JOURNAL OF RESEARCH of the National Bureau of Standards- A. Physics and Chemistry Va!. 69A, No. 3, May- June 1965

Acid-Base Behavior In 50-Percent Aqueous : Thermodynamics of the Dissociation of Protonated Tris(hydroxymethyl)aminomethane and Nature of the Solvent Effect*

Maurice Woodhead,! Maya Paabo, R. A. Robinson, and Roger G. Bates

(February 16, 1965)

Electro mutive-force methods a nd cell s without liquid junc ti on have been uti lized to dete rmine the acid ic dissociati on constant of protonated tris(hydroxymethyl)a minome th a ne 12- amino-2-( hy­ droxymethyl)- 1, 3- propanedi ulJ in 50 wt percent methanol solv e nt at seve n te mperatures fro m ]0 to 40 °C. The c hange of the di ssociat ion consta nt with te mpera ture has been used to calcul ate the c ha nges of enthalpy, entrop y, and heat capacity when the dissocia ti on takes pl ace in the sta ndard state. Compari sons with earli er measureme nts in the aqueous medium reveal no great difl'ere nces in the entha llJ Y and entropy, s uggestin g that wate r participates in prefere nce to metha nol in the proto­ lyti c react io n even in 50-percent mcthanol. It is shown th at electrostatic considerations alone a re unable to explain the solve nt efl'ect on the dissociation ene rgy, a nd a subs ta nt ia l " basic it y e fl'ect" is indicated . The activity-coeffi c ie nt te rm for the a mine hydrochl oride in eq uimolal a mine-salt bufl'e rs has been evaluated and compa red with s imila r data in the water solve nt.

T he di ssociation cons tant of an acid of charge type 1. Introduction A+Bo, namely the acid conjugate to the wea k un­ charged base 2-amino-2-{hydroxymethyl)-1, 3-p ro­ Acid-base studies of organic compounds only sli ghtly panediol or tri s{hydroxyme thyl)aminome thane ,3 soluble in water are some times conveni e ntly made in has been studied in 50-percent methanol from 10 to a solvent consisting of equal parts by weight of water 40 °C. The associated thermodynamic quantities and methanol. In order to facilitate the de termination have bee n derived. Buffe r solutions composed of of pH and pK in 50-percent me thanol, an operational this primary amine and its salt have proved extraordi­ pH scale has recently been established for this solvent narily useful for pH control in biological syste ms [2] _ mixture [1)2. The standard scale, defin ed in a manner consistent with thermodynamic di ssociation con­ 2. Experime'Iltal Methods stants and activity coeffi cients in 50-percent me thanol, is fixed by three suitable reference solutions, namely 2 .1. Materials an acetate buffer, a phosphate buffer, and a solution of sodium hydrogen succinate. An aqueous solution of twice-di stilled hydrochloric As a part of the earlier work, the di ssociation con­ acid was used as a primary standard. Its molality stants of . and dihydrogen phosphate ion was determined by gravimetric chloride determination; in 50-percent methanol were determined from 10 to the standard deviation derived from three determina­ 40°C These two acids are of charge types AOB ­ tions was 0.01 percent. The purity of four lots of and A- B=, respectively. Here A and B refer respec­ crystalline tris{ hydroxyme thyl)aminome thane (ob­ tively to the acid and its conjugate base. The results tained from commercial sources) was found to be for the enthalpy and entropy of ionization in 50- 99.92, 99.94, 99.94, and 100.22 percent b y percent methanol were of interest for their bearing with the standard solution of _ on the relati on between charge type and solvent Weight burets were used, and each sample was ad­ effec t. justed to the theoretical equivalence point (PH 4.54 in a 0.1 M solution of the ne utralized base) with the aid of glass-electrode measurements. If: Presented before the Di vision of Analytical Chemi stry at the 149th National meeting of the Am e ri can Chemical Society, Detroit , Mic h., on April 7, 1965.

I Guest wo rk er, on leave from l\'1a kerere Unive rsit y College, Kampala, Ug anda. .3 For brevity, this base will sometimes be refe rred 10 as " tri s" and the corresponding 2 Fi gures in brackets in dicate the lit erature references at the end of th is paper. hydrochloride as " tris hydrochloride." 263 For convenience, many of the cell solutions were , 2.2. Procedures prepared from a commercial grade of tris hydrochloride together with the free base. The emf of cells contain­ In general, the experimental procedures followed ing buffer solutions prepared in this way was compared those used in determining the dissociation constant with solutions of identical nominal molalities prepared of tris in water [5]. Electromotive force measure­ from tris and the standard solution of hydrochloric ments of the cell acid. Three buffer concentrations spanning the range covered in the study were compared in this way. The Pt;H2(g, 1 atm), tris' HCl(ml), tris(m2) in 50 wt percent difference in emf was found to be 0.39 m V with a methanol, AgCl; Ag standard deviation of 0.05 m V. The cells prepared with the tris hydrochloride gave the higher emf. where ml and m2 are molalities, were used. Thirty­ The recorded emf for cells prepared in this way was four solutions, all with buffer ratio close to unity, were adjusted to correspond to that obtainable with pure studied. When tris hydrochloride was used, a stock tris (assay 100%) and the standard solution of hydro­ buffer solution was prepared by weighing the free chloric acid. base, the salt, and water. The remainder of the solu­ On examination, the tris hydrochloride obtained tions were prepared by dissolving a known weight of commercially was found to be very close to stoichio­ tris in a known weight of standard hydrochloric acid. metric neutrality; measurements of pH and buffer The necessary weight of methanol was then added, capacity showed that the product contained no ap­ together with more water, to achieve the desired preciable excess of either the base or of hydrochloric solvent composition. acid. Analysis for chloride by gravimetry showed, Each cell contained one hydrogen electrode and one however, that the acidic and basic components, while silver-silver chloride electrode. The emf measure­ present in equivalent amounts, were both present in ments at the seven temperatures were made in a lower quantity than expected (about 99.1 percent of variety of sequences. A complete series required theoretical). Furthermore, samples of the salt pre­ from two to three days. The solubility of silver pared by the authors by neutralizing the pure tris chloride in a methanol-water solution of tris was not with hydrochloric acid were also found to assay from determined, as it had been found insufficient to require 99.1 to 99.6 percent. corrections in aqueous solutions [5]. Methanol IS The inert impurity in the commercial product, presumed to lower the solubility still further. thought to be water by the manufacturer, could not be identified.4 Drying at temperatures low enough 2.3. Results to preclude decomposition of the salt did not mater­ ially increase the assay value.5 Although drying The emf data are summarized in table 1. Cor­ brought about some improvement in the results of the rections have been made to the reference hydrogen carbon and hydrogen analysis, the figures were partial pressure of 1 atm with the aid of the recorded inconclusive: barometric pressure and the known total vapor pres­ sure of the methanol-water solvent at the temperature in question [4]. The emf recorded for those solutions Carbon, Hydrogen, prepared by weighing tris and the solid hydrochloride percent percent was further corrected for the known deficiency of ionized chloride in these solutions.

Commercial sample", ...... ".""""" "" .. " ,,. 30.81 7.83 30.56 7.69 3. Calculation of the Dissociation Constant Commercial sample, after drying""" .. """" 30.60 7.69 30.60 7.84 The calculation of pK, where K is the acidic dis­ sociation constant of 2·ammonium-2-(hydroxymethyl)- Theoretical ...... " ...... " 30.49 7.67 1,3-propanediol (that is, tris' H+) in water, has been described in detail in earlier papers [3, 5]. The cor­ The supposition that the impurity was electrochem­ responding dissociation constant in 50 wt percent ically inert was confirmed by a comparison of the methanol, referred not to the standard state in water correction to the emf observed (0.39 m V) with that to but to that in this solvent, is termed p(sK). The pro­ be expected from the known assay (0.46 m V). The cedure for obtaining p(sK) is entirely analogous to difference corresponds to only 0.001 unit in pK. that for the computation of pK (that is, g(wK)) in water. The methanol with which the solvents were prepared "Apparent" values of p(sK)' were computed from the was "Spectro Grade," of the same quality as that used emf E by the equation in the earlier studies in 50 wt percent methanol solvents [1, 4]. p(sK) I == p(sK) - f3! = (R; ~ sf;)/F + 2 log ml -log m2

4 Datta, Grzybowski. and Wilson [3] reported a similar low chloride assay for the samples of tris hydrochloride prepared for their study of the di ssociation of tri s in aqueous solution. 2AvI :; Analysis of the dried sample by gas chromatography and by Karl Fischer methods in­ dicated the presence of D.l to 0.3 percent of water. The authors are indebted to R. J. Hall 1 +BdvI (1) for these results and for the elemental analysis. 264 TABLE 1. Electromotive force of th e cell Pt; H ,(g, 1 atm}, tris HCI(m,), tris(m,) in 50 wt % methallol, Agel; Ag from 10 to 40°C (in volts) Te mperature , °C • 7.80 o 25 ° C

mf 10 15 \ 20 30 35 40 ____~ L_ ____~ ____~____ J~ • _____L- ____~ _____ o Series I: m2= 1.0080 fIJ I

0.009554 0.78772 0.78553 0.78343 . .009566 . 0. 77857 0.77626 0.77394 .0095 75 .7878 1 .78567 .78353 .78099 .7791 7 .77681 .77427 .01921 .77366 .77 117 .76898 .76646 .76365 .76097 .75839 .01922 .7733 1 ...... 76372 .76092 .75812

.02892 . 76635 . 76388 .76 135 .75862 . .02892 .76606 .76357 . 76079 .75830 .75584 .75298 .75015 .0387 1 .76056 .75799 .75538 .75276 .75001 .74713 .744 14 .03872 .76083 .75830 .75571 .75299 .75000 .74712 .74426 .04857 .75609 .75354 . 75086 .74800 .

.04857 .75646 . 75384 .75102 .74829 .74558 .74263 .73973 .04861 .75624 .75375 . 75 106 .74831 .74564 .74253 .73932 .05854 .75322 .75066 .74787 .74506 .74205 .739 11 .73607 .06849 .75042 .74 777 . 74503 .74222 .7392 1 .73616 .73307 .06852 .75031 .74759 .74482 .74203 .7391 5 .73610 .733 11

.07867 .74773 .74499 .74230 .7394 1 .73648 .73340 .73037 .07869 .74789 .74518 .74239 .73945 .73630 .73331 .7301 7 .08882 .74589 .74313 .74033 .73745 .7343 1 .73 121 .728 10 .099 10 .74397 .74 11 4 .73840 .73545 .73255 .72934 .726 18

0.01928 0.77339 0. 77 164 0.769 12 0 .76672 0.7638 1 0. 76 10 1 0. 75826 .03889 .75992 .75774 .75545 .75269 .74992 .74706 .744 17 .05880 .75248 . .7471 9 .74464 .74203 .73906 .73622 .07900 .74808 .74532 .74236 .73958 .73629 .73321 .73049 .09948 .74429 .74 149 .73845 .73,564 .7323 1 .72925 .72621 FI(;URE I . Plot of th e apparent p(sK) in SO-percellt methallol as a

Seri es III : nt2= fill function of m, at 25 °C. --- O . Seri es I. --- • Seri es II . 0.0 1922 0. 77405 0. 77154 0.76925 0.76673 0. 76415 0.76150 0. 75856 o Sel ;c, Ill. .03872 .76077 .75789 .75541 .75288 .75020 .74733 .7442 1 • Se ri es IV . .05854 .75304 .75029 .74774 .74494 .74200 .73907 .73595 .07864 .74796 .745 12 .74242 .73956 .73656 .73357 .73044 .09910 .7437 1 .74098 .73829 .73538 .73230 .72934 .72610 Figure 1 is a plot of the data at 25 °C. This straight line was obtained with a value of 0 for a: it corresponds Seri es I V: 1/1.2 = 1.0022 '" I ------to a slope - f3 = 1.220. The same valu e of a proved 0.009576 0.788 18 0.7857 1 0.78349 0.78 128 0.77888 0.77649 0.77386 suitable for the extrapolation at all te mperatures from .02894 .76588 .7633 1 .76075 .75825 .75,558 .75273 .74979 .04857 .75614 .753,57 .7509 2 .74824 .74536 .74239 .73945 10 to 40 °C. The intercepts p(sK) are summarized in .06853 .7501 5 .74743 .74469 .74 189 .73890 .73,579 .73270 table 2, together with the standard deviations of the .08890 .74534 .7426 1 .73982 .73700 .73396 .73089 .72780 intercepts and the values of p(wK) found in prev,ious

fI Tris h ydruchloride was used to prc pmt' the solutio ll s of Series I and II , but hydrochl ori c investigations [3, 5]. These "observed" values of acid was used for Seri es J II and IV . p(sK) can be represented within about 0.001 unit by the fo llowing equation, which is of the form proposed by Harned and Robinson [8]: where A and B are constants of the Debye-Hiickel theory [6, 7] and a is the "ion-size parameter." The 3689_57 values of the standard emf sEQ in 50 wt percent meth­ 8_5466 + 0_013381T anol have been reported elsewhere [4J- T The acidic strength of tris hydrochloride in this (2) solvent, as in water, falls in the region where sol­ volysis of both the free base and the protonated base TABLE 2. p(sK) values for the protonatedform of tris in 50 wt perce nt is minimal; hence, the buffer ratio is accurately given methanol from lata 40 °C by m2/ ml , and the ionic strength I is identical with ,--- , p l, K) pl. K) ml_ The thermodynamic p(J() is obtained by extrapo­

6.GO (7) 19.1445(Al - A2T+ A 3 P) (3) J mol - 1 where N is the Avogadro number, e the electronic 6.Ho charge, E the dielectric constant of the medium, and 19.1445(A 1 -A3P) (4) rs the radius of the (spherical) ion. The assumption J mol- 1 made here is that the solvent is a continuous medium with a dielectric constant equal at all points to the LlSo macroscopic dielectric constant. 19_1445(Az - 2A:I T) (5) J mol- 1 deg- 1 The dissociation of tris' H+ is an isoelectric process:

BH + +SH=B+SH~ 6.C~ -19.1445(2A3T). (6) J mol- 1 deg- 1 where BH + represents the protonated base and SH is the amphiprotic solvent. The change in electrostatic The values of these thermodynamic quantities in 50 energy on transfer from water to 50-percent methanol wt percent methanol are compared in table 3 with the is then same quantities for the dissociation in the aqueous medium [3, 5] _ The standard deviations in 50-per­ (8) cent methanol can be estimated by the procedure outlined by Please [13] _ Assuming a standard devia­ tion of 0.001 in p(sK) , the results of the estimate are where E' is the dielectric constant of 50-percent meth­ as follows : anol (56.3 at 25°C) and E is that of water (78.30 at 25 J mol- 1 DC). Thus 6.Gel will have a positive value if r BH +> r H+. Although the value to be assigned to the radius of the J mol-1 hydrogen ion (designated SHi , or simply H+ in the absence of precise knowledge of its solvated structure) may be in dispute, it is difficult to see how this radius could be larger than that of the protonated tris cation, BH+. 266 An atom model of the tris cation s hows that this ion The electrostatic energy of a univale nt ion is then is not unlike the tetraethyla mmonium ion in size and given by shape. A radius of 4 A has been ascribed to the latter [6], and it may be taken as a reasonable estimate of G l=e2 dr (1 0) the radius of the tris cation as well. An ion with this {11.5~ + (4 + ( oo !!:!....} e 2 rs Esatr2 JI.5 (Xr- Y) r2 J4 Eor2 radius contributes 0.87 kJ moJ- 1 to the electrostatic energy change on transfer from wa ter to 50·pe rcent methanol. wher e X= 0.4(Eo- Esat) a nd Y = 1. 5X- Esat. Upon The diffi culty in appJ ying eq (8) to a n acidic dissocia­ integration we obtain tion process li es in our ignora nce of the effective radius of the hydrogen ion. There is, howe ver, considerable G 1= e2 {_1_ 1 ) _ 0.417 + X In 0.375Eo evidence [15] that the hydrogen ion is intimately as­ (l __ e 2 Esat rs 1.5 Y P Esat soc.iated with fo ur wate r molecules in solvents con­ taining a con'siderable a mount of water, and we can + 0.25}. (11) reasonably ide ntify the radius of this hydrated hydro­ Eo gen ion with the diameter of the water molecule, 2.8 A. An ion of this size contributes 1.24 kJ mol- 1 to the electrostatic energy. For the transfer of a mole of ions from water to another The total electrostatic effect on dissociati on of the solvent (identified by a prime mark), we have protonated form of tris should therefore be 0.4 kJ mol - I. 2 The experimental value of - 1.45 kJ mol- lis ve ry dif­ LlGel =Ne {(~ _ _ 1 ) (l __1 )-0.417 (1,_l) fere nt and of opposite s ign. A similar anomaly seems 2 Esa! Esat rs 1.5 Y Y to hold for all protonated bases, for example o-chloro­ anilinium ion and m-nitroanilinium ion [12]. This + X,' 2 In 0; 3 7 5E~_ .!. ln 0. 375Eo+ 0.25 (~_ l)} . (12) result has been ascribed to an increase in the basicity (Y ) Esa t P Esat Eo Eo of the solv ent on the addition of metha nol, whic h may well be due to a degradati on of the water structure by methanol. A structure-promoting entity is more ef­ For an ion of radius 4 A, only the last term of eq (10) fective in a me thanolic solvent tha n in water, because appears, and the electrostati c energy of the ion is there are more opportunities for the water structure ide ntical with that calculated by the Born equation. to be promoted. Thus the electrostatic energy (LlG BH +) of the protona ted Hydroge n ion should be one of the best structure tris cati on is still 0.87 kJ mol- I. If the hydrogen ion promoters, and therefore we have a reasonable ex­ has a radiu s of 2.8 A, the first te rm of eq (1 0) di sappears planation of the increase in acidity of protonated tris and the integrati on of the second term is to be made on addition of methanol. The magnitude of the effect is surprising, howe ver ; it must be of the order of - 2 kJ mol- 1 if the total e ffect is -1.45 kJ mol- 1 and + 0.4 kJ mol- I must be ascribed to the electrostati c effect. 80 EO " 78.3 (WATER) It is worthwhile to consider whether this discre pancy may be due to inadequacies of the simple Born treat· 70 me nt. In a n effort to explain the Gibbs e nergy changes on the transfer of electrolytes from water to deuterium 60 oxide, Hepler [16] has recently considered the conse­ ·E O"56.3 (50% METHANOL) quences of assuming a model s uggested by the work of Ritson and Hasted [17]. Three regions of solvent 50 distribution around an ion are distinguished in this E treatment. From the surface of the ion of radius rs 4 0 to a distance 1.5 A from its center is a region of di­ electric saturation, with a dielectric constant Esat. For water solvents, Esat may be taken as 5 [16]. At 3 0 di stances (r) greater than 4 A from the center of the ion, the solvent has its macroscopic dielectric con­ 2 0 stant Eo. In the intermediate region, the dielectric constant varies linearly with r: 10

Eo-Esat ( ) " 5.0 E = 2.5 r - 1.5 + Esat· (9) 0 0 3 4 6 8 r S ( A) The variation of the di electric constant in water and F IGU RE 2. Variatio ll of the dielectric cOllstant of water and 50- in 50-percent methanol with di s tance from the center percent aqueous methanol in the vicinity of an iO Il ; rs is the distance of the ion is shown sche matically in fi gure 2. fro m th e center of the ion. 267

766 - 033 0 - 65 - 5 from 2.8 to 4 A. Equation (12) now becomes From density data [19], the partial molal volume of potassium dihydrogen phosphate can be estimated to be 39 ml mol- I; a value of 1.5 ml mol- I has been _Ne2 {_ (.l_1.) £ 0.7E ~ aGel - 2 0.107 Y' Y + (Y')2 In 2.8X' _ Y' ascribed to the potassium ion [20], leaving 37.5 ml mol- I for the dihydrogen phosphate ion. A mole of spherical ions with radii 2.5 A would have this partial molal volume and would contribute 1.64 kJ mol- l to -Xln 0.7Eo +0.25(~_l)} (13) the electrostatic energy. Y2 2.8X - Y Eo Eo Similar calculations are difficult to make for the bivalent hydrogen phosphate ion (HPO;), because the density data for sodium dihydrogen phosphate solu­ for the hydrogen ion. On substitution of the appro­ tions are fragmentary. The available data, however, aGH+ priate values of Eo and Eo we obtain = 1.35 kJ suggest a radius of about 2 A and, therefore, a contri­ mol- I for the transfer of a mole hydrogen ions from bution of 2.49 kJ mol- I to the electrostatic energy. water to 50-percent methanol. This figure must be quadrupled, however, because of It thus appears that the calculated gain in electro­ the double charge on this ion. The net effect due to static energy due to dissociation of the tris cation is hydrogen ion, H2 P04, and HP04 is 9.7 kJ mol- l now + 0.48 kJ mol-I, in even more marked contrast compared with the observed value oJ 7.1 kJ mol- I. with the observed value of -1.45 kJ mol-I. The cal­ It would be unwise to imply that these values of culation therefore serves to emphasize that, no matter the electrostatic energy calculated with only estimated how doubtful some of the assumptions about the ionic values of the ionic radii have any exactitude_ It is radii may be, the basicity effect in the opposite direc­ important, however, to note that whenever a reason­ tion must be of considerable magnitude, in fact about able assumption can be made about these ionic radii, 2 kJ mol- I. the electrostatic contribution is higher by 1 to 3 kJ Further evidence for the existence of a pronounced than the observed energy change. In other words, increase in solvent basicity when methanol is added to there is always a term of considerable magnitude for water to make a 50 wt percent mixture is found in the the "basicity effect" that does not figure in the elec­ energies of transfer of hydrochloric acid from water to trostatic treatment. this mixed solvent. The standard emf of the cell with hydrogen and silver-silver chloride electrodes in 50- percent methanol has been found [4] to be 0.19058 V at 5. Activity Coefficient of Tris Hydrochloride 25°C, or 31. 76 m V lower than the value in water. Thus the transfer of a mole of hydrogen ions and a mole of The success of the extrapolation procedure em­ chloride ions from water to 50-percent methanol is bodied in eq (1) in this and other similar situations 6 accompanied by an increase in Gibbs energy of 3.06kJ. justifies the substitution of the Debye-Hiickel formula The radius of the chloride ion is known [18] to be for the activity-coefficient term in the expression for 1.81 A. Using the Born model, we calculate that the the dissociation constant of a protonated amine, BH+. chloride ion should contribute 1.91 kJ mol- I which, Thus for the process together with 1.24 kJ mol-I for the hydrogen ion, gives 3.15 kJ mol- I for the transfer of hydrochloric acid. BH + +SH=B+SH ~ (14) This calculated figure is perhaps not in very serious disagreement with the observed value. Nevertheless, one can write [23] it is derived on the assumption that the macroscopic dielectric constant holds at a distance of 1.81 A. It a )1 /2 - Av'/ is in this region that the Hepler treatment gives results log y~ == log y ± (.2!! = v' + 0.5f3/ (15) markedly different from those furnished by the Born - h I+B& / equation. For example, the electrostatic term for the chloride ion is 3.08 kJ mol- I by the Hepler treatment. where y ± is the mean activity coefficient of the amine This value, together with 1.35 kJ mol- I for the hydrogen hydrochloride. ion, gives a total of 4.43 kJ mol-I for the transfer Straight-line extrapolations such as those shown in process from electrostatic considerations alone. By figure 1 could not be obtained when "reasonable" comparison with the observed Gibbs energy change values of 3 to 5 A were used for the ion-size parameter (3.06 kJ mol- I) it is again seen that the basicity effect & in eq (1), and the line shown corresponds to & = O. must amount to about 1.4 kJ mol-I. A similar anomalous behavior of the activity-coefficient Data are availabie for the solvent effect on the disso­ term in aqueous buffer solutions ' composed of other ciation of acetic acid, but, in view of the very unsym· aliphatic or aromatic amines and their salts has been metrical shape of the acetate anion, it is doubtful that observed in the course of a number of similar studies. either the Born equation or the Hepler treatment can These investigations have dealt with ammonia [23], be usefully applied to data for this acid. However, tris [5], 2-methyl-2-amino-propanediol [24], t-butyl­ the second dissociation of phosphoric acid is a more amine [22], ethanolamine [21], diethanolamine [25], suitable case, because of the higher symmetry of the oxygen atoms surrounding the phosphorus atom. 6 See, for example. measurements on ethanolamine [21] and (-butylamine [22]. 268 t~iethanolamin e [26], aminopyridine [27], and piperi­ dine [28]. The abnormally small or e ve n negative o value of Ii suggests that ion pairs of moderate sta­ bility exist in these buffer solutions, and in the study of piperidine it was Ro ssible to account for the results with an ion size of 4 A whe n a correcti on was made for ion-pair formation [28]. , , These observations are surprising in vi e w of the , fact that the activity coeffi cie nt of aqueous ammonium "- 50-percent " chloride at 0.1 m is not greatly differe nt from that of METHANOL, pota.ssium c hloride at th e same molality [29]. The Isoplestl c me thod by whic h these ac tivity coefficients , , we re determined is unfortunately not capable of , , furnishing precise data for activity coefficients much -0.20 '------;:!-;------"Il,--'-'------L-.::l below a molality of O_L 01 02 One can, however, derive the activity coefficients of -.1m am monium c hloride and tris hydrochloride in equimolal buffer solutions [BH+( m), B(m)] from the e mf data used FIGU RE 3. Comparison of log y ~ (e q (/5)) ill the two solvellts water t? de rive pK and from the slopes of the extrapolation and 50.percellt methanol. lines s uc h as those shown in figure 1 (see eq (15)). Tht' das hed Jines are the Dehye- Iluc ke l limili n/! s lopes. The results for the ac tivity coeffi cie nts a nd osmotic coeffi cients of ammonium c hloride and tris hydro­ ~ hl or id e are compared in table 4 with the correspond­ w g values for potassium c hloride [30]. It is apparent The data for tri s buffe rs in 50 wt percent methanol that no great differe nce exists in dilute aqueous cannot be used to derive the activity coeffi cie nts for solutions. The value (0.758) found in this ' way for tri s hydrochloride by eq (15), in the absence of infor­ the mean activity coeffi cie nt of tris hydrochloride mation concerning the activities of both li'js and the (0.1 m) !n the presence of tri s (0.1 m) is in good agree­ solve nt in the methanolic medium. It is of interest .me nt wIth the value (0 .770) found by isopi esti c meas­ however, to compare th e left-hand side of eq (15) fOI: urements [31] of 0.1 m tris hydrochloride without any equimolal buffers of tris and its hydrochloride (ml = m2) added tris. In 50 wt percent methanol with th at for the same The HuckE-I equation utilized in eq (1) describes the buffers in water. Such a comparison is s hown in activity coelt ;t' nt term by two paramete rs in two fi gure 3. The standard states in the two solvents separate terms. The results shown in table 4 mean diffe r, so that the activity coeffi cient becomes unity the refore, that the variation of the activity coe ffi c i e n~ at 1= 0 in each case. The Debye-Huc kel limiting of ammonium c hloride (and probably of amine hydro­ s.lopes for the two solve nts are indicated by dashed c hlorides as well) with ionic stre ngth is partitioned lInes, and the general s imilarity of the curves suggests between the two terms in a different manne r from th at that there are no great differences in th e patte rn of c haracterizing the behavior of the alkali me tal chlo­ behavior in th e two medi a of different compositions. rides. The reason for this differe nce s hould probably As expected, departures from ideality are (Treater be sought in the differe nt structures of the hydration at a given ioni c stre ngth, in the solve nt of lo~ e r di: shells of the two types of cation and in th e concomitant electric consta nt. Furthermore, the positive devia­ effects on the mi c roscopic di electric constant in th e ti ons from the limiting law are more pronounced in immediate vicinity of the ions. 50-pe rcent methanol than in water. Although thi s be havior is a conseque nce of a large r value of - f3 (eq (15)) in the me thanolic solvent it is TABLE 4. Comparison of the activity coefficients and osmotic co· impossible at the present time to state with ce r~ainty efficients of KCI, NH4 CI, and tris' HCI in aqueous solutions at whether it arises from diffe rences in the salt effect ' 25°C. on y ± or on (aSI'I!YB)' It is likewise impossible to decide on the basis of this evidence what is the true y _ for - ¢ fO I'- nature of SH in eq (14), that is , which of the two types n> of solvent molecules plays the predominant role in KCI NH.CI Tris·HCI KCI NH.,CI Tris' HCI the protolysis of BH+. Here again, there seems to be little evidence of a drastic change in the nature of 0.()()5 0.928 0.92.) 0.925 0.977 0.975 0.975 .0 1 .902 .899 .898 .968 .966 .966 the reaction process, such as would be expected if .02 .870 .865 .864 .9.>7 .955 .%4 .05 .8 17 .809 .808 .941 .937 .936 methanol replaced water to any large exte nt in the .07 .795 .786 .785 .9.34 .931 .930 solvation shells of the proton and the acid BH+ or . 1, .770 .760 .758 .927 .92:; .923 base B.

269 6. References [16] L. G. Hepler, Aust. J. Chern. 17,587 (1964). [17] D. M. Ritson and J. B. Hasted, J. Chern. Phys. 16, 11 (1948). [ 18] L. Pauling, The nature of the chemical bond, ch. X (Cornell [1] M. P aabo , R. A. Robinson, and R. G. Bates, J. Am. Ch,:,m. Soc. University Press, Ithaca, N.Y., 1940). 87,415 (1965). [19] International Critical Tables, Vol. 3, p. 80 (McG raw·Hill Boo k [2] R. G. Bates, Ann. N. Y. Acad. Sci. 92, 341 (1961 ). Co., Inc., New York, N. Y. , 1928). [3] S. P . Datta, A. K. Grzybowski , and B. A. Wilson, J. Chern. [20] R. A. Robinson and R. H. Stokes, Trans. Faraday Soc. 53, Soc. (London), 792 (1963). 301 (1 957). [4] M. Paabo, R. A. Robinson, and R. G. Bates, J. Chern. Eng. [21] R. G. Bates and G. D. Pinching, 1. Res. NBS 46, 349 (1951) Data 9, 374 (1964). RP2205. [5] R. G. Bates and H. B. Hetzer, J. Phys. Chern. 65, 667 (1961). [22] H. B. Hetzer, R. A. Robinson, and R. G. Bates, 1. Phys. Chern. [6] R. A. Robinson and R. H. Stokes, El ectrolyte Solutions, 2d 66,2696 (1962). ed., p. 125 and app. 8.1 (Butterworths Scientific Publica· [23] R. G. Bates and G. D. Pinchin g, J. Res. NBS 42, 419 (1949) tions, London, 1959). RP1982. [7] R. G. Bates, Determination of pH, p. 406 (J ohn Wiley & Sons, [24] H. B. Hetzer and R. G. Bates, J. Phys. Chern. 66, 308 (1962). Inc. , New York, N.Y., 1964). [25] V. E. Bower, R. A. Robinson, and R. G. Bates, 1. Res. NBS [8] H. S. Harned and R. A. Robinson, Trans. Faraday Soc. 36, 66A (phys. and Chern.), No.1, 71 (1962). 973 (1940) . [26] R. G. Bates and G. r. Allen, J. Res. NBS 64A (phys. and [9] A. L. Bacarella, E. Grunwald, H. P. Marshall, and E. L. Purlee, Chern.), No.4, 343 (1960). 1. Org. Chern. 20, 747 (1955). [27] R. G. Bates and H. B. Hetzer, J. Res. NBS 64A (phys. and [10] C. L. deLi gny , H. Loriaux, and A. Ruiter, Rec. Trav. Chim. Chern .) , No.5, 427 (1960). 80, 727 (1961). [28] R. G. Bates and V. E. Bower, J. Res. NBS 57, 153 (1956) ell] D. Rosenthal, H. B. Hetzer, and R. G. Bates, 1. Am. Chern. RP2705. Soc. 86, 549 (1964). [29] B. F. Wishaw ·and R. H. Stokes, Trans. Faraday Soc. 49, 27 [12] E. E. Sager, R. A. Robinso n, and R. G. Bates, J. Res. NBS (1953). 68A (phys. and Chern.) No.3, 305 (1964). [30] W. J. Hornibroo k, G. J. Janz, and A. R. Gordon, J. Am. Chern. [13] N. W. Please, Biochem. 1. 56, 196 (1954). Soc. 64, 513 (1942). [14] M. Born, Z. Physik 1,45,221 (1920). [31] R. A. Robinson and V. E. Bower, 1. Chern. Eng. Data, in press. [15] R. P. Bell and K. N. Bascombe, Di sc. Faraday Soc. 34, 158 (1957). (Paper 69A3-345)

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