PROTONATED FORM O F 2-AMINO-2-(HYDROXYMETHYL)-1,3-PROPANEDIOL
April, 196l
It can be said that it is erroneous to plot the points in this way, for each crc value in Table I11 corresponds not to a solution of constant total molality but to a, solution whose total molality varies (see Table I) between 4.02 and 4.51 31. This is true but, as Fig. 4 shows, the variation of ac with total molality is small and can be allowed for. At M = 4,crc is increasing by 0.0015for unit change in M . It is possible, therefore, to make a small correction to the ten values of ac in Table I11 to give data corresponding to a constant total molality equal to the mean of the extremes, 4.25 M. The corrected valueis are plotted as the lower curve of Fig. 5; there is less scatter of the points but still a definite downward trend with slope -0.0019, givingpc = -0.0004. A similar correction applied to the CYBdata (lower curve of Fig. 6) does not alter the constancy of O(B with changing x. The downward trend of the ac points in Fig. 5 with changing z at a constant total molality of 4.25 leading to Pc = -0.0004 is therefore fully consistent with the conclusion drawn from the ac) with changing M (Fig. 4) variation of (ax1 that ( p $~ pc) == -0.0004. The data a t M 4 have been used because they are the most complete and reliable. ,4t higher values of M , the limited solubility of potassium chloride restricts the range of x in which measurements cart be made. At lower values of M , the effect of experimental error is enhanced. Sever-
+
-
667
theless, by plotting (YC against z (Fig. 7) the same downward trend with increasing x is observed in all cases. Pc is certainly independent of m within limits of experimental error and the assumption of an average value of pc = -0.0005 is sufficient to bring consistency into all the measurements made in this work. TABLE V SMOOTHED VALUESOF
CYB AND oc 4 5 6 20 3 10 . 0 0095 0 0084 0 0084 0 0090 0.0098 - - c ~ B (0 013) (0 025) 0 0235 0 0230 0 0235 0 0246 0 0260 0 0275 oc BB = 0, Bc = -0 0005
m
05
..
Table V gives smoothed value of CZB and ac a t round values of the total molality. Finally, Fig. 8 shows how YB and yc vary with composition of the mixture at a constant total molality of 4. With PB = 0, log 2B is linear in x, increasing from -0.2390 when 2 = 1 to -0.2030 a t the limit when x = 0. If the pc term is neglected, log yc decreases linearly from -0.1061 when x = 0 to -0.2045 a t x = 1; the introduction of the Pc term causes a slight downward curvature shown by the broken curve in Fig. 8, leading to a limiting value of -0.2125 at = 1. It should be noted that these limiting values of log YB when x = 0 and of log yc when x = 1 are almost but not exactly the same and are much closer to log YB when x = 1 than they are to log yc when x = 0, in other words, on mixing both electrolytes tend to behave more like potassium chloride than sodium chloride.
DISSOCIATION CONSTANT OF THE PROTONATED ACID FORM OF 2A,1/IINO-%(HYDROXYMETHYL)-1,3-PROPANEDIOL [ TRISHYDROXYMETHYL) -AMINOMETHANE1 AND RELATED THERMODYNAMIC QUANTITIES FROM 0 TO 50’ BYROGER G. BATESAND HANNAH B. HETZER Division of Chemistry, National Bureau of Standards, Washington 85, D.C. Received N o v e m b e r 17, 1960
The thermodynamic dissociation constant ( K b h ) of the protonated form (BH+) of 2-amino-2-(hydroxymethyl)-l, 3 propanediol (tris-(hydroxymethy1)-aminomethane)has been determined at 11 temperatures from 0 to 50’ by measurement of the electromotive force of hydrogen-silver chloride cells without liquid junction. The results are given by the equation -log K b h = 2981.4/T 3.5888 0.005571T, where T is in “K. The changes of free energy, enthalpy, entropy and heat capacity were computed for the dissociation of the cation acid B H + in the standard state, as well as for the basic dissociation, H20 = BH+ OH-. For the acidic dissociation at 25”, AGO is 46,075 j. mole-’, AHOis 47,600 j. mole-’, ASD= 5.1 B j . deg.-’ mole-l, and AC,o is -64 j. deg.-l mole-’. The entropy changes for the isoelectric dissociation af cation acids (BH+) appear to indicate restrictive orientation of solvent molecules about the ions and the attendant hindrance of free rotation about carbon-carbon bonds. This simple picture is, however, unable to account satisfactorily for the observed changes in heat capacity.
-
+
+
+
interest both as an aGidimetric ~ t a n d a r d l - and ~ as a biological buffer,4-6 F~~brevity, it is known (1) J. H. Fossum, I’. C. Narkunas and J. A. Riddick, Anal. Chem.. 28, 491 (1951). (2) T. H.Whitehead, J . Chsm. Educ., S6, 297 (1959). (2) A. C. Holler. A i d . Chom., IS, 1359 (1956).
(4) G. Gomori, Proc. SOC.Ezptl. B i d . Med.. 68, 33 (1946). 15) H.Stormorken and T. F. Newoomb. Scand. J . Clin. and Lab. Invest., 8, 237 (1956). (6) G. G. Nahas and H. Rosen, Federation Proc., 18, 111 (1969); L. B. Berman. T.F. O’Connor,G. G. Nahaa and P. C. Luohsinger,
Physiologist, I, 10 (1959).
ROGERG. BATESAND HANNAH B. HETZER
668
the base is comparable to that of potassium hydrogen phthalate. Furthermore, aqueous solutions of the free base are not strongly alkaline and display no pronounced tendency to absorb atmospheric carbon dioxide.’t2 The negative logarithm of the basic dissociation constant of tris is found by measurements of pH7 and e.m.f.a to be approximately 5.9 a t 25”. The base is thus about one-sixteenth as strong as ammonia. It is sufficiently strong, however, that the neutralization curve obtained by titrating the base with a strong acid shows a sharp break a t the equivalence point, namely a t pH 4.7 for a 0.05 M solution.’S2 Buffer solutions formed by adding 5.7 to 47.7 ml. of 0.1 M hydrochloric acid to 50 ml. of a 0.1 M solution of the base, with dilution to a total volume of 100 ml., cover@the pH range 7.00 to 9.00 at 25”. Both a primary acidimetric standard grade and a buffer grade of the free base are now available from several commercial sources. Tris has been used to a considerable extent as a buffer in biochemical experiment^,'.^ its relatively non-toxic character even permitting its use in vivo.6 In studies of the heats of certain biological reactions in buffered media, the heat of ionization of the buffer acid must be known.lOJ1 It was therefore considered desirable to extend the measurements of the dissociation constant a t 20, 25 and 30” (made previously in this Laboratory’?) to cover the temperature range 0 to 50”, in order to permit the changes in heat content, entropy and heat capacity accompanying the dissociation to be computed.
Vol. 65
BH+=B+H+
(la)
where B represents the base and BHf is its conjugate acid. The constant for the equilibria 1 and l a (the acidic dissociation constant of BH+) is given the symbol K b h . Tris reacts with silver ion to a sufficient extent to permit the base to be used as a complexing agent in the titration, with silver nitrate, of sulfhydryl groups in proteins.16 Nevertheless, this reaction is not so extensive as to prohibit the use of the silver-silver chloride electrode in solutions of the concentrations employed heres or to require the application of corrections for a change in chloride molality. The equilibrium constant, Kf,for the formation of the diammine-silver complex, namely the process Ag+
+ 2B
Ag&+
was founds to be 2.7 X lo6 (log Kf = 6.43) if the solubility product constant (Ksp)of silver chloride a t 25’ is taken” to be 1.78 X Benesch and BeneschI6 found log Kf to be 6.56 a t 23” on the assumption that the formation of the diammine complex occurs in two steps.’* Combination of the e.m.f. equations with the mass-law expression for equation l a and with the two-parameter form of the Debye-Huckel equation gives -log
Rbh‘
-log
Kt,h
-
@??&I
=
In equation 2, E is the e.m.f. corrected as usual t o a partial pressure of 1 atm. of dry hydrogen, Eo Method is the standard potential of the cell,19A and B are The dissociation constant was determined by constants of the Debye-Huckel theory,20 and a* the measurement of the e.m.f. of hydrogen-silver and /3 are adjustable parameters, t,he first being chloride cells without liquid junction. The method the “ion-size parameter.” used was essentially that of Harned and Ehlers,I2 Experimental and the procedures were the same in nearly all respects as those used extensively in the study of Hydrochloric acid of reagent grade was diluted to a conother bases in this Laboratory (see, for example, centration approximately 6 M and distilled twice, the middle third being collected each time. A stock solution, approxireferences 13-15). The cell is represented as mately 0.1 M ,was prepared from the redistilled acid and wm Pt; Hz(g., 1 atm.), (CH~OR)&N&Cl(mJ,
(CH*OH)&NHz(mz), AgCl; Ag
where m is molality. The cell solutions contained tris and its hydrochloride in approximately equal molal amounts. The e.m.f. data yield directly the equilibrium constant for the dissociation process BH+
+H~O
B
+ %o+
(1)
or, since the activity of water is taken as unity in the infinitely dilute solution (7) 5. Glasstone and A. E. Sohram, J. A m . Chem. SOC..69, 1213 ( 1947).
(8) R. G. Bates and G. D. Pinching, J. Research Natl. Bur. Standor&, 48, 519 (1949). (9) R. G. Bates and V. E. Bower, A n d . Chem., 28, 1322 (1956). (10) J. M. Sturtevant, J. A m . Chem. SOC.,11, 1495 (1955). (11) R. J. Podolsky and M. F. Morales, J. B i d . Chem., 218, 945 (1956). (12) H. S. Harned and R. W. Ehlers. J. A m . Cham. Soc., 54, 1350 (1932). (13) R. G. Batea and G. D. Pinching, J. Reaeorch NaU. Bur. Slanda&, 49, 419 (1949). (14) R. G. Baten and V. E. Bower, iMd., 5 7 , 153 (1956). (15) R. G. Bates and H. B. Hetzer, ibid., ’ 4 8 , 4 2 7 (1960).
standardized by a gravimetric determination of chloride as silver chloride. The average difference among replicate determinations was zt0.03%. Trk-(hydroxymethy1)-aminomethane of primary acidimetric-standard grade assayed 99.9 f 0.1% when titrated under carbon dioxide-free conditions with the standard solution of hydrochloric acid. The end-point ( H 4.7) was detected by a pH measurement with the glass efectrode. The base was powdered and stored in a desiccator over Drierite for a t least 12 hours before use. The melting point was 171’ when the heat.ing rate was slightly less than 2 deg./ min . Three stock solutions containing approximately equimolal concentrations of the amine and its hydrochloride were prepared by mixing accurately-weighed portions of the base, of the standard hydrochloric acid, and, for one stock solution only, of carbon dioxide-free water. Each of the stock
(16) R. E. Benesch and R. Benesch, J. A m . Chem. SOC.,11, 2749 (1955); R. E. Benesch, H. A. Lardy and R. Benesch. J. B i d . Chem., 216, 6G3 (1955).
(17) B. B. Owen and 9. R. Brinkley, Jr., J. Am. Cham. SOC.,60, 2233 (1938). (18) J. Bjerrum, “Metal Ammine Formation in Aqueous Solutions.” P. Haase and Son, Copenhagen, 1941. (19) R. G. Bates and V. E. Bower, J . Research Nall. Bur. Standards, 63, 283 (1954). (20) R. A. Robinson and R. H. Stokes, “Eleotrolyta Solutione,” 2nd Ed., appendix 7.1, Academia Press, bo.. New York. N. Y.,1959.
PROTONATED FORMOF 2-AMINO-2-(HYDROXYMETHYL)-1,3-PROPANEDIOL
April, 1961
ELECTROMOTIVE FORCE OF m:
mi
0.10153
0.10293 .092~66 .08158 .07521 .07123 .06130 05537 .05017 ,044'77 .04027 .03035 .02069 ,015150 .010462 ,007648
.09122
.08077 .07479 .07012 .Of3046
05506 .04969 .04452 .03972 .02988 .02040 .015066 .010299 .007605
THE
669
TABLE I CELL Pt; Hn(o. 1 ATM.), (CHzOH)aCNH,Cl(mJ (CH20H)tCNH2(m),AgCI; Ag, FROM 0 TO 50" (IN
v.)
00 5 ' loo 15' 20' 25' 30° 35" 40° 45O 50° 0.78294 0.78121 0.77932 0.77731 0.77526 0.77344 0.77102 0.76878 0.76647 0.76404 0.76145 .78509 .78338 .78159 .77967 .77765 .77561 .77343 .77119 .76885 .76642 .76392 .78737 .78566 .78382 .78197 .77984 .77816 .77581 .77365 .77139 .76896 .76642 .78860 .78697 .78525 ,78334 .78149 .77944 .77725 .77508 ,77276 ,77035 ,76793 ,79015 .78851 .78674 .78496 .78306 .78112 .77888 ,77650 .77441 .77170 .79287 .79131 .78958 .78777 ,78594 .78422 .78196 ,77993 .77779 77530 77322 79304 79141 ,78961 ,78782 .78597 .78379 .78174 .77949 .77716 .77468 79460 .79685 ,79527 .79363 .79203 .79028 .78839 .78637 ,78433 .78218 .77987 ,76746 ,79877 .79721 ,79568 .79403 .79235 ,79033 .78853 .78635 ,78434 .78215 .77987 .80143 .79986 ,79833 .79673 .79500 .79332 .79088 .78927 .78730 .78516 .78282 ,80713 .80574 .80431 .SO274 .80106 .79947 .79763 ,79561 .79367 .79160 .78945 .81474 .81338 .81208 .81081 .80932 .80796 ,80604 .80447 .80261 .80071 .79864 .82108 .81989 .81869 .81741 .81601 .81459 .81293 ,81136 ,80962 .SO779 .80590 ,82921 .82822 .82713 .82599 .82484 ,82363 .82204 .82061 .SI904 .81741 .81560 .82280 ,83534 .83447 .83353 .83237 .83132 .83041 .82895 .82760 .82619 .82451
.....
solutions was diluted by weight with distilled water to prepare five cell solutions. Hydrogen was bubbled through each solution to remove dissolved air. The cells were filled as usual, air being excluded. The preparation of the electrodes has been described elsewhere.21 The initial measurements were made at 25". After the equilibrium values of the cells had been recorded, the temperature of the bath was lowered overnight to near O", and measurements from 0 to 25" were made on the second day. On the third day, the e.m.f. values from 25 to 50" were obtained, and a final reading a t 25" was made when possible. The reproducibility and stability of the cells containing tiis was excellent. The initial and final readings at 25" differed usually by no more than 0.1 mv., and duplicate combinat~onsof electrodes in the same cell agreed, on the average, well within =k0.05 mv.
8.82
8.77
Results The e.m.f. data are summarized in Table I. Each number is the average of two electrode combinations in the same cell. The e.m.f. was used to compute -log Kbh', the right side of equation 2, with various values of a*,the ion-size parameter. A curvature was apparent when a* values of $2 and -2 mere used. The best straight-line plots of -log Kbh' with respect to mlwere obtained with a* = 0. 'The results a t 0, 25 and 50" are shown in Fig. 1. The value of --log K b h ' a t ml = 0 (i.e., the intercept -log Kbh) :and the slope of the extrapolation line (- p ) were found by the method of least squares. The values of -log K b h are summarized in Table 11, together with (Ti, the standard deviation of the intercept. Values of the basic dissociation constant (&) are readily calculated from K b h and the autoprotolysis constant for waterz2by the relation, Kh = K w / K b h .
The present v:tlue of 8.075 for -log K b h a t 25" is in excellent agrelement with 8.076 found by Bates and Pinching.* At 20", thc present result is 8.214 and the earlier one 8.221. At 30", the two values are, respectively, 7.934 and 7.937. From measurements with EL glass electrode, Glasstone and Schram' found -log K b h = 8.03 at 25'. The values of -log &h in 0.6 M potassium chloride at 5 to 50" found by BernhardZaare about 0.3 unit higher than those given in Table 11. The dissociation constants were calculated from electro(21) R. G . Bates, "EJeotrometric pH Determinations," John Wiley and Sons, Inc., New York, N. Y.,1954,pp. 166 and 205. (22) H. 6. Barned snd R. B. Owen, "The Physical Chemistry of Electrolyte Solutions," 3rd Ed., Reinhold Publ. Corp., New York, N. Y., 1958. (23) S. A. Bernhard, J . Bioi. Chsm., 218, 961 (1956).
7.9 9
7.44
7.39
I
7.34 I 0.04
0
0.08
0.12
m,'
Fig. l.-Plot of -log Kbh' as a function of ml a t 0, 25 and 50". Calculations made with a* = 0.
TABLE I1 ACIDICDISSOCIATION CONSTANT (Kbh) FOR THE PROTONATED CATION O F TRIS-(HYDR0XYMETHYL)-AMINOMETHANE FROM 0 A T 25" TO 50". AGO, AHo, ASo AND Acpo t,
oc.
0 5 10 15 20 25 30 35 40 45 50
-log Kbh
Ui
8.8500 8.6774 8.5164 8.3616 8.2138 8.0746 7.9344 7.8031 7.6772 7.5543 7.4365
0.0OOS .0008 .0008
.0008 .0009
.0006 .0010 .0010
.0011 .0015
.0013 j. A(,pC, deg.
t
AGO, j. mole-1
AW, j . mole-:
j. deg.-1 ASO.
mole -1
mole -1
25
46,075
47,600
5.1
- G4
I
ROGER G. BATESAND HANNAH B. HETZER
670
metric titration data obtained with the glass electrode. Thermodynamic Quantities.-In order to derive the thermodynamic constants for the dissociation process, the values of -log Kbh were fitted to an equation of the form suggested by Harned and Robinson. 24 The resulting equation, the constants of which were determined by the IBhI 704 computer, is -log
Kbh =
2981'4 7 - 3.5888
+ 0.0055712'
(3)
where 2' is the temperature in deg. Kelvin. The mean difference between the "observed" values of -log Kbh and the values calculated by equation 6 for the 11 temperatures is f 0.0012 unit. By application of the customary thermodynamic relations to this equation for the change of -log Kbh with T , the following expressions for the standard changes of free energy (AGO), enthalpy (AHo), entropy (ASo), and heat capacity (AC,) for the dissociation of the protonated cation of tris-(hydroxymethy1)-aminomethane,were derived AGO = 57,078
+
-
68.7062' 0.10666T2 j. mole-' 57,080 - 0.1067T2 j. mole-' AS0 = 68.71 - 0.21332' j. deg.-l mole-l AC,o = -0.2132' j. deg.-l mole-' a H 0
=
(4)
(5) (6) (7)
These equations are valid from T = 2'i3.1G01i. to T = 323.16"K. The values of the quantities a t 25" are given at the bottom of Table 11. The estimated uncertainties are as follows: AGO, 6 j . mole-'; AHo, f 100 j. mole-'; ASo, f 0.5 j. deg.-'mole-'; and ACpo, f 5 j. deg.-'mole-'. The equation for the variation of the basic dissociation constant (Kb) of tris with absolute temperature ( T ) is readily obtained by subtracting the expression for -log Kbh (equation 3) from the corresponding equationz6 for -log ICw as a function of T. The resulting equation is
*
1489 9 -log Kb = A T
- 2.4958
+ 0.0114822'
(8)
from which the following values of the thermodynamic quantities for the basic dissociation a t 25" are obtained
+
+
BHf OHProcess: B H20 AGO = 33,819 j. mole-' AHo = 8,980 j. mole-' AS0 = -83.3 j. deg-1 mole-' ACPo = - 131 j. deg.-l mole-'
SturtevantlO has reported a calorimetric determination a t 25" of the enthalpy of ionization of the protonated (cationic) form of tris (BH+) in dilute solutions (the ionic strength of the final solutions was 0.013). His measurements lead to a value of 45,700 f 400 j. mole-', and this result may be regarded as A H o provided that the small enthalpy effect of dilution to zero concentration is ignored. The value found in this investigation is higher than Sturtevant's by nearly 2,000 j. Two determinations of the change in molar enthalpy for the ionization of BH+ in a 0.1 111 solution of the base which was 0.6 M with respect to potassium (24) H. S. Hained and R ;i.Robinson, Trans. Faiaday Sac., 36, 973 (1940). (25) Reference 20, p. 363.
Vol. 65
chloride have also been made. One of them," a direct calorimetric measurement, gave 48,500 f 400 j. mole-' and the other123utilizing electrometric titrations with the glass electrode to determine -log Kbh from 5 to 50", gave 48,950 f 800 j. mole-'. Discussion Dissociation Constants.-Tris is a trihydroxy derivative of t-butylamine, with one hydrogen of each of the three methyl groups attached to the tertiary carbon atom replaced by a hydroxyl group. As would be expected from the electron-attracting nature of the hydroxyl group,26the substitution of OH groups results in a decrease of base strength. Inasmuch as -log Kbh for the t-butylammonium ionZ7 is 10.45 a t 2 j 0 , this reduction amounts to approximately 2.4 units in log 16,. Glasstone and Schram7 found that the related compounds, 2-amino-2-methyl-1-propanol and 2-amino-2methyl-l,3-propanediol1 which have, on the tertiary carbon atom, one and two hydroxymethyl groups, respectively, are intermediate in strength, the latter being the weaker base. Entropy.-The therniodynamic constants for the dissociation of the conjugate acid form of tris in the standard state are compared in Table I11 with the corresponding quantities for the cation acids of 18 other nitrogenous bases. With the exception of 2,2'-bipyridinium ion and triethanolammonium ion, the tris cation is the strongest acid listed in the table. It is unique among acids of its charge type in displaying an increase of entropy upon dissociation. (Positive changes in entropy have, however, been found for the first dissociation steps of ethylenediammonium ion and hexamethylenediammonium ion.) Furthermore, the change of heat capacity appears to have a larger negative value than that for any other univalent cation acid so far studied. A fruitful, detailed interpretation of the changes of these thermodynamic quantities with changes in the structure of the cation acid is, unfortunately, not possible a t the present time. It seems certain, however, that solvation, with its accompanying changes in entropy and heat capacity, plays ;I significant part. Evans and Hamann29explained t,he increasingly negative values of ASo with substitution on the nitrogen in terms of changes in the holvation shell surrounding the (approximately spherical) ion. Bulky groups attached to the nitrogen atoms tend to exclude solvent and to increasc the entropy of hydration of the ion, thus making the value of ASo increasingly negative. Furthermore, the hydrophobic character of the alkyl groups added may well enhance this effect.28 It has likewise been observed29that the value of ASo becomes less negative as the alkyl chain lengthens. The increase in ASo is from 2 to 7 j. for each added CH, group, or always somewhat less than the rotational entropy of an additional carboncarbon This observation has led to the (26) A. E. Remick, "Electronic Interpretations of Organic Chemistry,'' 2nd Ed., John Wiley and Sons, Ino., New York, N. Y., 1949,p. 64; J. F. J. Dippy, Chen. Revs., 26, 151 (1939). ( 2 7 ) N. F. Hal1 and &I. R. Sprinkle, J . A m . Chem. Soc., 64, 3469 (1932).
April, 1961
PROTONATED
FORM OF 2-AMINO-2-(HYDROXYMETHYL)-1,3-PROPANEDIOL
TABLE I11 COMPARISOK OE' -.LOG Kbh, AH', A s o AND ACpO FOR D~ssO(T.4TION O F 19 CATIONACIDS(BH+)BT 25' Process: B H + B H+
THE
+
ACld
Ammonium13 hlethylamnionium28 Dimethylammonium28 Trimethylammonium2* Ethylammonium2Q Diethylammonium~~~ Triethylammoniuma Ethanolammonium31 DiethanolammoniumS2 Triethanolammonium33 n-Propylammonium3~ n-Butylammoniun~3~ Ethylenediammon .urn (2nd step) 34 Hexamethylenediammonium (2nd step)34 Piperidiniuml* 4-Aminopyridiniurn's 2,2 '-Bipyridinium35 Ephedriniuma Tris-(hydroxymethy1)aminomethane, protonated cation (this investigation)
9.245 10.624 10.774 9.800 10.631 10.933 10.715 9.498 8.883 7.762 10.568 10.640
52,200 54,760 49,620 36,880 56,820 53,430 44,200 50,540 42,410 33,450 57,180 58 090
9.928 49,450 10.930 11.123 9.114 4.352 9.544
58,200 53,390 47,090 14,120 45,150
8.075 47.600
-
1 . 9 - 14 -19.7 33 -39.7 97 -63.6 183 -13.0 .. -30.1 .. -56.9 193 -12.3 - 5 -27.8 49 -36.4 52 -10.5 31 - 8 . 9 12 -24.2
40
-13.8 -33.9 -16.5 -36.1 -31.3
35 88 - 15 103 67
5.1
- 64
belief that free internal rotation is impeded to some extent by the solvation shell a t the charge center ("chain-stiff enirig effect"). The positive change in entropy for the dissociation of t'he cation acid of tris can be interpreted qualitatively in terms of solvation. The free base is a primary amine structurally similar to t-butylamine. The value of ASo for n-butylammonium ion is -9 j. deg.-l mole-', but that for t-butylam(28) D. H. Everett and W. F. I
