U. S. At. Energy Comm., Rept. NAS-NS 3006 (1960). (16) Pietri, C. E., ANAL.CHEY.34, 1604 (1962). (17) Pietri, C. E., TJ. S. At. Energy Comm., Rept. NBL 170, 5 (1961). (18) Ibid., NBL 177, 22 (1962). (19) Ibid., NBL 188, 3’3, (1962). (20) Rodden, C. J., ed., “Analytical Chemistry of the Manhattan Project,” Natl. Nuclear Energy Series, Div. VIII, Vol. 1, p. 57, McGrsw-Hill, Xew York, 1950. (21) Soklina, L. P., Gel’man, A. D.,
Russian J . Inorg. Chem. 5 , 487 (1960) (Engl. trans. by The Chemical Society). (22) Staritzky, E., ANAL.CHEX.28, 2021
(1956). (23) Staritzky, E., Truitt, -4. L., “The Actinide Elements,” Xatl. Tuclear Energy Series, Div. IV, Vol. 14A, p. 813, McGraw-Hill, New York, 1954. (24) Stokes, R. H., Robinson, R. A , , I n d . Eng. Chem. 41, 2013 (1949). (25) Vogel, A. L:, “Textbook of Quantitative Inorganic Analysis,” 2nd ed., p. 250, Longmans, Green, London, 1951.
(26) Ibad., p. 304. (27) Waterbury, G. R., Douglass, R. XI., Metz, C. F., ANAL.CHERI.33, 1018 (1961). (28) Zachariasen, IT. H., Acta Crust. 1, 268 (1948). RECEIVEDfor review October 22, 1963. Accepted Mav 22, 1963. Work done under AEC Contract AT(29-1)-1106. Presented in part at the Sixth Conference on Analytical Chemistry in Nuclear Reartor Technology, Gatlinburg, Tenn., Oct. 9-11, 1062.
Acid-Base Equilibria in Tertiary Butyl Alcohol LELAND MARPLE and JAMES S. FRITZ Institute for Atomic Research and Department of Chemistry, Iowa State University, Ames, Iowa
b The dissociation of acids in tertiary butyl alcohol has been studied b y potentiometric, spectrophotometric, and conductimetric methods. Values for the over-all dissociation of perchloric and picric acids arid several tetrabutylammonium salts were estimated by the Fuoss-Kraus -reatment of conductance data. Potentiometric studies were carried out (at constant ionic strength to minimize activity coefficient variations. An acidity scale was established from potentiometric measurements a t a glas,s electrode and conductance values of dissociation constants. A method was developed for the evaluation of the over-all dissociation constant of weak acids using potentiometric data for hydrogen ion activities and conductance data for the corresponding anion activities. Over-all dissociation constants are reported for perchloric acid, picric acid, 2,4-dinitrophenol, and benzoic acid. Apparent dissociation constants from potentiometric measurements a t a constant ionic strength were determined for hydrotiromic, nitric, hydrochloric, picric, and p-toluenesulfonic acids.
T
ERTIARY BUTYL ALCOHOL has been shown to be a c r y useful solvent for the titration of weak acids with tetrabutylanimoniuni hydroxide (14). This solvent is espwially useful for differentiating titrations involving carboxylic acids and phenols because of the flat slope in the buffer region of the titration curve. I n solvents such as acetone, acetonitrile, and pyridine, the titration curves have 2, steep slope in the buffered region, owilig to tJhe interniolecular association of the acid anion with the free acid (4, 10, 16, 17). Evidently, this association is not appreciable in tertiary butyl alcohol.
Because of its excellent solvent characteristics, fundamental information on acid-base equilibria would be very useful. Taking into account previous investigations of acid-base equilibria in alcoholic solvents ( I , 2, 11-13, 15) and solvents of low dielectric constant (6, a),we felt that the main reactions in\ olved in the dissociation of an acid HX are: HX 8 H+X- (ion-pair formation); H+X- e H + X- (ionpair dissociation). The corresponding equilibrium constants are: K,= ( H + X X-)/(HX); K,j = (H+)(X-)/ (H+X-). The formation of ion pairs in tertiary butyl alcohol is undoubtedly significant (e), but probably not extensive. The over-all dissociation of strong electrolytes in dilute solutions (10-3M to 10-5M) was expected to be large on the basis of titration data. Since i t is convenient to interpret potentiometric data in terms of the over-all dissociation of a species, we adopted the use of the over-all constant for our work. This constant is defined (9) for a n acid as K H X = (H+)(X-)j (HX) (H+X-). I n the case of very low dissociation of the solute, (HX) (H+X-) will be very nearly equal to CEX (CHXis the analytical concentration of solute). T h r plan of research was to determine KH\ for 1-arious acids in trrtiary butyl alcohol by potrntiomrtric, bpectroor conductometric l)hotometric, methods. K e nerc able to apply the method of Fuoss and Kraus (5) in the determination of dissociation conitants from conductance data. I’nfortunately, conductance measurements for solutions of weak acids could not be obtained because the solutions were not sufficiently conductive. Potentiometric measurement was at first believed to be the best method for evaluation of dissociation constantb of weak acids. However, K H X values
+
+
+
varied with CHX unless a fairly high (lO-*M) concentration of tetrabutylammonium perchlorate (Bu4SC104) was added to keep the ionic strength constant. This was a n indication that the activity coefficients of the ionic species are markedly dependent upon the ionic strength. Subsequent analysis of conductance data did show that activity coefficients varied even at very low (10-5AU)concentrations of solute. While the addition of a large amount of Bu4NC104 does keep the activity coefficients constant during the potentiometric measurement of acidity of a weak acid, it complicates the simple equilibrium of HX as shown below
+
HX*H+ XTJ ClOi- TJ BuiK HClOi Bu4SX
(11
+
(For h p l i c i t y , ion-pair formi of solutes mill be omitted from all subsequent discussion.) 4 modified constant, K’Rx, can be applied to this equilibrium K‘HX= { [H+] (HClOa)) X { fX-1 (BurNX)J/(HX) (2)
+
+
Here, [H I] is the actual concentration of hydrogen ions (solvated with water) in solution (and not the activity). For a solution of HX in excess 13uciYC104,thr. expression for K”X bcromcb KlHX = [ [H+] (HC10,) ] ?, (HX). Values of the quantity ([H’j (HCIOJ) arc determined from c.m.f. mcawrcmeiitb by reference to the concentration-e.m.f. curve for perchloric acid. K”x may alao be evaluated from spectral measurements of the quantity { [X-] (BUISX) } . Another expression for the over-all constant KHy can be obtained by substitution of the equations IH+l = ( W + I (HClOa)l KHCQI/IKacio, ( S t H + ) (ClOi-)l ( 3 )
+
+
+
+
VOL. 35,
NO. 9, AUGUST
+
1963
1223
~~
~~
Table 1.
Constants for Conductance Curves for Solutes in Tertiary Butyl Alcohol Solute x, T O C. P Ly 0 KHX 1.48 1 . 1 4 x 10-4 9.62 122 HClO? 22 26.4 1.00 x 10-4 66.5 4.08 8 26.5 9.62 IlrNPl 3.26 8 . 2 6 X 10-5 9.62 74 10 26.0 RdNDNP 9.86 X loqB 65.5 4.08 8 26.0 9.62 R&BZ 2.50 8.73 X 9.62 86 13 26.6 IPi 1.92 5 . 7 0 X lod6 9.70 102 17 25.2 R47C101
RJ Br
17
9.62
26.0
+
102
1.02
4.34
x
10-6
terials. All tetrabutylammonium salts except the perchlorate, bromide. and iodide were prepared from carbonatefree tetrabutylammonium hydroxide. (which hold when the amount of added Tetrabutylammonium picrate, 2,4-dinitrophenolate, and perchlorate were tetrabutylammonium perchlorate is recrystallized from water-methanol large compared to the amount of acid present) into the expression for KHX. solutions. Water was removed from the dinitrophenolate by azeotropic disThe terms in parentheses are activities tillation with benzene. The picrate and the symbols f,H+ and f * X and perchlorate salt. were dried a t are the incan ion activity coefficients of room temperature. Water v a s evapHfand X- that we have used to aporated from the benzoate salt at a proximate the individual activity coefpressure of 2 to 3 mm. Hg until the ficients. It is assumed that the activity solution crystallized. The bromide (Southwestern Analytical Chemicals) coefficients of neutral molecules is equal and iodide salts (Rymark Laboratories) to the molar concentration--e.g., were w e d without further purification (HCIO1) = [HClO,]. The resulting or drying. expression for the over-all dissociation The potential variation with acid constant concentration for strong acids was ohtained in the following way: the solid K1rx = or liquid sample was added to 50.0 {[I%+] ______ (HCIO4)J 1 [X-1 (BurNX)) . ml. of 0.00974.18 BQNCIOI in tertiary butyl alcohol in the cell compartment. [Details of the reference electrode and salt bridge system were given in a previous paper (IC).] After 20 to 30 minutes’ stirring, a potential measurem:y be separated into tu70 parts, ment was made using a Beckman K EX and K”Hx. The K’HXpart is Model G p H meter. Exactly 25 ml. given by Equation 2. The other part of solution was withdrawn, and 25 ml. K’IHX= of fresh 0.00974M Bu~KCIOIwas added. After 10 to 15 minutes’ equilibration, Z < ~ C I O J C R ~ ~ NHX +) ( ~ (f,X * -)/ { ZCBCIO, the potential was measured again. I n (f,H+) ( C U - ) I ( K B ~ , N x most cases, the experiments were per(fix-)(BurY+)I ( 6 ) formed at room temperature. The dilution process was continued until the contains constants or constant terms acid concentration was approximately only. I n order to calculate the over-all 10-6JI. Sormally, equilibration for 5 constant from potentiometric measuret o 10 minutes was sufficient to obtain ments, it is necessary then to know, or a constant potential reading after a have estimates of, KBu4~Clo4,KH~IO,, dilution was made. Potential drift did K B u q Yand ~ , the activity coefficients of occur upon prolonged equilibration in H+ and X-. some cases, but it was on the order of 2 I n the work reported, values for to 3 mv. over a period of several hours. The reproducibility of the electrode KIHXfor a number of normally strong system is discussed elsewhere (14). acids, and values for the over-all conTetrabutylammonium iodide, brostant for picric acid and 2,4-dinitromide, or perchlorate was used t o mainphenol were determined by a comtain constant ionic strength in the exbination of conductance and potentioperiments involving weak acids. The metric measurements. The constant, solubility of the bromide salt is greater K ’ l I ~for , picric acid was determined by than t h a t of the other salts, and thus it spectrophotometric measurements and is the best to use a t the higher ionic compared to the value obtained by strengths. The procedure used for the measurement of the acidity of the weak potentiometric measurements. acids was the same as that used for the strong acids, except in the cases where EXPERIMENTAL actual titrations were performed. Sulution- of pert*lilorics,nitric, hydroConductance measurements were (.liloi.ic., 11) c l r u b ~ ~ ~ r nand i c , bulfuric acids made with an Industrial Instruments, were prepared from commercially availTnc., Conductivity Bridge Nodel R C : ~ 1 1 1 ~ 1(wnr(~iitrat(~(1 aclueoua wlutiun,, I6 132 U t 1000 cJcleY. ‘I’he elcctrodez other acid solutions were prepared were platinum black and approximately from Eastman White Label grade ma1 sq. cm. in area. A cell constant of [X-]
([X-] (BucXX))K B “ ~ Y :( XK/ B ~ ~ N x (.f+X-) (BurN+)I (4) =
+
+
+
+
1224
ANALYTICAL CHEMISTRY
+
0.104 was determined from the conductance of a 0.0100M KCl solution. The temperature during the measurementswas held constant to within 0.2’ C. Dilutions were made by removing 50.0 ml. from exactly 75.0 ml. of solution, and replacing the amount taken out with pure tertiary butyl alcohol. h Cary Model 14 spectrophotometer was used for the analysis of picric acid. Solutions of tetrabutylammonium pcrchlorate were used for referenee samples. Silica cells were used throughout. Conductance of Solutes in Tertiary Butyl Alcohol. Although the dielectric constant of tertiary butyl alcohol is relatively low (11.5 at 26’ C.) we assumed that the Fuocs-Kraus (5) method for the determination of dissociation constants would be applicable. Conductance measurements were obtained for solutions of perchloric and picric acids, and several tetrabiitylammonium salts. Preliminary values of the cquivalent conductances a t infinite dilution were obtained by extrapolation of the A0 2’s. CQ2curves. Values of
+
a =
8.18 X ~ O % O / ( D T ) ~82/r7(L)7’)1’1 ’~
6
(8aSe2/1000DkT)1/Za
=
w r e calculated using a dielectric constant of 11.5 and a viscosity of 0.0425 poise. The ionic radius, a, used in the calculation of the 6 correction terms was calculated from the Stokes-Einstein equation using one half the equivalent conductance at infinite dilution for the equiuilent conductance of an ion. Plots of fC1’z us. X1l2, where X = (1 - -y)/-y2, were linear in every case d i e n the concentration of t,he solutionr 1va.c in the range of 5 X to 5 X 1O-jM. h summary of the final valucs for the equivalent conductance at infinite dilution that give lines that intercept the origin is given in Table I. Equilibrium constants evaluated from the slope of the fC1’2 us. X1!2plots are alw given in Table 1. Qualitatively, the dissociation constants are in the order of magnit’ude espected. The fact that perchloric acid in a stronger arid than picric is in agreement with the behai-ior of these acids in other nonaqueous system.. We speculated that for the tetrabutylammonium salts the greater the charge distribution of the anion formed by dissociation. the greater would be the extent of diqsociatioii. The data presented in Table I seem to bear o u t tlic validity of this speculation. Activity coefficient,s were e;tirnnt,cd from plots of fC”* us. C1’2, which were constructed from conductance data. Since we were interested in activit,y coefficierits of species in the presence of a large amount of tetrabut8ylanimoniuni perclilorate, we evaluated the activity coefficicntr a t C1’2 = ( B L I , X C ~ O , ) ~ / ~ . The error involvcd in tbiq rnetliod shoiild not I)c t,oo Iargca (i\viiig to t l i c siitiihity of tlic degree of diasociatiuri of iiiort of tlie solutes.
Potentiometric Determination of Dissociation Constants. T h e dissociation of perchloric acids was studied first because i t was t h e strongest of t h e acids available for examination. I'otcntiitls a t t h e glaslj electrode n-ere obtained as a function of €IC104 content at a constant concentration of ~u,?iC104. The water :ontent, 0.0257,, of the solutions was constant at the amount of water in the solvent. Figure 1 shows the plot of log CHCIO, 1;s. e.ni.f. As was espected, the curve showed a linear portion at the very low concentrations of acid. Although the slope of the linear por1,ion of the curve is 60 mv., no inference can he made on the estent of dissociation of HClO4 owing to the presence of the large concentration of Ku4SC101. The amount of undisqociated HCIO4 in solutions can be evrtluated from the dissociation constants of HC104 and Bu4NC1o4. Thus, me calculate that the ratio (H+)/(HC104) = KECIO,/ (Clod-) is only 0.484. Using f*H+ = 0.416 evaluated a t C1i2 = 0.00974.11, the calculated H+ activity is equal to 0.224 CxcIO,. This aclivity, combined with the potential for a 10-4.11 HClOe solution leads to a v d u e of 40.610 volt us. the S.C.E. reference for the standard HJH + potential. This value is used in subsequent calculations of H+ activity since the same electrode was used throughout this study. The dissociation of p-toluenesulfonic, hydrobromic, nitric, h:rdrochloric, and picric acids was also studied in perchlorate media. T h e potential measurements as a function of acid content are shown in Figure 1 I n each case, there is a greater curvziture t o the line a t the higher concen1,ration of acid, than for HCIOP. The curvat.ure is due mainly to the incomp.'ete dissociation of the acids. --Issuming t h a t the change in acid concentration from 10-sJl to 10-4M has little effect on the dissociation of the acid by virtue of changes of activity coefficients (this becomes valid as the strength of the acid decreases and the ionic strength is determined b y the salt content) and the junction potentials are constant] cine can use the potentiomctric data tc calculate constants of the type k"=::. Here, { [H+] (HC104)1 , is evaluated b y reference to the esperimentally determined concentration-e.1n.f. curve (curve A', Figure 1) for perchloric acid. [For perchloric acid, Caclo, = [E[+] (HClOI).] A summary of the values obtained for these constants is given in Table 11. -1 test of the validity of the espression for K'iIs was made by calculating t.he ratio [ [ H T ] (HC:104)1 2/(HC1) at several concentrations of HC'l. Values of this ratio are giver. in Table 111. The constants so calcuhted are reasonably constant and do not show any distinct trend. We a.c:il)e what variation there i+ to the diffixlty of making potential measurements accurate to within -2 t o 3 inv. The constants of the type K I R K may also be obtained from s1)ectral measureiiwnts. l>or I ) I I ~ ~ I I ) S Cof~ coniparis(1~1, the spcctrul \ d u e of was obtained from absorption :ipectra of picric
+
+
+
I
10-61 t
200
/
I
I + 300
c250
I + 350
+ 400
E M F , MILLIVOLTS VS S C E
Figure 1 .
Acidity of strong acids in tertiary butanol
Ionic strength maintained b y addition of 0.00974M tetrabutylammonium perchlorate
A. 6. C.
D. E. F.
Perchloric acid Picric acid Hydrobromic acid p-Toluenesulfonic acid Hydrochloric acid Nitric acid
acid in 0.0097431 BurSClO4. T h e quantity { [Pi-] (BurXPi) I where Pi- is the picrate ion concentration, was calculated from the absorption at 425 mp. The spectrum of pure picrate waq obtained by the addition of a slight excess of Bu4NOH. Picric acid absorption is very slight at this wavelength. The value obtained, 2.16 X 10-4, is remarkably close to the e.m.f. The agreement value of 2.22 x is particularly good in view of the 5 to 10% uncertainty of both values. The over-all dissociation constant for picric acid was estimated by calculation of the constant KNBp,, Mean-ion activity coefficients for hydrogen ion and picrate ion were obtained from conductance measurements of perchloric acid and BurKPi solutions. Using the values K B u p N p , = 1.00 X K H C ~=O ~ 1.14 X and K B ~ ~ N=C5.70 ~ ~ ,X 10-6 gives K'lHpl= 5.0 X Thus, the over-all constant K E P I is 1.1 .X 10-5. This is in good agreement with
+
Table 111.
the conductance value of 8.73 X 10 fi, considering the number of factor3 involved in the calculation. If i t is assumed that tlic activity coefficients of c104- and 13uaS+ are constant with small changes in ionic strength] then the change in K'RP, should be calculable from the change in K"EIPI. Comparison of tlic valvulated
Table II. Dissociation Constants K ' m of Acids from Potentiometric Measurements
0.00074M Bu&CIOa in Tertiary 15utyl
Alcohol Solvent Acid -l(Ig K'i1.u 3.; Hydrobromic 3.65 Picric 3.81 p-Toluenesulfonic 5.0 Hydrochloric 5.1 Kitric
Dissociation Constants K ' H K for Hydrochloric Acid a t Various Concentrations of Acid
0.00074V Bu4XCIO~in Tertiary Butyl Alcohol Solvent F1C)I c,ancri. 1 [H+1 HClOi) K'IiCl 1 . 0 x 10-531 6 . 1 X 10-6M 9 . 5 x lo-'$ 1.8 x 10-6M 1.0 x 10-5 5 . 0 x 10-5.u
+
1.0 5.0
x 10-".11 x 10-dJ1
:.< 1 0 - 5 A f G . S x 10-5.11 2.8
1, 1
1.1
x x
1 0 -,j lo-"
VOL. 35, NO. 9, AUGUST 1963
1225
IO
a IO \ J
w
v)
d I
g b 10-
g a I-
z u W
z
I
0
1
0
10-
I
I
I
0.0
Figure 2. butanol
t
I
I
I
l
l
1
100 EMF, MILLIVOLTS VS. SCE
Acidity of 2,4-dinitrophenol
1
1
1
IO’
200
Figure 3.
in tertiary
l
2,4-Dinitrophenol, no added phenolate salt 0 . 0 0 9 7 4 M BulNC104 6. 2,4-Dinitrophenol, 0.001 OOM Bu4N-2,4-N02 Phen. 0 . 0 0 9 7 4 M Bu4NClOa C. 2,4-Dinitrophenol, 0.001OOM BurN-2,4-N02 Phen.
Tertiary Butyl Alcohol Solvent 9.74 X 10-aM_______ BuaSClOa 2.0 X l0-.aL\IBu,SC104 HClO4 concn.,a HC104 concn.,”
K’HPi
moles/liter
1226
ANALYTICAL CHEMISTRY
x x
I
I
I
I
I
I
l
l
1
Acidity of benzoic acid in tertiary butanol
with added HClOd. Unfortunately, any correction for the spectral shift would be very uncertain. Better results were obtained for the effect of Bu4KC104 on the constant Klgp,. I n this case, there was no evidence of a spectral shift as the amount of perchlorate was varied. The calculated ratio K‘(0.00974A1.f)/K’(0.00200M) w-aq 2.75. The observed ratio of the constants was 2.71. Thus, i t appears that the expression for K”HX is fairly accurate in predicting changes in acidity with electrolyte concentration. The use of potential measurements as a method for determination of dissociation constants of acids considerably weaker than the mineral acids was examined. The measurement of potentiak of acid solutions in perchlorate media i-, in general, unsatisfactory as a result of the iinhuffcrerl naturc of the
0.00 7 . 9 5 x 10-6 1.17 x 1 0 ‘ 8 . 0 0 x 10-6 1.17 5.85 6.0: x 10-5 1.17 x lo-’ Concentration of picric acid is 3.7 X lW5J1.
I
-200 -100 EMF, MILLIVOLTS yll,SCE
Table IV. Dissociation Constants K ’ H s for Picric Acid from Spectral Measurements as a Function of Perchloric Acid and Tetrabutylammonium Perchlorate Content
moles/li ter 0.00
l
Ionic strength maintained by addition of tetrabutylammonium bromide in B, and by tetrabutylammonium perchlorate in C and D A. Benzoic acid, no added perchlorate, 0 . 0 0 9 7 4 M ButBz 6. Benzoic acid, 0.001 OOM Bu4NBz, 0.00974M Bu4NBr C. Benzoic acid, 0.001OOM Bu4NBz, 0 . 0 0 9 7 4 M BurNClO4 D. Bu~NBz,0.01OOM HBz, 0.00974M BuaNClOa
A.
and observed changes in KnHpi was made in two ways. I n one, perchloric acid was added to picric acid in 9.74 X 10-3X Bu4KC104 and the picrate absorption a t 425 mp used to calculate KBBpi. I n the second, the Bu4SC104 content was changed from 2 to 9.74 X 10-3.11. I n the first case, the predicted change of K N H pfor i a change in HC104 concentration from zero to 5.85 X 10-4JP is a 1% increase. Verification of this increase was impossible, since the experimental wror was much larger. It was interesting to note, however, that the ronstants I
