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Charmian J. O'Connor University of Aucklond Auckland, N e w Zealand
Correlation of Composition of Acid Solutions with ~ c t i & and Acidity Functions
A n increasing number of kinetic investigations in concentrated solutions of mineral acids are being undertaken, but the physical constants which are needed to understand the role played by the mineral acid are spread over many and varied chemical publications, and little attempt has been made to correlate one with the other. For example, Hammett Acidity functions are related to molarity ( 1 ) and activity coefficientsto molality (t), and in the same kinetic investigation it may be necessary to relate the percentage composition with either the Hammett Acidity function or the activity coefficient (3). Presented below (Tables 1-5), therefore, are correlation tables of percentage composition with molarity, molality, activity coefficient, water activity, and Hammett Acidity function for aqueous solutions of hydrochloric, perchloric, phosphoric, and sulfuric acids. Nitric acid bas been deliberately left out of this survey since its behavior is often anomalous and it tends to act as a nitrating agent and not only as a solvent with high protonating properties. The values of all the constants quoted are measured a t 25"C, hut the values of molarity are often calculated from density data at 20°C. The density a t 25'C is not expected to differ significantly from this. The molarity
Table 1. Correlation of Percentage Composition of Hydrochloric Acid Solutions a t 25'C with Molarity, Molality, Activity Coefficient, W a t e r Activity, and Hammett Acidity Function
yoacid wlw
[MI moles I-'
m
Y
a,
Reference (d6), D157. Reference (d), pp. 483, 504. Y Vap. Press H20 Reference (27), Vol. 3, p. 301. The values of a, quoted here are -3% lower than those calculated from the osmotic coefficientsgiven in Robinson and Stokes "Electrolyte Solutions" (2) by use of the relationship log a , = 0.007824m@ where .+ is the osmotic coefficient. Reference (1). The values of Arnett and Mach $(3) agree well with these.
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=
pp~1OIMnmole 1-1
where p is the percentage composition of the acid solution, p A is the density, and M A the molecular weight of the solute. The molality m (the number of moles of solute/1000g solvent) was calculated from the expression =
105 loo - - I ) /MA mold (100 - p
The water activities have been calculated from water vapor pressures by use of a, = p/po where pu is the vapor pressure of water a t 25°C and p that over the system. y is defined as the molal activity coefficient. For over 30 years the main basis for discussions of organic processes in strongly acid solutions has been the Ho acidity function, invented and developed by Hammett and his students (4). The Hofunction provides an operational means for estimating how the degree of protonation of a Br@nstedbase changes as a function of acidity in acidic media and is of tremendous
Table 2. Correlation of Percentage Composition of Perchloric Acid Solutions a t 25'C with Molarity, Molality, Activity Coefficient, W a t e r Activity, and Hammett Acidity Function
% acid w/w 5 10 15
-Ho
Sources of Data p*BOO
M (the number of moles of solute/liter solvent) was calculated from the expression
[MI moles I-'
m
0.51 1.05 1.62 2.23 2.88 3.58 4.34 5.15 6.02 6.98 8.01 9.13 10.33 11.60
0.523 1.100 1.765 2.49 3.32 4.26 5.36 6.63 8.15 9.95 12.10 14.92 18.45 23.20
Sources of Data Reference (88). For values >40% .D A . - wlw . Reference (27). . .. Vol. 3, p: 54. Reference (d), pp. 483, 504. 7 Calculated from the osmotic coefficients given in Robinson a, and Stokes ( 8 ) bv use of the relations hi^ loe a.. = -0.007824&iw~ere + is the osmotic coefficien? ~~
Table 4. Correlation of Percentage Composition of Sulfuric Acid Solutions a t 25'C with Molarity, Molality, Activity Coefficient, W a t e r Activity, and Hammett Acidity Function
[MI moles 1-1
%acid w/w
Sources of Data Reference (31), p. 1136. Reference (32). The values by Larson (33) in the range y 0.2-4.0 m significantly differ from these hut no claims are made that thev are better. Those of Mason and ~ l & n(34) in the &nge 0.24.0 m differ yet again hut these may not he valid since they depend upon an ionic activity coefficientfor 0.1 m HaPo,. Reference (Sg). Reference (23). These results differ only slightly from t,hose of Heilbronner and Weber (35)measured a t 19°C. Values of - H a at 25OC have also been measured for polyphosphoric acid solutions (2.7-83.5 wt % PlOsH 2 0 systems) by Gel'bshtein, Ampetova, Scheglova, and Temkin (38). These values agree well with those of Dawning and Pearsan (37) in the range 62-86% PxOr content at 25'C.
p~20'
value for the quantitative treatment of acid catalysis in strong acids. Hammett and Deyrup used nitrated primary anilines to establish their acidity function scale, hut since 1950 authors have suggested that Brensted bases of widely different. size or structure might follow different acidity functions even though they were of the same charge type. Hammett defined an acidity function Ho, where Ho
=
-log aa*f~/fna+ = p K P +
Y
-go
QW
Sources o f Data p*'o0 Reference (Sf), p. 1147. r Reference (2), p. 477. a, Reference (58). This paper correlates an extensive series of researches on aqueous sulfuric acid. The agreement in the values of a, quoted is very satisfactory
values also agree veil with those edeulated from water
~iblbles"the celeulated;alues of a, = p/p, differ by as much as 30% from the values of Gimque, el al. (88). Reference ( 1 ) . For values >60% w/w, Reference (40). The values of Ryabava, Medvetskaya, and Vinnik (411 differ slightly from these.
-Ho
Table 5.
Values of -HA, -Hoar -Ho, -H-, -HO1", and - Hn in Aqueous Solutions of Sulfuric Acid a t 25'C
- - H I , - HR',
+ log [B]/[BH+I
whose value measures the tendency of a solution to transfer a proton to a neutral indicator base B, to form the conjugate acid BH+. I n 1951, Gold and Hawes (5) defined an acidity function Ja = HO
m
+ log a,
in order to apply Hammett's concept of acidity functions to the equilibria between alcohols and carbonium ions. I n 1955, their conclusions were found not to be generally valid throughout the entire range of sulfuric acid concentrations and a quantitative investigation of 18 arylmethanols and their respective carhonium ions (6) in the range 0.5-98% HzSOngave rise to the function Cowhere Co - Jo = log (fn+/jnosf)
However, Lowen, Murray, and Williams (7) in 1950 had already defined an acidity function H R for a carhinol indicator, which they did not determine in absolute terms, but computed values in the range 65-90% HHOa relative to an arbitrary zero. At the
Sources -HA -Ho H
-HI
-,yo,,' -HI -HR' -HE
o f Data Reference (20). See references given in Table 4. ( - H O henzo~henaneaciditv function) Reference (22). ~eference(is). Reference (19). Reference (14). Reference (17). Reference (16).
present time this function is called H R , both to indicate the priority of nolhenclature and also the close relatiouship to the original H o concept. I n 1959 (8)i t was found that the equilibrium between diarylolefin-diarylalkyl cation followed more closely the relationship H R - log a, and the use of HR' for H R log a, was first introduced by Iiresge and Chiang (9) to account for the loss of tritium from 1,3,5-trimethoxybenzene. In the range of perchloric acid concentrations used ha' = (hJ2 and thus a plot of log k versus - H o Volume 46, Number 10, October 1969
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gives a slope of 2.0. They postulate a single mechanism for all acid-catalyzed aromatic hydrogen exchange hut with varying degrees of proton transfer in the transition state and different acidity dependencies for the degree of protonation of different aromatic compounds. They suggest that protonation of toluene and benzene might be a still deeper function of acid strength. Many deviations from Ho are now known, showing clearly that rather than two acidity functions corresponding to two broad classes of bases-those that protonate on carbon, whose protonation is represented by Ho,and those that protonate on nitrogen and oxygen, whose protonation is correlated with (HR - log &) (e.g., see Bunnett (10))-there is more likely a continuum of functions for protonation equilibria similar to that described by Bunnett (11) in the area of kinetics. It will be noted from Table 5, that Hodoes not represent one edge of the continuum. I n short, i t is clear that the idea of a generally applicable indicator-based acidity function, as originally envisaged, is an unattainable ideal. I n 1957, Bonner and Lockhart (18) measured the value of an acidity function H+, where H+ = -log a d . j ~ ~ + / j m=, *pK.*A*a++ log [AH+]/[AH?+l and this function is the measure of the tendency for a proton to transfer to a univalent cation base AH+ to form the conjugate acid AH2=+,in the ranges 3&55% and 75-95% HpSOa. The parallelism found between the relationships H+ and Ho show that in these regions these two constants either differ by a small constant value or are identical, and any divergence between these functions, if i t occurs a t all, must appear in the lower regions of acidity. Brand, Horning, and Thornley (15) have calculated that the difference between H+ and HO H+ - Ho = log ~ B ~ A E , - + / ~ ~ E + ~ A E + is only -0.28 log unit in pure sulfuric acid. This difference may not be significant, since the value of the acidity function changes rapidly with medium composition in this region. Hinmau and Lang (14) comment that . . . the considerahle variation of acidity function with indicator
structure is pertinent to the significance of H- rtndH+functions. When the structures of the indicators differ from those of the HO bases, the effect of charge is likely to he overshadowed by the effect of the indicator structure itself, rendering the terms Hand H + meaningless as representatives of acidity functions dependent on charge alone.
An H- acidity scale based on the protonation of anions, where
+ log [A-]/[AH]
H- = -log aw . f ~ - / j m= pKaAH
has, however, been established. I n 1961 Phillips (16) measured the values of the Hacidity function in aqueous solutions of HC1 (&37%). A feature of the results is the weak acidity of concentrated hydrochloric acid solutions in respect to ionization of a negatively charged base, in contrast to the strong acidity of such solutions in respect to the ionization of a neutral base. Thus for 6 N HC1, H- = -0.18, Ho = -2.12. Phillips (15) suggests that the H- function may be calculated for other mineral acids providing the values of Ho and the activity coefficients are known. 688 / l o u r m l o f Chemical Education
Boyd (16) has measured the values of H- in aqueous sulfuric acid using cyanocarbou acids as indicators. Boyd (17) also measured the variation of activity coefficient with acid concentration in aqueous sulfuric acid solutions for a number of indicators appropriate to the Ho, Haf, and H- indicator functions. All ionic indicator activity coefficients were referred to a common standard ion, the tetraethylammonium ion, and i t was found that from any one of the acidity functions and activity coefficientdata the other two may be calculated over a considerahle range of concentration. The symbol H- has also been used (18) to record the measure of proton abstracting power of a base (thioacetamide) in strongly alkaline solution (1-6 M NaOH). Arnett and Mach (19) showed that tertiary aromatic amines failed as Hammett bases and in 1&90% aqueous H2S04followed a function they called H,"', and Hiuman and Lang (14) followed the protonation of indoles in 0.1-12 M HpSOa and 0.1-6 M HClOa and devised an acidity function HI. Yates and his coworkers have established an HA acidity scale which is applicable to the protonation of amides in aqueous solutions of sulfuric (80) and hydrochloric (21) acids. Bonuer and Phillips (28) constructed an Ho acidity scale over the range 4&90% aqueous sulfuric acid using substituted benzophenones as indicators. Below 60% sulfuric acid the scale is nearly coincident with the other 2 scales for which data is available (see Table 4), hut above 60% acid the divergence from the Hammett scale (1) is even more marked than, but in the opposite direction to, that of Jorgenson and Hartter (40) who used primary aromatie amines as indicators. The Hobenzophenone acidity function is nearly linear with percentage composition of sulfuric acid over the range 40-90% w/w. This scale might be useful in kinetic studies in sulfuric acid in which protonation of an oxygen center in a reactant is essential for reaction. Arnett and Mach (83) have recently summarized the acidity functions Ho, Hol", HR, and HR' in aqueous hydrochloric and phosphoric acids and have shown that in these media as well as in sulfuric acid (Table 5), the order in which the acidity functions change with acid concentration is HR > HE' > HO"' > Ha. Using such functions as (Hol" - Ho) as a criterion of acidity function failure, it is found that these terms have a roughly linear relationship to the acid molarity in these media and in perchloric acid, but that slopes of plots of Ha' Ho versus molarity fall in the order perchloric > sulfuric > phosphoric > hydrochloric, suggesting that sulfuric and perchloric acids are the worst media of the four as far as acidity function failure is concerned. I n conclusion it can be seen that the indiscriminate use of acidity functions for mechanistic interpretation i s hazardous. Not only do different Brp[nsted hases follow different acidity functions, hut the differences between them vary from one strong acid to another. Careful mechanistic studies should include measurements of the actual acidity function for the series of bases under kinetic investigation and both rates and equilibria should be measured in the same media (24, 85). Literature Cited (1) P m b . M. A., AND Lowe, F. A,, Chstn. RNS.. 57. 1 (1957). ~ H., 8 , "Electrolyte Solutions" (2nd (2) Roex~son.R. A., *no 8 ~ 0 ~R. Ed.), Butterworths Publieationa Ltd.. 1959. (3) O'ConNon, C., ~ ~ T U R N T. E A,. Y . J . Cham. SOC.,(B)1211 (1966).
