salt of CIusiiis, Coldman and Pcrlick,ls luKcther with tho cspansiori coefiicieiits of l e d , copper2 and rock salt3 were used to givc numericd v:Lluos of CP/aT. 0 was takcn as 88lO for lead, 31!2.813for
copper arid 280'6 for rock salt. The graph of CP/CYT us. e/?' is shown in Fig. 1, where all of the results for copper and rock salt have bcen superimposed on the results for lead. This has bccn done bv multiplying the copper values by 2.30 and the rock salt values by 4.62. The straight line portion of the curve of Fig. 1extrapolates to a negative value of about 3000 cc. atm./dcg. mole. Thus, the value corresponds roughly to the second term of (7). Anharmonic effects are absent. 0 Pb The large deviations from the straight line occur x233 - 0 NOT x 4 6 2 at low temperatures where O/T is greater than 5. This is expected, as at low tcmpcratures, y shouId I dccrease.10 Using Barron's relationYfor y corresponding to the nearest ncighbor model for both 0 I I I I lead and copper, the dcviations from the straight 0 1 2 3 4 5 6 7 8 line function are shown for thesc two substances BIT. as the dotted curves. The agreement is satisfacFig. 1. tory. The deviations of the rock salt points do not agree with Barron's relation3 for that substance. Except for the last term on the right-hand sidc, this The experimental points deviate by over a factor relation resembles Gruneisen's relation for y. of three from a curvc demanded by the theory. Howevcr, (7) involves the compressibility as a From the results shown in Fig. 1, the heat caconstant and the more easily measured Cp rathcr pacity and thermal expansion data for lead, copper than C,. Still, with this relation deviations from and rock salt are quitc self consistent. Lead obeys Gruneisen's law can be discussed. We will retain Gruneisen's law between 22 and 300'K. Satisthe temperature terms in relation 7 only so that the factory values (within a few per cent.) for the cornentire relation is a function of B/T. pressibility of lead as a function of temperature to The best wav of using relation 7 as a correspond- aboiit 25OK. can be computed, assuming that y ing state function seems to be by comparing the is independent of tempernt we. Using Barron's results of this research for lead with previous work deviation function for y, the compressibility of for copper and rock salt. The heat capacity of both lead and copper can be computed for temcopper taken from the work of Giauque and peratiires from 300 to about l l 0 K for lead and to Meads,13 the values for lead from that of Meads, about 3O'IC for copper. Forsythe and Giauque,14 and the values for rock
;J
1
(13) W. F. Giauque and P. F. Meads, J . A m . Chem. Soc., 68, 1897 (1941). (14) P. F. RIeads, W. R. Forsythe. and '8. F. Gisuque, ibul., 68, 1902 (1941).
(15) IC Clusius, J Goldinan and A . Perlick, %. Xaturforschung, 4, 424 (1949).
(16) R . I€. Fowler, "Statistical Meclranics," Cambridge Univorsity Prcss. 2nd Edition. 1936, p. 126
N.Rl.R. STUDY OF THE IONZATI'OS OF ARYL SULFOSIC ACIDS BY ROBERT H. DINIUSAND GREGORY R. CHOPPIN Department of Chemistry, Florida State Uniuersitzj, Tallahassee, Florida Received Ju2v Si, 1961
Xuclcar magnetic resonance spectra of p-toluenesulfonie acid, 2-naphthnlcnesuilfonic acid and 2,7-naphthalenedisulfonic acid were measured as n function of concentration. The acid ionization constant for p-tolucwsulfonic acid calrulatcd from the chemical shifts is 22 f 3. A comparison of tlic chemical shifts for these sulfonic acids and L)onrx-50 cation cxchange resin of 4 and 16% divinylbenzcne content indicates that the cation exchanger resin is the stronger acid.
Aryl sulfonic acids such as p-toluenesulfonic acid have been used in a numbcr of investigations1.2 as model compounds for the elucidation of the cornplex physical chemistry of polystyrene-divinylbenzene sulfonic acid ion exchange resins such as DOweX-50. I n conjunction with an investigation of (1) G. E. Mcyers and G. E. Boyd, J . Phya. Chem., 60, 521 (1986). 0.D. Bonner, V. r. Holland a n d L. L. Smith, %bad., 60, 1102
(2)
(1956).
hydrated Dowex-50 resin by nuclear magnctic rcsonance technique^,^ it has seemed feasible to study these model compounds by the same techniques. Several previous rep0rts4~5have demonstrated the (3) R. 11. Dinius, G . ~ t Choppin . and nr. T. Cineruon, to be submitted for publication. (4) H. 9. Gutowsky and 11. Saika. .I. Chem. Pliys., 21, 1688 (1953). (5) G. C. Hood, 0.Redlich and C. A, Reilly, abad., 22, 2067 (1954); also G. C. Hood, A. C. Jones and C. A. Reilly, J. Phys. Cham., 63, 101 (1950).
N.M.H.,STUDY OF IONIZATIOX 014'ARYLSULFONIC ACIDS
k'eb., 1962
value of Ihe study of strong acids by nuclear mag-
268
x.-z 7-napninl~ewaicuitonc acid
netic resonance and recently the results of such
0 - - 2 - naphlhabnsnul+bnle 0 - - o-1olucnasuifonlc
an invcstigation of polystyrenc sulfonic acid havc beeu reportedS6
atid
ocid
30-
Experimental Reagents.-C.r.
p-toluenesulfonic acid was used as obtained from Eastmaxi Chemical Co. with no further purification. 2-Ns hthalenesulfonic acid and 2,7-naphthulcnedisulfonic acizwere purified from technical grade material by recrystallization from concentrated hydrochloric acid solutions. Saturated aqueous solutions were prepared from the purified crystals and the desired concentrations obtained by dilution with distilled water. The molarities of all solutions were determined by titration with standard sodium hydroxide solution. N.M.R. Spectra.-The proton magnetic resonance spectra of thcse three acids were measured as. a function of the acid solution concentration using a Varian Associates high resolution N.AI.R. spectronierL-1operating at 60 megacycles per see. The bide barid tcchiiique utilizing external standards waa used to obtain reference signals. The room and magnet gap were thermostated to 25'. Cyclohesane was u s d as the external refcrcncc and from a knowledge of the difference in resonance frequencies of cyclohexane and watrr, the chemical shifts of the acid solutions were calculated with respect to the frequency of pure water. All the shifts, expressed in cycles per second, were toward lowcr field strengths. The observed chcimcal shifts were corrected for changes in the bulk magnetic susceptibility of the Bolutionu. Thc magnetic susceptibilities wcre obtained by observing the splitting of the resonance lines induced by shaping the sample container from a cylinder to a sphere and placing the transition zone in the magnetic field.' The susceptibilities obtained in this ~ a have y becn compared with the v:ilues obtained from Pascal's constants and found to agree within 3-5y0. The results of the n.m.r. mcasuremcnts are presented in Table I.
0 .
020x v)
0
02
0.1
04
03
P. Fig. 1.-The chemical Rhift plotted as a function of thc mole fraction of protons on hydronium ions.
I5 0
100
I
12
t
-
TABLE I CIIEYICALSmms "0-
Frcquency, c.p.8.
Resonance shift (S), y.p.in.
P
0.024 .115 .221 .439 .964 1.282 1.989 2.929 3.469
0.0017 .0084 .017 .036 .087 .117 ,186 .291 .342
0.232 .462 .940 1.880
2-Naphthalencsulfonic acid 1.014 217.6 0.081 0.087 1.040 221.2 .141 .174 1.053 231.4 .311 .346 1.119 257.2 .741 .808
0.0065 ,0132 .0294 .069
0.1631 .4570 .9125 1.368 1.828
1.009 1.042 1.115 1.175 1.251
Density
0.064 .300 .590 1.181 2.373 2.885 3.787 4.733 5.075
1.002 1.017 1.034 1.063 1.115 1.135 1.170 1.208 1.229
Obsd.
pToluenesulfonic acid 214.0 0.020 219.1 .lo5 224.6 .197 236.8 .401 267.2 .908 286.0 1.221 326.8 1.901 383.6 2.847 415.4 3.377
04
03
02
p.
Cor.
larity
I
01
90;
Fig. 2.--The ratio of chemical shift to mole fraction of protons on hydronium ions as a function of the mole fraction of protons on hydronium ions for p-toluenesulfonic acid.
2,7-Naphthalenedisulfonicacid 220.3 230.9 251.5 276.3 300.8
0.126 .302 .646 1.059 1.467
0,120 .312 .TO4 1.163 1.632
0.0096 .0310 .0517 ,0918 .1302 The n.m.r. spectra of the undisoeiated aci'd s were measand the ured in non-ionizing solvents (CIICl, and C~1-1,~) shifts with respect to water within cxpcrimcntal error were found to be 6.51 p.p.m. This compares with thP reported value of 6.7 f.0.3 p.p.m. for thc alkyl and benzene sulfonic acids.8 (6) L. Kotin and M. Wagasawa, J . Am. Ckem. Soc., 83, 1026 (1961). (7) W. Stewart and R. Click, private communication.
0011 0 001
0 01
01
3
P
Fig. 3.-Log
of the chemical shift plottcd as a function
pf the log of the mole fraction of protons on hydronium
ions.
During tho course of this investigation, it was observed that solutions of p-toluencsulfonic acid underwent photochemical decomposition in the prcsence of ultruviolrt radiation, resulting in the development of a ycllow color with evolution of SO?. Prolonged heating on a steam-kmth in the dark failed to providc any visible evidence of this decomposition. (8) L. H. Meyer, A. Saika and 13. S. Gutowsky, J . Am. Chem. SOC., 76, 4567 (1953).
Discussion Figurc 1 indiontcs that p-toluencsulfonic acid and 8-naphthalcnesulforiic acid have a very similar curve for the chemical shift, plotted as a function of P, the molc fraction of protons or1 hydronium ions. In calculating P, only the acid group and water protons arc considcred and not thc aromatic hydrogens. Assuming complcte dissociation, if x is the stoichiometric mole fraction of the acid, P equals 3s/(2-z) for the monobasic acids and 3x for the dibasic acid. The greater slope for 2,7-naphthalenedisulfonic acid possibly could be interpreted as meaning that it is a stronger acid than the ptoluenesulfonic or 2-naphthalenesulfonic acid (see equation). However, the two sulfonic acid groups of this dibasic acid are not completely independent and t,hc effect of the ionization of one group upon the ionization of the second group is unccrtain. Consequently, the suggcstcd interpretation of relative acid strength must be regarded as only tentative. Only for ptoluenesulfonic acid is the solubility sufficiently large to allow high cnough values of P to be investigated so that analysis of the data to calculate the acid constant is possible. The degrces of dissociation were calculated from the shifts by the equation SjP
=
as, + (1 - a)Sz
(1)
where S is thc total chemical shift in p.p.m., S1is the shift of the hydronium ion and SZis the shift of the undissociated acid. For 82 the valuc of 6.51 p.p.ni. was used. Although the value of 8 1 would be expectcd to be the same in all acids, it has been found that in fact the anion influences the observed hydronium ion shift. The value of SI is obtained by plotting the values of the slope SIP as a function of P as in Fig. 2 and extrapolating to P = 0. A value of 14.5 p.p.m. is obtained for the p-tolucnesulfonic acid as compared to previously reported valves of 11.8, 9.2 and 13.1 p.p.m. for " 0 3 , I-IC104 and H2S04.5.9The cakulation of a, the degree of dissociation, is more sensitivc to the value of SIthan of Szas can be seen from the revision of the SIP equation to the form cy
SIP =---SI
- S?
- Sz
The equs tion for thc acid dissociation constant is I@ = __a__
C(1 - a )
(3)
( 8 ) 0 C. IIoorl and C. A. Itrilly, J . Cliem. I'hys., 27, 1128 (18;7).
whew fi is the acitivity coefficient of tho undisso&tcd moI(:cuIe, Cis thc coiicentration of the acid in moles per liter and a is the activity of p-toluenc-
sulfonic acid. In thc inscrt in Fig, 2, log K@is plottcd us. molarity. The values of a were calculated using data of Ronner, et Thc valuc of I< calculated in this fashion is 22 f 3, which is comparable to that of nilric acid. Bonner and RogersL1 report that niesitylencsulfonic acid has an ionization cbonstant of thc same order of magnitude but lower than nitric acid. In Fig. 3, thc chemical shifts are shown on a loglog plot as B function of I-' for ptoluencsulfonic acid, polystyrenesulfonic acidG and I>owex-50 cation cxchangc resin of 4 and of l G % divinylbenzcne cor~tent.~Both this curve and an analysis of the polystyrenesulfonic acid for the acid dissociation const ant indicatc that the latter is quite similar to p-toluenesulfonic acid in its acid strength. Although the rcsiri is too concentrated even in thc most hydrated state to allow rcliable calculation of an acid constant, the indications are that the 4% DVB rcsin is stronger than the p-tolucnesulfonic acid. Also the indication that the 4% DVB resin is stronger than the 16% DVB is reasonable, since the more extensive organic crosslinking would result in a lower effectivc dielectric constant in the vicinity of thc sulfonate group, lowering the acid constant. It must be understood that this analysis of the relative acid strengths of the resins and p-tolucncsulfonic acid is based on equation 2, assuming S2 is the same for $111 thcsc sulfonic acids and that S I for thc rcsin is equal to or grcatcr than 14.5 p.p.m., which does not scem unreasonable. The observed linc widths for dilute solutions of the p - toluenesulfonic, the 2-r~aphthslcnesulfonic and thc 2,7-naphthalenedisulfonic acids were approximately 0.9 cyclc. As thc concentrations of the solutions approached saturation and increased in viscosity, thc absorption linc width increascd to 1.5-2 cycles. This broadcning is consistcnt with reported viscosity effects.I2 The authors wish to thank Drs. E, Gruntvald and M. Emerson for their assistancc in this research. The Atomic Energy Commission has supported this rcsearch under Contract AT-(40-1)-1797. (10) 0. rj. Bonner, G. D. Easterling, I). I,. West and V. F. IIoIIand, J . A m . Chem S o r , 77, 242 (1955). (11) 0. D Bonncr and 0. C. Rogers, J . Phys. Chem., 64, 1480 (1960). (12) J N bhoolery and B. Alder, J Chem. I'hux , 23, 806 (1055).
