficients appropriate t o any new equilibrium (or rate) relative t o the same standard ion would allow the activity coefficient combination in eq. 7 to be constructed. Thus any acidity function, Hz, could be used in principle to represent the hydrogen ion activity in any other equilibrium or rate. Of course, there may well be experimental difficulties in carrying
1555
(6) F. A. Long a n d M. A. Paul, ibid.,57, 935 (1957). (7) H.Zoilinger, A n n . Reu. Phys. Chem., 13, 391 (1962).
1556
RICHARD H . BOYD
out measurements of activity coefficients truly representative of the molecular classes involved. I t is the purpose of the present paper to report measurements in aqueous sulfuric acid (up to -70% concentration) of the dependence on acid concentration of the activity coefficients of indicator molecules appropriate to three acidity functions. These are, first, the original HO function of Hammett based primarily on the protonation of substituted anilines. Second is the H R function based on the dehydration of triarylcarbinols t o carbonium ions.8 In this case, eq. 1-4 require some modification, ROH
HR
+ H + 2K + + H ~ O
(8)
P I ~ R OH log (CR+,ICROH)
(9)
= -log
aH+
+ log
fR+aHz 9 ~
.fROH
where an,o is the activity of water. The third function is H- which is based on the dissociation of cyanocarbon acids. $, lo
Experimental Methods and Results Activity coefficients were measured via solubility of the indicators in the acid solutions. Thus
f = f'(C'/C) (11) where f is the activity coefficient of the indicator and C is its concentration in a given acid solution in equilibrium with solid indicator. The primes refer t o a solution of different acid Concentration. The reference state (f = 1) is taken t o be a dilute solution of indicator in pure water, so t h a t f = (CO/C) where Cois the solubility in pure water.
dfX
(12) For a 1-1 salt, f = f t =
An experimental limitation on the activity coefficient measurement is imposed by the interference of the protonation equilibrium. Molecules should be chosen which are representative of the class involved. Further, these models must remain protonated or unprotonated (depending on which type of activity coefficient is being measured) over the entire acid concentration range. In the case of the neutral molecules considerable protonation can be tolerated providing only the neutral species in solution is measured. The solutions were equilibrated by mechanically shaking a considerable excess of finely divided solid indicator in 7-10 ml. of acid solution for several hours to overnight. The equilibra0.02" in a water-bath. tion flasks were thermostated at 25.00 Samples for analysis were removed by means of a 2-ml. pipet fitted with a fritted glass filter tube over the tip. Dilution was often necessary to obtain convenient optical densities. The concentrations were then measured spectroscopically in either a Cary model 15 recording spectrophotometer or Beckman model DU spectrophotometer. The charge types of the ionic indicator activity coefficients appropriate to the HO and HR function are positive (JBH- or f ~ + and ) must, of course, be measured in combination with a n anion (fBHtf.4- or f ~ + f . t - ) .The 1,1,2,3,3-~entacyanopropenide ( P C P - ) anion was chosen for this purpose as i t is not protonated in the aqueous sulfuric acid solutions ~ s e d . ~ fBHtfA.l~ or fR.f.tmay be measured as fi2 of a dilute solution of the salt BH+Aor R + A - in the acid solution. The present work was greatly aided by the availability of a suitable anion for combination in salts with indicator cations. Salts of Hammett indicators were prepared by mixing warm equimolar solutions of the substituted aniline, in sufficient acid to ensure protonation, with sodium pentacyanopropenide in water. The salt precipitated on cooling to the ice point. I t sotnetiines precipitated partially as an oil in which crystallization was easily induced by scratching. All of the anilines were purchased commercially. In the case of the weaker bases (p-nitroaniline, for example) measurements in the most dilute acid solutions were not made due t o the dissociation of the cation. Extrapolated values were arrived a t by assuming the variation of the activity coefficient in the less concentrated solutions is the same as for salts of the stronger bases (aniline, for example). The pentacyanoprrjpene anion spectral absorption (A,, 410 mp) was used as the measure of concentration. (8) N. C . Deno, J . J. Jaruzelski and A . Schriesheim, J . A m C h e m Soc., 77, 3044 (1955). (9) R . H . Boyd, ibid., 83, 4288 (1961). (10) R. H. Boyd, J . Phys. C h e w . , 67, 7 3 7 (1963).
VOl. 85
Salts of Triarylcarbonium Ions.-Tri(P-methoxyphenyl)-carbonium pentacyanopropenide was the only salt studied. This carbonium ion was selected because i t remains ionized in relatively dilute acids8 It was prepared in a manner similar to t h a t of Deno, et ~ l .except , ~ t h a t the product was not isolated as such. The final reaction mixture was extracted with 207, sulfuric acid. The desired salt was precipitated from the aqueous acid b y adding a n exactly equimolar amount of sodium pentacyanopropenide. Care was required in preparing a n exactly stoichiometric salt. Due to the extreme insolubility of the salt a slight adsorbed excess of one of the ions can cause a serious error in the solubility determination through the common ion effect. The prepared salt was washed several times by equilibrating with 20% sulfuric acid and filtering. Measurement of the extinction of both the cation and anion peaks of the equilibrated solutions was used as the criterion of the stoichiometry. These were found to be in the proper ratio8Joand the ratio was independent of the solubility in different acid concentrations. Cyanocarbon Salts.-The pentacyanopropenide anion as explained above was used in combination with the cations of the Ho and HR indicators. Tetraalkylammonium salts (other than the tetramethylammonium) of pentacyanopropene were made by mixing equimolar aqueous solutions of tetraalkylammonium bromides or chlorides (Eastman Organic Chemicals Co.) and sodium pentacyanopropenide. The latter was prepared via the free acid from the tetramethylammonium salti1b y ion exchangell in hot water followed by potentiometric titration with sodium hydroxide. Tetraalkylammonium salts (other than the tetraethylammonium) of bis-(tricyanoviny1)-amine ( i x . , 1,1,2,4,:,5hexacyano-3-azapenta-1,4-diene) were prepared in a slmllar manner t o the above from the tetraethylammonium salt." Neutral Indicators.-The neutral Hammett indicators were purchased commercially (Eastman Organic Chemicals Co., K and K Laboratories, Inc.) with the exception of 2,4-dichloro6-nitroaniline which was prepared as a custom synthesis by Aldrich Chemical Co. These indicators were appreciably protonated a t the higher acid concentrations. They were thus measured either undiluted or diluted with acid of the same concentration so t h a t the protonation did not interfere until the neutral base absorption became small relative to the protonated cation. Triphenylcarbinol (Matheson, Coleman and Bell, Inc.) was recrystallized several times from hydrocarbon solvent (Skelly~ converting the solve B). Deno and Perrizzolo's p r o c e d ~ r e 'of alcohol in the equilibrated solution to carbonium ion (prior t o spectroscopic analysis) by dilution with concentrated sulfuric acid was adopted, Protonation in the equilibrated solution at the highest acid concentration was corrected for by measuring the solution diluted with both concentrated acid and acid of the same concentration and taking the difference. Ethyl cyanoacetate (Eastman Organic Chemicals Co.) was a special case since it is liquid at room temperature and has no appreciable ultraviolet-visible absorption above 200 mp. I t s solubility was determ;ned by observing the volume required to titrate the acid solution t o cloudiness, This was checked by Kjeldahl nitrogen determination on the acid solution and gave good agreement. The effect of mutual solubility on the activity coefficient obtained from eq. 12 is unknown. p-Chloro-X-tricyanovinylaniline was prepared according t o McKusick, et al .14 This compound is a weak acid which remains undissociated in acid above 0.01 molar. The solubilitv d a t a are presented in Table I. Protonation Studies.-In order to provide additional information on activity coefficients, the protonation ratios CBH+/CB of three Hammett indicators were measured. These were 2,6dichloro-4-nitroaniline, 2,4-dichloro-6-nitroaniline and 2,4-dinitroaniline. The first of these apparently has not been m ~ ~ ~ r e d before and the previous data' on the others are from visual colorimetry without close temperature control. All measurements were made in 10-cm. cells t h a t had been thermostated a t 25.00 f 0.02" and immediately measured after removal from the therniostat. The data are presented in Table 11.
Discussion 1. Dependence of Activity Coefficients on Indicator Concentration.- -To be useful, the ionic activity coefficients should be independent of indicator concentration and f(C+,A-) = d f z ,where f+ is independent of the indicator anion and vice-versa. The indicators used here are rather insoluble and the resulting solutions, low in concentration in indicator, should satisfy the above (11) C. L. Dickinson, 13. W. Wiley and B. C. McKusick, J . A m C h e w . Soc., 82, 6132 (1960).
(12) W. J. Middleton, E. I.. Little, U . 13. Coffman and V. A . Endehardt, ibid.,80, 279.5 (19.58). (13) N. Deno and C . Perrizeolo, ibid.,79, 1343 (1957). (14) B . C. McKusick, R. E. Heckert, T. I,. Cairns, D . U . Coffman and H. F. Mower, ibid.,80, 2806 (1958).
June 5, 1963
.
(PCP-) and bis-(tricyanoviny1)-amine (bis(TCV)A-) The activity coefficient ratio ~ T E A + / ~ T M+ Ais the same nearly to within experimental error when calculated
conditions. This point was tested experimentally with tetramethylammonium (TMAf) and tetraethylammonium (TEA +) salts of pentacyanopropene SOLUBILITIES' AND
TABLE I ACTIVITYCOEFFICIENTS~OF INDICATORS TEA
T M A + PCPWt. % HzSO4
0 4.82 9.62 19.03 29.1 40.0 50.5 60.2 70.0
(Amax 410
mr) log f
2 . 0 1 x lo* 3.06 3.51 3.86 4.73 7.45 15.3 37.9
-0.183 ,243 - ,284 ,372 - ,569 - ,883 -1.277
+
Wt. % HzSOk
PCP-
+
-
Wt. o/o HzS01
0 4.82 9.62 19.03 29.1 40.0 50.5 60.2 70.0 78.2 88.5
TMA Bis- (tricyanovinyl)-amine (Amax 467 m r ) D log f +
0.817 X l o 2 -0.098 ,082 - ,064 - ,135 ,451 - ,943 -1.510 -2.244
-
-
1.320
-0.208
1.876
-0.361
6.38
-0.892
27.35
0-Chloroanilinium PCP (Amsx 410 mr) D log f +
-
0.260 X lo2 0.360 ,380 ,453 .605 1,183 3.01 7.77 17.50
1.89 1.94 1.90 1.64 2.43 3.88 6.20
x
103
-0.142 - ,165 - ,241 - .367 - .658 -1.064 -1.49' -2.03c
O-Nitroanilinium
(-0.18)" - .19 - .18 - .12 - .29 - .49 - .70
Phenyltrimethylammonium (Amax 410 mr)
+
6.21 X lo2 3.57 2.52 2.66 3.07 4.71 12.4
+
(-0.12)d - .18 .14 - .04 .10 .14 .00 - .29
1.200 1.325 1.49 1.85 3.20 7.63 23.6 41.3
-0.162 - .205 - ,256 - ,350 - ,589 - ,966 -1.456 -1.699
PCP -
2 ,G- Dichloro-4-nitroaniline (Amax 367 mr) D log f
0.395 ,375 ,360 ,335 ,360 ,550 1.01 2.15
(-0.14)e .10 .25 .22 .16 - .02 - .44 +
0.875 0.950 1.435 2.075 9.45 33.15 240
(-0.20)' - .24 - .41 - .58 -1.23 -1.78 -2.64
2,4-L)ichloro-G-nitroaniline (Amax 420 m r ) D log .f
0.555
0.022 ,039
.071
-
-
,039 ,143 .407 .735
,518 ,497 .472 ,541 ,870 1.74 3.20
7.53 x 102 8.76 8.41 6.35 4.75 4.15 5.00
-
Tri- (9-methoxyphenyl) carbonium PCP (Amax 480 ma) D log f
PCP -
log f
D 0.825 x 102
-1.72' Triphenylcarbinol (Amax 430 m r ) D log f
0.212 3 . 3 1 X loa 3.81 3.50 2.79 2.03 1.85 2.55 4.98
H2SO4
0 0.48 4.82 9.62 19.03 29.1 40.0 50.5 60.2 70.0
ACIDSOLUTIONS, 25"
410 m r ) log f
3.77 4.72 4.55 4.37 5.14 10.65 33.10 122.0 661
Anilinium+ P C P (Amax 410 m ~ ) D log f
bis-(tricyanoviny1)-amine (Amax 467 m r ) D log f
m-Nitroanilinium + P C P -
Wt. % HzSO4
D
-0.161 - ,210 - ,258 - .346 - ,680 -1.070 -1.528 -2.063
Wt. %
0 4.82 9.62 19.03 29.1 40.0 50.5 60.2 70.0
( b s x
log f
D 0.500 X lo2 .725 ,810 .905 1.11 2.39 5.87 7.64 10.31
IN SULPURIC
TBA+ PCP-
(Amsx 410 m ~ )
D
TEA
0 0.48 4.82 9.62 19.03 29.1 40.0 50.5 60.2 70.0
1557
INDICATORS IN SULFURIC ACID
0.030 ,048 ,070 ,011 - ,195 - .497 - ,762
-0.1gE - .16 - .04 .08 ,14 .06 - .ll - .42
7.50 15.50 N-Ethvlanilinium+ P C P (Arnx 410 mr) D log i
2 . 0 7 X lo2 2.70 2.68 2.39 2.26 2.89 5.55 16.35 38.0
-0.116 ,113 - ,063 - ,038 - ,145 - ,428 - ,897 - 1.265
-
0-Chloro-F-tricyanovinylaniline (Amax 358 m r ) D log f
4.00' 3.50 3.25 2.91 2.91 3.94 6.85 12.95 30.6
0.058 .090 ,138 .138 ,006 - ,234 - ,509 - ,884
2,4-Dinitroaniline @msx 348 mr) D log f
5.78 5.93 6.35 7.00 8.85 14.78 32.3 72.5 182.5
(Footnotes a through h are on following page)
-0.012 - ,042 - ,084 - ,185 - ,408 - ,748 -1.100 -1.500
0.150 ,098 ,090 ,040 ,031 ,040
0.15 .34 .37 .73 .83 .73
N.N-Dimethvlanilinium (Amsx 410 mr)
D 1.388 X loz 1.98 2.13 1.95 1.99 2.63 4.65 10.10 38.8
+
PCP-
log f
-0.153 ,172 - .147 - ,157 - .277 - .525 - .862 -1.446
-
Ethyl cyanoacetate
D 1.3Sh
log f
1.26 1.20 1.13 1.21 1.84 3.73
0.041 ,062 ,088 .058 - ,126 - ,433
2,4,6-Trinitroaniline (hrnax 412 m r ) D log f
1.350 1.460 1.675 2.44 4.50 10.92 27.40 59.1 63.8 210 1500
-0.034 - ,094 - ,256 - ,523 - ,908 -1.307 -1.642 -1.926 -2.192 -3.046
Vol. s5
KICHAKIIH. BOYD
13%
All solubilities are expressed l i s optical deiisity of 1-cm. equilibrated solution without dilution a t tlle wave lengtli indicated (Amsx). Approximate molar concentrations may be calculated from the following extinction coefficients ( C = D / e ) ; e = 2.3 X l o 4 (410 mG), P C P - (ref. 10); 3.1 x l O 4 (467 mp), bis-(tricyanoviny1)-amine (ref, 10); 1.05 X 105 (483 m p ) , tri-(9-niethoxypheny1)-carboniumion (ref. 8); 1.5 X lo4 (346 mp), p-chloro-n-tricyanovinylaniline(ref. 14); 1.07 X lo4( 367 nip), 2,6-dichloro-4-nitroaniline(this work) ; 4.58 X lo3 (420 mp), 2,4-dichloro-6-nitroaniline(this work); 1.4 X lo4(345 m p ) , 2,4-dinitroaniline ( M . E. Carsten and H . X. Eisen, J . A m . Chem. Soc., 75,4451 (1953));8.53 X 103(414nip),2,4,6-trinitroaniline (this work); 4.0 X 104(431m p ) , triphenylcarboniurn ion (ref. 13); abbreviations: PCP- = pentacyanopropenide, TMA = tetramethylammonium, TEA + = tetraetliylamrnonium, T B A + = Corrected for protonaActivity coefficient,f = Do/D where DOis optical density of solution in pure water. tetrabutylammoniuni. tion by assuming solubility product relation ( K = C+ C.-) holds and from protonation ratio, K = CA-/CH.~(ref. 9, 10). Co = (dl/R l)C-, where Co is corrected anion concentration and C- is measured concentration. Estimated from Debye-Huckel f Estimated by comparison with T E A + PCP-. 8 Compound ionizes theory. E Estimated by comparison with anilinium+ PCP-. Solubility expressed as volume (nil.) added to 25 ml. of acid solution. in pure water. +
+
TABLE 11 PROTONATION EQUILIBRIUM DATAIN SULFURIC ACID AT 25" -~--2,4-Dichloro-(j-nilroaniline (A,,,.x lug CBH+
Concn., wt. "lo
~
CB
420 mp)-
-2,6-Dichloro-4-nitroaniline
d log CBH+/CB d %
34.6 40.7 46.9 52.4 57.4 62.2
40.7 46.9 49.7 52.4 57.4
-0.552 - ,132 ,123 ,372 .914
wt.
-0.983 0,071 - ,5523 ,079 - ,066 ,096 .462 .lo0 ,965 ,098 1.43 pK' = -3.15 pK values are from comparison (ref. 5 ) with
-
70
CBH+ log Cn
Concn.,
2 . Use of a Standard Ion.-As discussed in the Introduction there is an advantage in measuring the ionic activity coeficients relative to a standard ion. In this work we have chosen the tetraethylatniTionium ion (TEA+) for this purpose. This allows us t o discuss the activity coefficient variations as single ion activity coefficient variations. For example, we define
or =ff.I.eA-jA= J'*'('rEAi',
0.068 .091 ,093 .lo8
/>K = -3.24 Hascombe and Bell's value (ref. 19) of
f roin either relatioii below
f*A.
307 mp)-d log CRH+/CB d%
(Anlax
pep-.)
(15)
The right-hand equality iii eq. 14 indicates the experimental origin of the data in this particular example. As long as only comparisons of the variation of activity coefficients between different ions are made, the choice of the standard ion is not important. However, it is clearly a convenience to pick one that has no functional groups that would be expected to lead t o specific interactions with the solvent. Thus the variation with acid concentration of the activity coefficient of the standard ion would be kept to a minimum. Den0 and his co-workers16,16 have pointed out the lack of specific solvent interaction with aryl carbonium ions and protonated olefins and argue that the activity coefficients should remain near one over the entire composition range in sulfuric acid solutions. There is, of course, no way or necessity of proving the above, but the tetraalkylammonium cations should enjoy similar advantages of minimum specific interaction effects. In addition, they are readily available and are completely stable over the entire composition range. The tetraethyl derivative gives solubilities in a convenient range with the pentacyanopropenide anion. It perhaps should be pointed out that there is a ininor difference in behavior between f+ * and f- *. Although the standard ion is chosen t o minimize specific interactions with the solvent its charge effect is still present. Thus f+* is of the type f+jl = f+', and (15) S . Denu, P. Groves. J. Jaruzelski and M . Lugasch, J. A t n . Chem. S O L . , 8 2 , 4719 (1960); N . Deno, P. Groves and G. Saines, i b i d . , 81, 5790 (1959). (16) K . Dcnu a n d co-workers, private cummunications (to be published).
----2.4-Dinitroaniline
(A,
348
51.3 55.2 58.9 62.6 65.8 67.5
-0.945 - .514 - ,071 ,355 ,688 ,850 $K = -4.42 1.02 for 4 chloro-2-nitroaniline.
a&)-----
0.112
.no
.115 .lo4 ,095
exhibits typical Debye-Huckel behavior in dilute solution ( a moderate decrease in log f* as the electrolyte concentration increases). On the other hand, f+* is of the type f+'/f+. The charge effect largely cancels and no Debye-Hiickel variation is expected. These effects can be clearly seen in our data for f+* and f-* in Fig. 1 and 3. The interionic effects also introduce some ambiguity in our reference state (eq. 11). This has been taken to be the solution in pure water, but it is not infinitely dilute. In most cases the solutions of ionic indicators in pure water are dilute enough that the difference in activity coefficient between our reference state and infinite dilution could amount t o only a few hundredths of a unit in log f. For some of the more soluble ionic indicators i t could amount t o as much as one-tenth unit. 3. Hammett f l o Indicators.- --The variation of activity coeficients with acid concentration of ionic Hammett indicators is shown in Fig. 1 . These are expressed relative to the tetraethylaninionium cation as explained above. The variations for neutral Hanimctt indicators are shown i n Fig. 2 . There are several conclusions that may be reached regarding these variations. The variation of log J"H-* corresponds to a sizable positive deviation froin ideality in all cases. This appears to be due to a specific interaction between the solvent and the -NH:!+ group on the indicator. Taft" has suggested such an interaction previously and attributes it t o hydrogen bonding between the -NH3+ group and the solvent. Den0 and co-workerslfihave also stressed the probable role of these interactions in Ho behavior. If a water is more strongly hydrogen bonded t o the anilinium ion than either the bisulfate or hydroniutn ion (the latter presumably being due to the repulsive charges) such a positive deviation would occur with increasing acid concentration in the region measured. Above %yoacid concentration where there is no longer free water (i.e., not bound directly in the hydronium ion) and neutral HzS04appears, a different region is to be expected. The curves for log fBH , * show evidence of flattening out as this concentration is approached. The specific participation of the -NH3+ group is shown b y the results in Fig. 3. Successive N-alkyl substitution of the anilinium ion results in f BH * approaching that of the tetraethylammonium cation. (17) K . W. Taft, Jr., J. A m . Chem. SOL.,82, 2065 (1060)
INDICATORS IN SULFURIC ACID
June 5 , 1963
1559
3-
2-
c ; c M
'I
-1
t -2
L 0
I
I
10
20
I
I
30 40 Sulfuric acid,
1
I
L
50
60
70
Fig. 1.-Activity coefficient data for ionic indicators, expressed as/+* = f + / j T E A + orf-* = TEA+^-, T E A + is tetraethylammonium ion : 0 , pentacyanopropenide anion; 0, bis-( tricyanoviny1)amine anion; (3, tri-(9-methoxypheny1)-carboniumcation; 0 , m-nitroaniliniurn cation ; a , aniliniurn cation ; 0,p-chloroanilinium cation; 8 ,p-nitroanilinium cation.
The neutral molecules (Fig. 2) demonstrate the presence of a specific interaction with the nitro group. Increasing the number of nitro groups causes an increasing negative deviation in log f B . Such an interaction was noticed with nitrobenzene many years ago by Hammett and Chapman.18 We can now turn to the question of the independence of structure of f B H - / f B among the Hammett indicators. It appears that among the indicators consisting of aniline substituted in the ring with one nitro group and halogens, f B H +* and f B - are separately reasonably independent of structure up to -60% acid concentration. The presence of the halogen appears to have little influence on f B H + * (cf. p-chloroanilinium with anilinium, Fig. 1). It would also be expected to have little influence on f B but we have not demonstrated this experimentally. The presence of a nitro group presents the possibility of specific interaction effects as discussed above. In the neutral molecule its effect is nearly independent of whether it is ortho or para (cf 2,6dichloro-4-nitro- with 2,4-dichloro-6-nitroaniline, Fig. 2 ) . In the protonated forms, BH+, the m and p nitro-substituted anilinium ions appear to have a real difference (Fig. 1). However, measurements with w-nitroaniline are restricted to dilute s o l ~ t i o nwhere ~~~ ~ B H + *is nearly one so that this difference has little practical effect. The 0- and p-nitroanilinium ions appear to have very similar activity coefficients (fBH'*) as evidenced by the protonation behavior. Since the neutral molecule activity coefficients ( f ~ ) (18) L P H a m m e t t and R P C h a p m a n , J A m Chem S o c , li6, 1282 (1934).
I
I
10
20
I
I
30 40 Sulfuric acid, %.
I
50
60
70
Fig. 2.-Activity coefficient data for neutral indicators: 8, 2,4,6-trinitroaniline; 0 , 2,4-dinitroaniline; 0 , 2,4-dichloro-6nitroaniline; 8 , 2,6-dichloro-4-nitroaniline; (3, ethyl cyano0 , p-chloro-K-tricyanovinylaniline; 0 , triphenylacetate; carbinol.
3t 1
I
I
I
I
1
I
I
30 40 50 60 70 Sulfuric acid, (, Fig 8 -Effect of N-substitution on aniliniurn ion activity coefficient: 0, aniliniurn ion; (3, N-ethylaniliniurn ion: 0 , N,Sdimethylanilinium ion; 0 , trirnethylphenylarnrnoniurn ion 0
10
20
are nearly identical, differences in ~ B Hwould show up in the slope of log R = log ( CBH-/CB) ( = PKB log U H - log ( f B H + / f B ) ) 'IS.concentration plots. Our measurements (Table I1 and those of Bascombe and Bell19) show that the plots for 4-chloro-2-nitro-, 2,6-dichloro-4nitro- and 2,4-dichloro-6-nitroanilineare parallel in the regions of overlap. Inclusion of two nitro groups to reach higher acid concentrations with Ho, however, presents some difficulties. The neutral molecule activity coefficient for 2,4-dinitroaniline is parallel to that of the mononitro compounds (cf. Fig. 2) in the region where protonation overlaps (-50-60%). However, it diverges 4
+
(19) K. W. Bascombe and R P Bell, J Chem Soc , part 1 , 1096 (1959).
1560
RICHARD H. BOYD
by -0.2 log unit between 0 and 30%. Although this effect is relatively minor, it illustrates that an acidity function scale may not necessarily be perfectly consistent even if the log R plots are parallel. In the prestnt case the log R plots have a significant difference in slope between the dinitro and mononitro indicators (cf. Table 11). The higher slope for 2,4-dinitroaniline indicates that f B H + for this compound has a less positive deviation than for the mononitro compounds. Above -60% acid Concentration, then, an inconsistency of the order of 10-20% in the slope of H o is introduced. The use of 6-bromo-2,4-dinitroaniline to extend the scale to above 90% acid concentration1b5 probably does not introduce any further inconsistency. Beyond this point, however, the consistency of HO is an open question. Although, for the indicators discussed above, the independence of indicator structure of f B H + and f B separately appears to be as good as , f B H + / f B , there are examples where the ratio is a help. Bascombe and Bell's results1gfor N,N-dimethyl-2,4-dinitroaniline show that log R is parallel to that of the mononitroanilines (region of overlap -24-37%). This is likely the result of a fortuitous compensation of a decreased positive deviation in log f B H - from N-substitution by a similar decrease (larger negative deviation) in log f B due to the additional nitro group. In contrast, however, N,N-dimethyl-2,4,6-trinitroaniline shows a considerably greater slope in log R than 2,4-dinitroaniline in the same concentration range'.'' (-65-70%). This is probably the result of decreased positive deviation due to N-substitution that is not compensated by a change in log f ~ The . results in Fig. 2 indicate that, although the N-substituted indicator has an extra nitro group which could result in a considerable difference in log f ~ in, the region of overlap, the log f~ curves may well be nearly parallel. A somewhat smaller difference in slope for log R between p-nitrodiphenylamine has also been attributed by Taft17 t o the effect of N-substitution on f B H - . 4. HR Indicators (Triarylcarbinols).-Since the indicators of this type, for the acid concentrations studied here, are very similar in structure and somewhat difficult to prepare, only one ionic and one neutral model were chosen for study. For tri-(pniethoxypheny1)-carbinol, , f +~* shows little variation with acid concentration below -50%. This is consistent with the lack of functional groups capable of strong specific interaction with the solvent. That this should be the case has been pointed out and emphasized by Den0 and co-workers, particularly in their studies of hydrocarbon protonation.15 The nature of the deviation of fR+* above -50% acid concentration is not known. The fact that log R curves for a large number of these indicators are parallel8 suggests it may be a function of the size of the molecule relative to the tetraethylammonium cation. There are some differences among the variations of log f+* for tetraalkylammonium cations ( c f . tetramethyl-, tetraethyl- and tetrabutylammoniuin pentacyanopropenides in Table I), The neutral molecule triphenylcarbinol shows a positive deviation which levels out a t -40% acid and may well decrease a t higher acid concentrations.20 5. H- (Cyanocarbon) Indicators.--The pentacyanopropenide and bis-(tricyanoviny1)-amine anions were chosen as representative of the cyanocarbon anions and are strong enough acids to remain dissociated over the acid concentration range studied. Their activity (20) T h e solubility of this compound h a s been previously reported by Den0 and Perrizzolo (ref. 13) t o be nearly invariant with sulfuric acidconcentration. We h a v e been unable t o confirm this and our d a t a for triphenylcarbinol appear t o be more consistent with their d a t a for diphenylcarbinol.
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coefficient variations are very similar (Fig. 1) and one is encouraged to believe that f A -* is relatively independent of structure. The deviation in log fA-* is negative and becomes increasingly so over the entire composition range. Thus, we suppose t h a t the anion has a stronger interaction with the hydronium ion than the other solvent species. Since the hydronium ion begins to disappear above 85% acid, variation in log fA-* may well level out above this point I t is interesting to note that although the direct charge effect on the ionic indicators species may be small, the indicator charge may well be important in determining the nature of the ion-solvent interaction. Thus, charge attraction renders hydronium ion interaction favorable with the cyanocarbon anions. Charge repulsion renders it unfavorable with the anilinium ions. The resulting activity coefficient variations are then in opposite directions. Models for neutral cyanocarbon acids (HA) proved difficult to arrive at. Ethyl cyanoacetate was chosen to represent methyl dicyan~acetate.~, lo Up through the protonation region of the dicyano compound (-30-50% acid) the model shows relatively little variation with acid concentration. For its similarity to bis- (tricyanoviny1)-amine, p-chloro-N-tricyanovinylaniline was selected. Its behavior is similar to ethyl cyanoacetate, the deviation becoming negative a t slightly higher acid concentration. 6. The Relationships between Acidity Functions.On the basis of the activity coefficients reported here we can discuss the behavior of the acidity functions relative to each other. For convenience in comparison, the three functions studied here may be written
+
+
-Ho lOgfTE\+ l o g U l P - logfBHi* IogfB (16) - HfH log fTTEa-= l o g U H + - lOgfR'* l o g J R O H (17) where Hlr' = HI, - log U H Z O -HIOgfTEA' = l o g a H + logs.\-* - I O g f H A (18)
+
+ +
+
and where, as usual, f * is relative to the tetraethylammonium cation, Experimentally, -HR' is found to rise much more rapidly with acid concentration than -Ho (see Table 111). Several factors are responsible for this. First of all, ~ B H + *has a sizable positive deviation, whereas log f R +* shows relatively little variation. In addition, a t lower concentrations (
