J. Phys. Chem. 1980, 84, 1725-1729
1725
Hammett Acidity Function, Ho,of Hydrobromic Acid and Its Ionic Dissociation' Y.
Marcus," E. Pross, and N. Soffer
Department of Inorganic and Analytlcal Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel (Received July 19, 1979)
The Hammett acidity function, Ho,of hydrobromic acid was determined at 25.0 and 60 "C by means of nitroand chloro-substitutedaniline indicators and compared with similar data for sulfuric acid, obtained concurrently, and for perchloric acid, from the literature. Care was taken to remove traces of bromine from the hydrobromic acid solutions, which otherwise cause difficulties. The data were examined according to the approaches suggested severally by Wyatt, Dawber, and Hogfeldt, with the view of obtaining the degree of dissociation CY of the hydrobromic acid. It was concluded, however, that the empirical relationships on which these approaches are based are not sufficient to give valid estimates of a for an acid as strong as hydrobromic acid.
Introduction Hydrobromic acid counts among the very strong acids, which are completely dissociated in dilute and even in moderately concentrated aqueous solutions. There are, however, some indications2that at high concentrations it is less completely dissociated than perchloric acid, HC104, or sulfuric acid (the first proton), H2SO4 Among the methods utilized to obtain the degree of dissociation, a, of acids is the comparison of their Hammett acidity function with that of a completely dissociated acid at given
concentration^.^^^
According to Wyatt,3 for a strong acid HA in the concentration range where the degree of dissociation a = 1, the following expression holds: Ho = K + log (2aw/(l - awl) + log F(uw) (1) where K is a constant, aw the water activity, and F(aw) = 1 Alaw A2aW2 . , . The derivation of this expression was based on an empirical observation by Brand6 concerning concentrated sulfuric acid and on the assumption of the applicability of Raoult's law to free water, Le., aw = xHz0,discounting the water bound in ion hydrates. Five pararneters were required to express Ho(H2S04) = f(aw) at 25 "C: K = -5.02, AI = 20, A2 = 150, A3 = 500, and A4 = 625, for the concentration range 2.3 5 cH2S0,/M I9.1 (Ad mol dm-3) with the data available at that times3 Ojeda and Wyatt6 modified eq 1 by including a term BcHA on the left-haind side, where B is a salting-out constant. Dawber' rewrote it in the form -Ho log ( 2 ~ w / (1 - aw)) + log F ( u ~=) -K'+ BcHA (2) where the left-hand side is known, provided F(aw) is known. Dawber ~ b t , a i n e d from ~ - ~ the linear relationships of the left-hand side of eq 2 against cHA,for low cm values, the parameters given in Table I. An inconsistency is committed by using Wyatt's F(aw) in eq 2. However, F(aw),a power series in aw, is a sufficiently flexible function to permit good fits with B = 0, so that the term with B is redundant and the inconsistency is removed. There is also the objection that Setchenov's equation is actually a limiting one, i.e., lim(cHA 0) y I = BCW,and that it should not be expected to be valid in the concentration range where Ho is measured. Finally, the quantity -K'+ Bcm was found to reach a maximum after its initial linear part, at around 3.5 M, even for the strong acids H2S04and HClQ4,for which a E 1 much beyond this concentration, and no decrease of that quantity should occur. These objections do not apply to Wyatt's original treatment, which was applied3 also to weak acids, HB, for
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0022-3654/80/2084-1725$01 .OO/O
TABLE I: The Parameters K' and B of Eq 2 for Several Strong and Intermediate Strength Acids acid HW4 HClO,
K'
B/(dm3mol-')
-5.00 -4.98
0.040 0.053 0.030
-5.06
HNO, HO,SCH, HIO,
-4.83 -5.02 -4.19 -4.79 -4.85
0.058 -0.109 0.204
0.18 0.13
ref a 7 a
8 9 8 a, b a,c
a Estimated by present authors. From actual slope of graph (Figure 1 in ref 8). From data of ref 8 , recalculated.
which CY < 1. The factor 2 in the term 2aw/(l- aw) in eq 1must then be replaced by (1 + a ) / a . If Ho(HB) is compared with Ho(HA) at the same water activity, CY
= (2 antilog [Ho(HB)- Ho(HA)],, - 1)-1
(3)
prouided that eq 1 is a universal function for all strong acids HA (where a l),and applies with the same K and F(aw) also to the ionized part of HB. An alternative treatment is based on the observation of Bascombe and Belllo that (b(H0) 5 -Ho - log CH+ = BCHA - h log Uw (4) is a common function for sulfuric and perchloric acids up to cHA = 8 M, with the salting constant B = 0.1 dm3 mol-l and the proton hydration number h = 4. Hogfeldt assumed that (b(Ho)is a universal function for all strong acids HA as long as CY = 1, not insisting, however, on the particular form of eq 4. For all acids, strong or weak, he assumed that CH+ = antilog [-Ho- (b(HO)], hence for a weak acid HB a=
CH+/CHB
= [antilog (-Ho - (b(&))]/CHB
(5)
or, when the strong and weak acids are compared at the same molarity a = antilog [Ho(HA)- Ho(HB)],
(6)
This dispenses with the necessity to know the exact form of = f'(Ho),provided that its universality has been established. In this work the applicability of these approaches to the estimation of a of hydrobromic acid is examined. The difference A H 0 = &(HA) - Ho(HB),which appears in eq 3 and 6, is expected to be small for as strong an acid as hydrobromic acid. It is therefore imperative to compare Ho data for this acid (HB) with those of a completely dissociated acid (HA) under conditions which mimize both systematic and random errors in each set of Ho values.
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0 1980 American Chemical Society
1726
The Journal of Physical Chemistry, Vol. 84, No. 13, 1980
Measurements were therefore made with the same indicators for both hydrobromic and sulfuric acids, in spite of the existence in the literature"J2 of Ho data for the latter acid adequate for other purposes. These literature values and those for perchloric acid13J4were used to try to establish the universality of Ho = f(aw) and 9 = f'(Ho)for the completely dissociated acids at 25 and 60 "C. If this is accomplished, the estimation of a of hydrobromic acid from Ho= f(aw)and Ho= P'(c) at these temperatures may be attempted.
Experimental Section Chemicals. Hydrobromic acid of analytical reagent grade (BDH of 48 and 60 wt % and Fluka of 48 wt %) was purified from traces of bromine by passage through an anion-exchange column16 (Dowex 1x8) previously transformed into the bromide form by successive passage of 2 M NaOH, 2 M KBr and 0.1 M KBr. This and all subsequent operations with this acid were carried out under nitrogen in a glovebag, otherwise slow air oxidation produces enough bromine to attack the indicators and cause yellowing of the acid. The acid concentration of stock solutions of HBr was determined by weight titration with 1M KOH, standardized with primary standard potassium hydrogen phthalate, to 10.11%. Sulfuric acid of analytical grade (Palacid) was diluted with water to 60 wt %, and its concentration was determined as above. More dilute solutions of the acids were prepared by weight dilution. The indicators used (4-chloro-2-nitroaniline, 2,6-dichloro-4-nitroaniline,and 2,6-dinitroaniline (Fluka), 2,4and dinitroaniline (BDH), and 2,5-dichloro-4-nitroaniline 2,4-dichloro-6-nitroaniline(I.C.N. Pharmaceuticals)) were recrystallized from ethanol. Procedures. Stock solutions of the indicators were prepared by weighing appropriate amounts of the indicators and dissolving them in weighed amounts of HBr or H2S04. The relatively basic and acidic solutions were prepared by diluting these stock solutions by weight with water and with 70 or 98 wt % H2S04, respectively. Working solutions were prepared in 10-cm3portions by weighing indicator stock solution, water, and acid stock solution. The solutions were thermostated at 25.0 and 60 "C (accurate to f O . l and 11 "C, respectively), and the absorbance was determined in cells with 0.1-, O h - , LO-, and 3.0-cm light paths in thermostated cell holders in a Cary-14 spectrophotometer. The reference cell was filled with water, since neither the purified hydrobromic acid nor the sulfuric acid absorbs light at the wavelengths utilized. The indicator weight and light path were selected so as to give absorbance values A of maximal reading accuracy (ca. 0.6). The wavelength of maximal absorbance of the relatively basic solutions (Table 111) was used, as a rule, for the determinations. The weight data were used to obtain the wt % w of the acid, hence its molality m = w/(lOO - w)M, where M is the molar mass (0.080917 kg mol-' for HBr and 0.098083 kg mol-l for H2S04). From this the density was calculated from appropriate power series N
d/(g ~ m - =~ C ) ( U+~bit)mi 0
(7)
where t is the Celsius temperature and a, and bi are parameters (shown in Table 11; see paragraph at the end of the text regarding supplementary material) obtained by least-squares fitting16 of the data.17 The densities were used to obtain the molarity of the acid c = O.Olwd/M and of the indicator. Molar absorbances of the indicator in the basic, acidic, and working solutions, Eb = A ~ / c Iea, = Aa/cm+, and t = A / ( c ~ CHI+), respectively, were calculated. From
+
Marcus et al.
TABLE 111: Dissociation Constants of the Indicatorsu indicator a 4-chloro-2nitroaniline b 2,5-dichloro-4nitroaniline c 2,4-dichloro-6nitroaniline d 2,6-dichloro-4nitroaniline e 2,4-dinitroaniline f 2,6-dinitroaniline
wavelength, - p K ~ r25 "C - p K ~ p60 "C nm 1.03 f 0.03
1.16 f 0.06
425
1.77 f 0.03
1.87 t 0.06
372
3.12
0.06
3.17
0.06
430
3.25 f 0.03
3.20
0.06
370
f
f
0.10 368 0.10 442 For the choice of the p K ~ values p and their error limits, see Discussion. 4.28 f 0.07 5.26 f 0.13
4.15 5.05
f
f
these, the value of log I = log (cI/cHIt) = log [ ( E - t,)/(eb - E ) ] was obtained, and finally the acidity function Ho = log I + p&It from the dissociation constants of the indicators shown in Table 111. The probable errors in the quantities were computed by assigning an error of 10.5 mg to each of the weights of the stock solutions, the water, and the acids and of 10.2 mg to the weight of the indicator used to prepare the stock solutions. This latter gave a systematic error of 10.01 to all values of log I. An error of 0.004 was assigned to the reading of the absorbance (the difference between that due to the solution and the base line), and this constituted the major contribution to the random errors, which, together with the weighing errors of the solutions, were sometimes much smaller than and sometimes larger than the ztO.01 unit systematic error. The errors in w and c are indicated by their significant figures. The errors in Ho take into account also those in PKHIt, given in Table 111.
Results The results obtained with ca. 20-60 wt % hydrobromic acid and sulfuric acid at 25 and 60 "C are shown in Tables IV-VI1 (supplementary material) as sets of values of w , aw, c, log I , and -Ho for each indicator. The data for hydrobromic acid are plotted in Figure 1 and compared with the data of Vinnik and co-workers18(available at 25 "C only), who took precautions not to introduce bromine into their solutions. (These data were adjusted to the PKHIt values listed in Table 111). In order to apply eq 3 and 6, it is necessary to compare the acidity function values at the same water activity or molarity, respectively. To facilitate the interpolations, and since in the ranges examined Ho = f(aw) and Ho= f'(c) are linear for both acids as well as for perchloric acid, we made linear regression calculations, resulting in the parameters shown in Table VIII. The water activities corresponding to w for the three acids at the two temperatures were obtained as shown in the Appendix. Perchloric and sulfuric acids are considered to be the strongest acids in aqueous solutions and to be completely dissociated (a 1)up to ca. c = 8 M or down to ca. aw = 0.2, as shown by Raman and NMR data.27-29It was established that, indeed, the functions Ho= f(aw) and HO = f'(1og c) are indistinguishable for these two acids at 25 "C, within the experimental errors of Ho(-10.03 in general) (see Figures 2 and 3). At 60 "C, however, only the function Ho = f'(1og c) is common for these two acids (Figure 3) whereas the function Ho= f(aw) shows differences which appear to be systematic and outside the combined experimental errors (Figure 2). It should be noted, however, that whereas at 25 "C the Hodata are directly taken from the 1iterature,"-l4 only the paper of
The Journal of Physlcal Chemistty, Vol. 84, No. 13, 1980 1727
Hammet! Acidity Function of Hydrobromic Acid
TABLE VIII: Paraimeters for the Linear FunctionsH , = p t qa, and Ho = u t wc and the Correlation Coefficients rW0,aw) and r(H,,c) acid
ref
HBr
0
a
H,SO,
a
b a
b b b This work.
HClO, a
teomP,,
C -
25 60 26 26 60 60 26 60
P
q
-4.482 + 0.032 -4.733 i 0.061 -4.698 * 0.040 -4.684 i 0.090 -6.119 * 0.046 -4.866 i 0.064 -4.984 i 0.029 -4.640 f 0.066
t 3.969 f 0.059
r(H0,aw1 0.9915 0.9938 0.9962 0.9708 0.9976 0.9969 0.9981 0.9977
t4.271 * 0.099 t3.919 i 0.069 t3.986 f 0.164 t4.630 i 0.071 t4.318 i 0.080 t 4.446 i 0.066 t4.046 i 0.096 Inter- and extrapolated from literature data; see Discussion. 25
OC eC
I
0
120
,e
8
. o
r(H,,c) -0.9930 -0.9976 -0.9964 -0.9963 -0.9987 -0.9993 -0.9970 -0.9961
U
U
0.168 * 0.036 0.068 * 0.041 -0.060 * 0.049 -0.036 f 0.036 t0.166 i 0.029 t0.044 * 0.020 t 0.583 f 0.061 t 0.499 f 0.108
-0.442 i -0.394 * -0.468 i -0.457 * -0.600 * -0.448 f -0.589 * -0.668 i
I
I
0.006 0.006 0.008 0.006 0.006 0.004 0.009 0.018
O
I
HCIO~,~HHSO~
0 0
O
0
30
D
40 I
I
50
WHBr
E
Figure 1. The Hammelt acidity function -H, of hydrobromic acid as a function of its wt %, w& Filled symbols, 60 "C; empty symbols, 25 "C (of these, ones with uncertainty 5 0.04 have heavy outlines), this work. The indicator$ used are (a) circles, (b) squares, (c) diamonds, (d) upright triangles, (e) hanging triangles, (f) ovals; for meaning of letters see Table 111. Crosses are from the work of Vinnik et ai.'* at 25 OC.
Johnson and co-workers1' gives Ho data at 60 "C (for sulfuric acid), while extrapolation is necessary for the data of Tickle and co-wolrkers12(for sulfuric acid at 15, 25, 35, 45, and 55 "C) and of Attiga and Rochester14(for perchloric acid a t 15,25,35, and 45 "C). These results conform to the expressions
+ 2.23 X 10"w2 (8) d[Ho(HC104)]/dT = 4.0 X 10-5w + 3.0 X 103u2 (9)
d[Ho(H,S04)]/dT '= -4.4
X
10%
from which the values at 60 "C are obtained by extrapolation. (It should be noted that the data of Johnson and co-workers" on sulfuric acid do not agree with eq 8, the right-hand side being +6.0 X 10-5w + 2.0 X 10"w2 in the range of interest.) The two sets of data for perchloric acid13J4at 25 "C are whereas at 60 "C mutually consistent within k0.03 in Ho, only one set is available. For sulfuric acid the mutual consistency is worse. The best is within the two most recent sets of data"J2 at both 25 and 60 "C, in the range of interest 2 5 w 5 70. Older data of No for sulfuric show worse discrepancies. The major reason for any inconsistencies is the choice of the pKHI+values used to convert from log I for each indicator to Ho, made so as to have a "seamless" transition between data obtained with a series of indicators with increasing pKHI+'s. These discrepancies (visualized in Figures 2 and 3) are major contributors to the standard deviations listed for the iegression
100
0 75
0 50
0 2 5 ow
Flgure 2. The Hammett acidity function -Ho of perchiori~'~~'' (squares) and sulfuric11*12 (circles) acids as a function of their water activities aw at 25 "C (empty symbols) and at 60 "C (filled symbols: right oridinate moved down half a unit). The lines through the symbols extend through the reglons where a common functlon describes the data for both acids.
parameters in Table VIII. If these parameters are inserted into these equations, the results are a = (2 antilog [-p(HA) + p(HB) - aw(q(HA) q(HB))I - 11-l (10) a = antilog [u(HA) - u(HB)
+ c(u(HA) - u(HB))]
(11) where HA = H2S04and HB = HBr. The calculated values of a at round wHBr values are shown in Table IX. Because of the significant uncertainties of the parameters p , q, u, and u, and of the closeness of Ho(HA) and Ho(HB),the uncertainties in the values of a calculated by either eq 10 or eq 11 are rather large. One way to circumvent this difficulty, and thereby to reduce the systematic variance of the data, is to compare the primary log I data obtained for the two acids with the same indicator rather than to employ the derived Ho values. Values of log I for sulfuric acid were interpolated for the c and aw values at which log I data for hydrobromic
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The Journal of Physical Chemistry, Vol. 84, No. 13, 1980
TABLE IX: Degree of Dissociation and Sulfuric Acids at 25 and 6 0 "C
CY
of Hydrobromic Acid Calculated from Eq 10 and 11 and H, Data for Hydrobromic 25 "C
W
m
aW
C
20 25 30
3.09 4.12 5.30 6.65 8.24
0.8472 0.7737 0.6797 0.5676 0.4426 0.3228 0.2332 0.2190
2.86 3.72 4.66 5.68 6.79 8.01 9.35 10.81
35 40 45 50 55
10.11 12.36 15.10
Marcus et al.
410) 0.460 0.459 0.456 0.453 0.451 0.450 0.451 0.451
0.233 f 0.223 i0.209 f 0.192 i- 0.174 i- 0.156 f 0.143 t 0.141 f
.
60 " C I
a(11) 0.568 f 0.159 0.555 f 0.170 0.544 f 0.180 0.527 i 0.191 0.513 t 0.202 0.498 f 0.212 0.489 f 0.222 0.468 t 0.232
aW
c
0.6999 0.5930 0.4740 0.3614 0.2804
4.56 5.54 6.61 7.75 8.97
410) 0.496 0.444 0.395 0.356 0.332
f
f f f. f
0.176 0.141
0.111 0.088 0.077
411)
0.553 0.491 0.431 0.374 0.323
f f
f
f f
0.071 0.068 0.065 0.060 0.058
acid are available, for each indicator individually. Such interpolations bring in systematic errors not larger than f0.02, considerably less than those in Ho, evident in the values of p and u in Table VIII. This comparison is shown in Table X (supplementary material), and it is apparent that the derived a values are similar in magnitude to those in Table IX, but often with smaller uncertainties, as expected. The main conclusion from these results is that over the range 3 5 cHBr/(mol dm-3) 5 11 (20 5 wHB*- I 55, 3 5 mH&/(mol kg-l) I 15) at 25 "chydrobromic acid is about half dissociated, with little change in CY over this concentration range. The results at 60 "C are similar.
behavior of this acid is generally known to be otherwise, Le., that it is fully dissociated up to ca. cHBr = 6 M and only slightly associated beyond this concentration (see also conclusions from vapor pressure and activity coefficient data,2 and from proton magnetic resonance data3a),the fault must be sought either in the data or in the breakdown of the premises on which the treatments are based. We believe that our data are essentially correct. The care taken in the preparation of the hydrobromic acid solutions (to make them free of bromine) and the weight dilutions paid off in data of minimal uncertainties (Tables IV-VII) * A word is in order here concerning the choice of pKHI+ values employed to convert log I to Ho values. The accuracy of the values at 25 "C and the inherency of cumulative errors as pKH+becomes more and more negative along the series of indicators have been discussed by Rochester.34 Reexamination of his list in view of some newer results not considered by him (ref 11, 12, 14, and the present work) leads to modifications (Table 111). With the chosen values of pKHI+,our Ho values for sulfuric acid conform very well to the values in the literature11J2 at both temperatures (Figures 2 and 3). The same applies to the hydrobromic acid datalg at 25 " C (Figure 1). We therefore conclude that the low degree of dissociation resulting from the application of eq 3 and 10 and of eq 6 and 11 must be due to shortcomings in the theories on which these equations are based. The introduction, in which the derivation of eq 3 is briefly explained, records the proviso that eq 1 should universally hold for all strong acids ( a = l),with the same K and F(aw). This condition is seen to be met at 25 "C for HC104 and H,S04 (Figure 2), but these acids are structurally similar, and there is no guarantee that the same parameters hold for acids with a structurally different anion, such as bromide. It is possible to add a term to eq 1which is anion dependent (e.g., describing its hydration), which would not cancel out in the difference equation, eq 3. However, there is no way to distinguish between incomplete dissociation of HB and possible anion dependencies of H o of HA and HB. The same is true also for the application of eq 6 which demands that 4 = f'(Ho)be a universal function. This universality is, again, demonstrated in Figure 3 to be true for HC104and H2S04for both temperatures, the functions being (p(25 "C) = O.lO(-Ho)-' - (0.185 f 0.019) + (0.687 f 0.007)(-&) +- (0.019 f 0.015)(-H0)2(12a)
Discussion The rather amazing conclusion arrived at in the last paragraph, that hydrobromic acid is incompletely dissociated already at 3 M, is a direct consequence of the application of the treatments of Wyatt (leading to eq 3 and 10) and of Hogfeldt (leading to eq 6 and 11). Since the
However, there is nothing inherent in strong aqueous mineral acids that requires eq 1 2 to hold also for an acid with a structurally different anion, such as bromide. If, again, anion hydration is invoked, the consequences can
-"i
j_
2C
t
/
t. Figure 3. The Hammett acidity function -Hoof (squares) and sulfuric'1~12 (circles)acids as a function of their molar concentrations (logarithmic scale, log c/(mol dm-3)). Data at 25 "C (empty symbols) and at 60 "C (filled symbols; right ordinate moved up half a unit). The lines through the symbols extend through the regions where a common function describes the data for both acids.
(p(60 "C) = O.lO(-Ho)-l - (0.185 f 0.019) + (0.663 f O.O07)(-Ho) + (0.036 f 0.002)(-Ho)' (12b)
The Journal of Physical Chemistry, Vol. 84, No. 13, 7980 1729
Hammett Acidity Function of Hydrobromic Acid
be demonstrated more easily than in the previous case. Suppose that a term -hx log aw is added to the right-hand side of eq 4, the anion X being either A or B. Then the , ) should be added to the square term ( h -~hB)(log 6 brackets in eq 6. The symbol 6w signifies the mean water activity of HA and HB, at a given c. Since Ho was found to be linear with both c and aw (Table VIII), and since for 0.8 Iaw I0.3, log aWis approximately linear with aw,the replacement of (hA- hB) log Ew by h + kc, where h and lz are constants, should introduce no major error. With this addition to eq 111 the data in Table VI11 at 25 "C give eq 13. Positive values of h and k, comparable with 0.218 log = -(0.218 f 0.061) - (0.016 f 0.010)~+ h kc (13) and 0.016, respectively, can explain the apparent low a values recorded in Tables IX and X, and can lead to more reasonable values. Unfortunately, there are no obvious ways to arrive at independent h and k values. Even for only moderately strong acids, a values obtained from acidity function data do not agree too well with those obtained from Raman or nuclear magnetic resonance data. Tests were madezzfor nitric and methanesulfonic acids for which seemingly adlequate Ho and a data are available. As Tables XI and X.11 show (supplementary material), agreement o f a froin Ho data by both eq 3 and eq 6 with the independent a values is only fair. That any measure of agreement at all is achieved, however, is due to the fact that eq 3 and 6 require only minor adjustments for anion hydration. This means that eventually, when ways to introduce these adjustments are found, possibly from data for salt solutions, the general method for deriving a from Hodata could still be applied.
+
Acknowledgment, This research was supported by a grant from Israel Chemicals Ltd. Appendix The water activities were calculated from osmotic coefficients as follows. At 25 "C the osmotic coefficient of hydrobromic acid is19 @(HBr)= 1 - 0.2634m-'[(l + 1.6468m1/') - 2 In (1 41.6468m1/2)- 11/(1.6468m1~z)] 0.14342m + 0.01359m2 4.274 X 10-5m3- 6.851 X 10-5m4 (Al)
+
+
that of sulfuric acid iszo $(H2S04) = 1 - 1.3581ml'' - 55.455m3/4 208.74rn7ie - 288.80m + 177.71m9/8- 41.127m5I4 + 0.002039m25/8- 0.0006468m27/8(A2) and that of perchloric acid id9 $(HC104) = 1 - 0.2342m-'[(l + 1.7125m1/') - 2 In (I + 1.7125m1/2)- l / ( l + 1.7125m1/'!)]+ 0.04628m + 0.00900m2 - 4,658 X 10-4m3+ 6.945 X 10-6m4(A3)
+
The water activity is aw = exp(-O.O18015vm~), where 0.018015 kg mol-' is the molar mass of water, and v (=2 for HBr and HC104and 3 for H2S04)is the number of ions into which the acid formally dissociates. The water activities at 60 " C are less well known. The vapor pressure and composition data of Duckerz1yieldz2 aw(T) = aw(298 K) + 1.09 X lO"rn(T - 298) (A4a) for hydrobromic acid, in the range of 0.7 I m/(mol kg-l) I11.3 and 25 5 t/"C 5 100, i.e. 9 8+ 3.82 X 10-3m (A4b) aw(333 K) -- ~ ~ ( 2 K) The partial heat content and heat capacity data of Glueckauf and Kitt23for sulfuric acid yieldz2eq A5 valid
aw(333 K) := aw(298 K)
+ 1.225 X 10-3m2- 9.80 X 10-5m3+ 1.925 X 10%n4 (A5)
up to 20m and consistent with the water activity data of Harned and Owen,24reported only to 7m. Water activities for perchloric acid were reported by Galkin and co-worke r ~for ' ~ 0 and 50 "C, but the derivative d2aw/dTdm showed many irregularities, so that these data were judged unreliable. Instead, activity coefficient data of Haase and co-workers,z6given for 10,25,and 40 "C and 0.1 Im/(mol kg-l) I 14.0, were evaluated parametrically,z2to yield finally eq A6. aw(333 K) = aw(298 K) + 3.36 X 10-4m2- 1.40 X 10-5m3 (A6) The densities required to convert w to c a t 60 "C were obtained from eq 7 for all three acids from the parameters in Table 11. Supplementary Material Available: Table 11, containing parameters for the density eq 7 for HBr, HzSO4, and HClO,; Tables IV-VII, containing data w, aw,c, log I , and Ho for hydrobromic acid at 25 and 60 OC and for sulfuric acid at 25 and 60"; Table X, containing data aw, A log I and a, and c, A log I , and a for 25 and 60 "C; and Tables XI and XII, containing data w, c, aw, Ho, a(exptl), a(eq 3), a(eq 6) for nitric and methanesulfonic acid, respectively (14 pages). Ordering information is available on any current masthead page. References and Notes (1) Part 3 of a series on the ionic dissociation of hydrobromic acid. For part 1, estimation from vapor pressure and activity Coefficient data, see ref 2; for part 2, NMR study at 6-60 OC, see ref 33. (2) Y. Marcus, J. Chem. Soc., Faraday Trans. 7, 75, 1715 (1979). (3) P. A. H. Wyatt, Discuss. Faraday Soc., 24, 162 (1957). (4) E. Hogfeidt, J. Inorg. Nucl. Chem., 17, 302 (1961). (5) J. C. D. Brand, J. Chem. Soc., 997 (1950). (6) M. Ojeda and P. A. H. Wyatt, J. Phys. Chem., 68, 1857 (1964). (7) J. G. Dawber, J . Chem. Soc., 1056 (1966). (8) J. G. Dawber, J . Chem. Soc., 1532 (1966). (9) J. G. Dawber, Chem. Commun., 58 (1968). (10) K. N. Bascombe and R. P. Bell, Discuss. Faraday Soc., 24, 158 (1957). (11) C. D. Johnson, A. R. Katritzky, and S. A. Shapiro, J . Am. Chem. Soc., 91, 6654 (1969). (12) P. Tickle, A. G. Brims, and J. M. Wilson, J. Chem. Soc. B, 65 (1970). (13) K. Yates and H. Wai, J. Am. Chem. Soc., 86, 5408 (1964). (14) S. A. Attiga and C. H. Rochester, J. Chem. Soc., Perkh Trans. 2 , 1624 (1974). (15) H. Irving and P. D. Wilson, Chem. Ind. (London),653 (1964). (16) Thanks are due to S. Giikberg for the computations. (17) (a) International Critical Tables, Voi 111, 1929, p 54-57; (b) R. Haase, P. F. Sauerman, and K. H. Ducker, Z . Phys. Chem. (Frankfurf am Main), 47, 237 (1965). M. I. Vinnik, R. N. Krygiov, and N. H. Chirkov, Zh. Fiz. Khim., 30, 827 (1956). W. J. Hamer and Y. C. Wu, J . Phys. Chem. Ref. Data, 1, 1047 (1972). J. A. Rard, A. Habenschuss, and F. H. Spedding, J. Chem. Eng. Data, 21, 374 (1976). K. H. Ducker, Dipolmarbeit, University of Aachen, 1960. Y. Marcus, unpublished results, 1979. E. Glueckauf and G. P. Kitt, Trans. Faraday Soc., 52, 1074 (1956). H. S. Harned and B. 8. Owen, "Electrolyte Solutions", 3rd ed.,Reinhold, New York. 1958. u 574. V. I.Galkin, L. SI iiiich, Z. I. Kurbanova, and L. V. Chernykh, Zh. Fir. Khim., 47, 443 (1973). R. Haase, K. H. Ducker, and H. A. Kuppers, Ber. Bunsenges. Phys. Chem., 69, 97 (1965). K. Heinzingerand R. E. Weston, Jr., J . Chem. Phys., 42, 272 (1965). A. K. Covington, M. J. Tait, and W. F. K. Wynne-Jones, Proc. R . SOC. London, Ser. A , 266, 235 (1961). G. C. Hood and C. A. Reiliy, J . Chem. Phys., 27, 1126 (1957). M. A. Paul and F. A. Lona. Chem. Rev.. 57. 1 11957). M. J. Jorgensen and D. R. &-Tarter, J. Am. Chem: Sdc., 65:878 (1963). R. S. Ryabova, I.M. Medvetskaya, and M. I.Vinnik, Zh. Fiz. Khim., 40. 182 (1966). N. Soffer; J. Shamir, and Y. Marcus, J. Chem. Soc., Faraday Trans. 7 , in press. C. H.Rochester, "Acidity Functions", Academic Press, London, 1970, p 67.
