The Hammett acidity function H0 in H2SO4SO3 mixtures; superacidity

J. Inorganicand Nuclear Chemistry, 1955, Vol. 1, pp. 119-125. PergamonPressLtd., London

THE HAMMETT ACIDITY FUNCTION Ho IN H~SO4--SO3 MIXTURES; SUPERACIDITY By CHARLES D. CORYELLand RICHARD C. Fix Department of Chemistry and Laboratory for Nuclear Science,tl~ Massachusetts Institute of Technology, Cambridge, Massachusetts, U.S.A.

(Received November 1954) Abstract--The comparative quantitative acidities of mineral acids H+(CIO4 -) and H+(HSOc), the two superacids, then HI, HBr, HC1, HNOs, CIsCCOOH, and H F are reviewed in the light of the Hammett and Michaelis acidity functions H0 and G. The great power of the Hammett quantitative acidity function H0 is emphasized, with evidence being provided for the independence of charge in Hammett general acidity function H x with charge type of'the indicator in concentrated water-type solutions. The Lewis-Bigeleisen extension of the Hammett function H0 to HsSO4--SOs mixtures, using vapour pressure of SOs as a measure of H0, is reviewed, and an error separating Ho from --log all+ is removed. The Lewis-Bigeleisen data provide by this interpretation new information on the polyacids HzO(SOa)n, and the superacid anhydrous SO~. The effective proton activity of anhydrous SOs is given as 1014"1 referred to that in 1M HsO + as unity.

SOME twenty years ago HAMMETT [H1-4] introduced a family of experimentally established functions describing acidity in terms of proton activity. These are useful for concentrated aqueous solutions of strong (mineral) acids. The function, called H0, for a unipositive indicator acid HB + with an uncharged conjugate base B, is congruent with pH in very dilute aqueous solutions, but differs from it by an activity term (which becomes appreciable) as the molarityM of the strong acid exceeds unity. The function is defined as: O 0 = --log10 a s + - - log10 (fB/fmt +)

(l)

where a s + is the activity of acid (normally considered as the hydronium ion HzO+ ) and fBH+ and J~ are the activity coefficients of the reference acids and bases. HAMMETT [H3] has shown that the activity term becomes essentially independent of the solute concentration in strong acid media. (2) The function H 0 is conveniently established from indicator studies, but may also be determined from rate studies [H2, D1, K1], and is determinable for a given mineral acid with an error of less than 0-2 in logarithmic units, with suitable objective selection among indicators. The function is known [H2] for H2SO 4 up to 18M, for HC10 4 up to 7M, for HC1 up to 6M, for H N O z up to 8M, and for CC13COOH up to 5M. (3) There is little information available about the other i1~ This work was supported in part by the U.S. Atomic Energy Commission. is) Other families, e.g., H.e. H+, H_, H_e, are possible for references based on the bases HeB++, HB +, BOH-, BO =. An experimentally defined Michaelis acidity function G for the indicators based on the acid dependence of semiquinone formation of the various acid-base forms of thionine, H2Thi+++, has been established by MICHAELISand GRANICK[MI]. A plot of G versus the (volume) molarity of H2SO4 M gives a curve which is parallel to the plot of HAMMETT'SHo vs. M. The parallelism demonstrates the lack of dependence of the activity term on molarity of H2SO4, already anticipated by HAMMETT[H3]. cz) There is no reason why the H-type functions cannot be evaluated for mixed mineral acids, such as HNOs--HeSO4, and indeed some of the perspicacious work of INaOLO'S school [I1] implies this for nitrating mixtures. 119

120

CHARLES D. CORYELL and RICHARD C. Fix

functions t4) except in alcohol-water media of low dielectric constant studied by GRtmWALD [G4, G6], SWAIN [$5], and others, where the activity function causes trouble. SCHWARZENBACH[$2] has discussed indicators on the extended H 0 (pH) scale. It can be shown that the H 0 function for H2SO4 follows the empirical rule: --H 0 ~

0.5M

-- 0.3

(2)

over the range 1 < M < 17.8 (10-95 per cent H2SO4), with an average deviation of 0.08. The values for 90, 95, and 100 per cent H2SO4 (by weight) are --8.17, --8-74, and --10.60 iS) [H2]. These numbers show that in pure H2SO4 the proton activity exceeds that in 1M H~SO 4 by the factor 101°'6. Similar results have been obtained with HC10 a. Concentrated solutions of H~SO 4 and HC104 are thus identified as spectacular superacids of roughly identical acidity behaviour [H2] at the same molarity. The hydrohalogen acids other than HF are medium superacids, decreasing in the order HI, HBr, and HC1; and HNO 3 is a weak-strong acid, c6) not much stronger than C13CCOOH. BELL [B1] gives pK values (negative logarithm of ionization constant K) for the hydrohalides as HF 4, HC1--7, H B r - - 9 , HI --11. SCHWARZENBACHIS1] has estimated thepK values H~F+ --9.0, HF +5.0, H2C1+ - 10, HC1 --3, H3SO4+ --8.3, H2SO4 --3.1, HzC104 + --14, HC104 --8.6. These values are based on computations, for water as solvent, for isoelectronic species together with semi-theoretical estimate of the dependence of effective dielectric constant of water on structure. HAMMETT [HI, H2] showed the general utility of the indicator method, by which H 0 is measured within 4-2 H units (log units) from that of the acidity constantpKBH+ of an indicator by: n o ---- log ((B)/(BH+)} + pKBH+ (3) where the concentrations of the neutral and protonated forms of the indicator B are indicated by parentheses. He lists pKBn+ for numerous indicators, the strongest acid being the 2,4,6-trinitroanilinium ion ofpK value --9.29. In one of the latter research programmes of an extraordinarily creative career, G. N. LEWIS with J. BIGELEISEN [L1] found an indicator 2,2'-dinitro-4,4'-dibromofluorescein that resisted oxidation or sulfonation in fuming sulfuric-acid solutions up to 0.534 mole-fraction SO 3 in the H20--SO 3 system, at which acidity it is 80 per cent in the proton saturated form. iv) Thus the Lewis-Bigeleisen indicator is probably H4B+4(or H6B+6if the nitro groups have added protons): (a) An isolated study of CORYELLand SHEPHERD[C2, $4] on H_ in H2SO~--H~O up to 6M, using picric acid as an indicator, shows that H - and H0 become parallel above about 4M, separated by about 0.8 log units. ts) There is some ambiguity about the reference value --10.60 for 100 per cent H2SO~. BRAND [B3] proposes -- 10'89 or perhaps -- 11'05. (6~ The classical (thermodynamic) ionization constant of HNO3 was measured by REDLICH and BIGELEISEN [R1] as 21 ± 4by Ramanspectrometry; morerecentmeasurements by GOLDRING[G2,G5],using precision absorption spectrometry [G3], gives the value 7 ~ 1 for the ionization constant at zero ionic strength, with a AH ° of ionization of 1-1 ± 1"1 Kcal/mole. YOUNG[Y1, G5] has developed Raman spectrometry further for studies of the thermodynamic and concentration ionization constants of HNO3, HzSO4, and HSO4-. DOSTROVSKYand co-workers [A1, D3] have developed an O 18 isotope tracer method for the semiquantitative estimation of the acidity of acids HOX, which supports the evaluation. iv) It is likely that the neutral molecule R(NO2)~(COOH)(OH)(=O)(--O--) has in the proton-saturated form added protons to the carboxyl group (--pKnn+ ~ 8 ) , splitting out water, to the phenolic group (estimated --pKaa+ ~ 7 ) , to the oxo group = O of the 2,10-anthraquinoid (pyronine) dyestuff (estimated --pKnR+ ~ S ) , and to the oxo bridge - - O - - of the middle ring of the anthraquinoid structure --pKBa+ = ~10-3 (as established from the Lewis-Bigeleisen data). It is possible that the nitro-groups also add protons in the region of acidity under study, without, however, seriously perturbing the general interpretation, or affecting the absorption spectrum. The basicity of nitro groups is discussed by BRAND [B3].

The Hammett acidity function Ho in H~SO~--SOa mixtures; superacidity

Br

H ]

H20 +

+

Br i

+ OH

//\//\ O2N

C

+

(H+?)

l

c=o

121

(4) NO2 (H + ?)

\,/ and the Hammett function studied is probably H+3. However, as indicated in footnotes 2 and 4, all of Hammett functions H~ are parallel functions of composition, and, as LEWIS and BIGELEISENimply, H+3 can be tied to the rigorously defined H 0 for extrapolation to H~SO4--SO a mixtures. The important contribution of their paper [L1] is to permit a carry-over of acidity function to use the logarithm of the vapour pressure of SO a as a measure of generalized acidity (Hammett style) up to pure SO a (vapour pressure 0-33 atm at 25°C). Indeed, by fitting the dinitrodibromofluorescein data for three superacid mixtures to the end of HANMETT'S data (based on trinitroaniline), LEWIS and BIGELEISEN[L1] calibrated the H o of pure SO 3 as --14.1 with a probable uncertainty of less than 0-3 H units. The Lewis-Bigeleisen calibration (their Fig. 5) is presented here ~8~as Fig. 1. The solid circles give approximately log aso 3, plus 14.56 (standard state, SO a gas, 1 atm) as calculated by them. There is an accessory piece of interpretation in Fig. 5 of the Lewis-Bigeleisen paper that is probably illusory, namely the proposal that log au+ goes through a maximum just before 50 m o l e - ~ SO a (100 per cent H2SO4). This illusion is apparently related to an ambiguity in LEWIS and RANDALL'S famous textbook [L2], which says that the escaping tendency (fugacity) of a component of a solution might fail to increase with mole fraction in a solution of highly viscous or glassy character. It is the purpose of the present paper to display the power of the Hammett treatment of inorganic acids, as fortified by the brilliant Lewis-Bigeleisen extension, and to show that it is proper to retain equation (1) of this paper even for pure SOa, as one limit of an acid system based on production of free protons. LUDERand ZUFFANTI[L3] report on the work of HANTZSCH, LEWIS, USANOVICH, and others treating acidity in systems like BF3, A12CI~, and SnC14, where the proton activity cannot be defined, but acidity can still be interpreted quantitatively. Let us now return to the system HzO--SO 3, or better H2SO4--SO 3. It is known that the following acids exist in concentrated H2SO 4 and fuming sulfuric acid (H2SO4--SO 3 mixtures): H2SO 4, pyrosulfuric acid H2S20 v and trisulfuric acid H2S3010. Indeed GOODARD, HUGHES, and INGOLD [G1] prepared nitronium salts of these (NO2 +) (HS207-), (NO2+)~($207=), and (NO2+)2($3Olo=). It is probable [G1] that there exist higher polymeric sulfuric acids H~S4013, etc., typified by H2S,~O~+1. The existence of polymerization reactions and of metastable liquid phases in pure SO 3 suggests that n may become a very large number in SO 3 nearly free of H2SO 4. Let us call the typical acid in such a medium H20(SO3)~. (8) This figure is presented here by courtesy of the Journal of the American Chemical Society and of Dr. BIGELEISEN.

122

CHARLESD. CORYELLand RICHARDC. FIX The principal ionization reactions in such superadd systems should be :Ira

(5) (6) (7) (8)

H2SO4 + H 2 0 = Ha O+ + HSO42H2SO 4 = H3SO4+ + HSO4H2S20~ + H2SO4 ---- H3SO4+ + HS207H2S3Olo +i- H~S207 = HaSzO7+ + HS3Olo-

I

I

I

I

I

I

I

14--

i 0

12-0 0

I

I0--

° I

I ,a

a

8--

o D

8

o,

l

e

°°...

! I

0

•

I I

@

i

Ii

i

I

I

40

50

O0

70

80

100

90

~o~%so,. HzO.SOs S~lstem I 0

I I l- I I0 &O ,to 4,o

Mole~

I

SO

I

~o

503 .

I

70

I

80

I

cio

I moo

H~SO.'SO~ S 3 s t e .

FIG. 1.--[Taken from LEWlS, G. N., and BmELEISEN,J., J. Amer. Chem. Soc., 65, 1149 (1943).]--The acidity function, --H0, measured by Hammett and Deyrup plotted against mole-~ SOa in the H20--SOa system, open circles. The Lewis-Bigeleisen experimental extension, squares, and their extension based on the vapour pressure of SO a, solid circles, plotted against m o l e - ~ SO3 in the H~O--SO3 system, and against mole- ~ SOa in the H2SO4--SO3 system. The dotted curve is the questionable Lewis-Bigeleisen interpretation of log aR+.

The Lewis-Bigeleisen Fig. 5, shown herewith as Fig. 1 with their questionable log aa÷ branch shown as a dotted curve of downward trend, indicates that removal of the base H~O as the mole-fraction SO 3 increases, leads to a sharp rise in --I-Io just before 50 per cent SOs (as first shown by HAUUErT) because of the obvious reaction: SOs + H 2 0 = H2SO4 (9) The build-up of polyacids in the region just beyond 50 mole- ~ SOz in the H 2 0 - - S O ~ system leads to a further increase in acidity to a - - H 0 value of 14 at about 75 per cent tg~ The relative strengths of these acids have been evaluated by GZLLESPm [GI]. Including the molarity of HeSO4 (18.7, or 10-2 moles per kg), the concentration equilibrium constants are 1.5 × 10-6 for equation (6) and 2.8 × 10-3 for equation (7). The higher acids are still stronger [G1].

The H a m m e t t acidity function Ho in HsSO~--SOs mixtures; superacidity

123

SO 3. After this, n becomes fairly large, and successive polyacids are of about the same strength. (10) The production of acidity by the polyacid HzO(SO3) ~, taken as a pure individual, would follow the equation: 2HzO(SO3) . = H30(SOz). + + HO(SOz)n-

(10)

Since the co-existent acids of neighbouring different values of n are of closely similar strength when n is a fair-sized number, this equation is adequate, although a sharper treatment would show H20(SOz)n+ 1

-~- H20(SO3) ~ = H30(SO3), + -[-

HO(ZO3)n+ 1

(11)

It is convenient to express the proton-producing reaction in H~SO4--SO a mixtures as

HaO(SO3), + = H + q- H20(SOa) n

(12)

, formally parallel to the generalized acid equation HB +

= H + -+- B

(13)

The anion for H B + is accordingly HO(SO3)~-+1 or to adequate sharpness HO(SOa)~-. It is probable that the neighbouring polymers of the family H20(SO3) ~ are in fluid equilibrium, since indicator measurements and vapour-pressure measurements are not reported to show time lags until anhydrous SO 3 is reached [B4]. It is obvious that the protons of equations (12) and (13) are suitably solvated. The tremendous range of - - H 0 values shows that the free energy of solvation Ill) of a proton by H20 is about 14.5 Kcal per mole lower than the solvation in pure H2SO 4 to form HzSOa+ (i.e., 1.365 × 10-6). Taking the extrapolated Lewis-Bigeleisen - - H 0 of 14.1, it is apparent that H20(SO3) . provides a free energy of solvation Ill1 of a proton by this acid which (for very large n) is about 4.8 Kcal (i.e., 1"365 × 3.5) higher than by H 2 S O 4.

The limiting - - H o value of 14.1 found by LEWIS and BIGELEISENis the limit of proton activity produced by equation (12), as n goes to infinity. Here, in pure SO 3, --log aa+ has a finite value, the highest attainable in the H 2 0 - - S O 3 system, rather than a low value following the maximum at 100 per cent H 2 S O 4 indicated in Fig. 1 by the dotted paraboloid curve. We consider the quantitative measurements of LEWIS and BIGELEISEN[L1] to be such an important extension of the armament of HAMMETT [HI, H2], that we present in Table 1 interpolated numerical values of H 0 at various rounded mole percentage of SOs in the systems HzO--SO 3 and H2SO4--SO3. LEWIS and BIGELEISENtook the vapour pressures of H2SO4--SO 3 mixtures from the International Critical Tables [12] and of pure SOs from an extrapolation of the data of BERTHOUD [B2]. (12) ~x0) This argument, as pointed out by Professor T. F. YOUNG, ignores cyclic polymers of SO3, especially (SOn) 3. The authors feel that this, if important, would act effectively as an inert diluent. ~1~) It should be pointed out that as the component HsO goes to the vanishing point, --H0 shows no sign of discontinuity. Thus it is apparent that solvation of H + in pure SOs is accompanied by virtually the same free-energy decrease as the solvation of H + by HaO(SO3),. tlS) A more recent set of vapour pressures of SOs at various compositions and temperatures is given by BRAND and RUTHERFORD[B4].

124

CHARLES D. CORYELLand RICHARD C. Fix TABLE I.--INTERPOLATEDHo VALUES

H2SO4--SOs % SO3

HsO--SOs SOs

0 18 33 46 57 67

50 55 60 65 70 75

H~SO4--SO3 Ho

-- 10-60 ~

--11'1 --12'3 --13-3 --13"7 --13"9

% SOs

HzO--SO3 SOs

Ho

75 82 89 95 100

80 85 90 95 100

--14-0 --14"03 --14"05 - - 14.06 --14"1

a Reference value of HAMMETT[H1, H2]; compare footnote (5) in the text.

It is interesting to reverse the treatment to predict that the vapour pressure of pure SO 3 above 1M H2SO a is 10-~4"7, since the H 0 of 1M H~SO~ is 0.09. It is interesting to note that DENO [D2] has estimated the H o of 9 0 ~ N2H 4 - - 1 0 ~ H20 as +19, and SCHWARZENBACH [$3] has estimated the H 0 of saturated N a O H solution as +19. CONANT and WHELAND [C1] have measured basicities in ether solution that would correspond to H o values in the neighbourhood of +31, while BELL [B1] and SCHWARZENBACr~estimated the pK~, of CH 4 as +50. The studies in organic solvents are plagued by problems of low dielectric constant. It might be more profitable for inorganic chemists to work with a witch's broth of a eutectic of (Li,Na,K,Rb,Cs)20. The senior author expresses his indebtedness over a period of many years to a large number of colleagues, including particularly Professors Louis P. HAMMETT, LEONOR MICHAELIS, LINUS PAULING, GEORGE SCATCHARD, GEROLD SCHWARZENBACH, C. GARDNER SWAIN, and.T. FRASERYOUNG, and including former students W. BURTON LEWIS, HAROLD F. PLANK, LIONEL S. GOLDRING, a n d DAVID J. SHEPHERD. REFERENCES [A1] AMBAR,M., DOSTROVSKY,I., SAMUEL,D., and YOFFE,A. D., J. Chem. Soe., 1954, 3603-11. [B1] BELL, R. P., Acids and Bases. Their Quantitative Behaviour, John Wiley and Sons, Inc., New York, 1952, Table 6. [B2] BERTHOUD,A., Helv. Chim. Aeta, 5, 513 (1922). [B3] BRAND,J. C. D., J. Chem. Soe., 1950, 997. [B4] BRAND,J. C. D., and RUTHERFORD,A., J. Chem. Soe., 1952, 3916. [CI] CONANT,J. B., and WHELA~, G. W., J. Amer. Chem. Soc., 54, 1217 (1932). [C2] CORYELL,C. D., and SHEPHERD,D. J., unpublished work, University of California at Los Angeles (1941-2). [D1] DEANE, C. W., J. Amer. Chem. Soe., 67, 329 (1945). [D2] DENO, N. C., J. Amer. Chem. Soe., 74, 2039 (1952). [D3] DOSTROVSKY,I., WeizmannInstitute of Science, Rehovoth, Israel, personal communication, 1954. [G1] GILLESPIE,R. J., J. Chem. Soe., 1950, 2492 and 2516; GODDARD,G. R., HUGHES,E. D., and INGOLD,E. K., J. Chem. Soc., 1950, 2559. [G2] GOLDRING, L. S., Ph.D. Thesis, Department of Chemistry, Massachusetts Institute of Technology, 1950; see also GOLDRING, L. S., and CORYELL, C. D., Massachusetts Institute of Technology, Laboratory for Nuclear Science and Engineering Progress Report, July 1, 1950. [G3] GOLDRING,L. S., HAWES,R. C., HARE, G. H., BECKMAN,A. O., and STICKNEY,M. E., Anal. Chem., 25, 869 (1953). [G4] GRUNWALD,E., and BERKOWITZ,B. J., J. Amer. Chem. Soc., 73, 4939 (1951). [G5] GURNEY, R. W., Ionic Processes in Solution, McGraw-Hill Book Co., Inc., New York, 1953, p. 139.

The Hammet acidity function H0 in HsSO4--SO3 mixtures; superacidity

125

[G6] GUTBEZAHL,B., and GRUNWALD,E., J. Amer. Chem. Soc., 75, 565 (1953). [H1] HAMMETT,L. P., Chem. Revs., 16, 67 (1935). [H2] HAMMETT,L. P., Physical Organic Chemistry, McGraw-Hill Book Co., Inc., New York, 1940, Chapter IX. [H3] HAMMETT,L. P., and DEYRUP, A. J., J. Amer. Chem. Soc., 54, 2721 (1932). [H4] HAMMETT,L. P., and PAUL, A. M., J. Amer. Chem. Soc., 56, 827 (1934). [Ill INGOLD,C. K., MILLEN,D. J., and POOLE.H, G., jr. Chem. Soc., 1950, 2576; see also the 22-paper sequence J. Chem. Soc., 1950, 2400-2684. [I2] International Critical Tables, McGraw-Hill Book Co., Inc., New York, 1928, p. 213. [K1] KRIEBLE,V. K., and HOLST, K. A., J. Amer. Chem. Soc., 60, 2976 (1938). ILl] LEwis, G. N., and BIGELEISEN,J., Jr. Amer. Chem. Soc., 65, 1144 (1943). [L2] LEWIS,G. N., and RANDALL,M., Thermodynamics and the Free Enerffy of Chemical Substances, McGraw-Hill Book Co., Inc., New York, 1923, p. 207. [L3] LUDER,W. F., and ZUEFANTI,S., The Electronic Theory of Acids andBases~ John Wiley and Sons, Inc., New York, 1946. [M1] MICHAELIS,L., and GRANICK,S., J. Amer. Chem. Soc., 64, 1861 (1942). [R1] REDLICH, O., and BIGELEISEN,J., J. Amer. Chem. Soc., 65, 1883 (1943). IS1] SCHWARZENBACH,G., Z. phys. Chem., 176, 133-53 (1936). [52] SCHWARZENBACH,G., Z. Electrochem., 47, 40-52 (1941). [53] SCHWARZENBACH,G., and SULZBERGER,R., Helv. Chim. Acta, 27, 361 (1944). [54] SHEPHERD,D. J., M.A. Thesis in Chemistry, University of California at Los Angeles, 1942. [$5] SWAIN,C. G., Massachusetts Institute of Technology, private communication, 1952. [Y1] YOUNG,T. F., Rec. Chem. Proff., 12, 81 0951).