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Ionic equilibria in neutral amphiprotic solvents of low dielectric constant: Buffer solutions
Talanra,Vol. 36, No. 6, pp. 615421, 1989 Printed in Great Britain. All rights remved
0039-9140/89 $3.00+ 0.00 Copyright 0 1989 Pergamon Press plc
IONIC EQUILIBRIA IN NEUTRAL AMPHIPROTIC SOLVENTS OF LOW DIELECTRIC CONSTANT: BUFFER SOLUTIONS ELISABETH BOSCH and
MARLRo&
Departament de Quimica Analitica, Universitat de Barcelona, Barcelona, Spain (Received 10 February 1988. Revised 11 November 1988. Accepted 17 January 1989) Summary-The ionic equilibria in neutral amphiprotic solvents (isopropyl and rerr-butyl alcohols) have been established, and equations to calculate pH values in solutions of acids, bases, salts or their mixtures, developed. The effect, on the dissociation equilibria, of the presence of small quantities of water or other solvents in the bulk solvent used has been taken into account in the proposed equations. On the basis of these equations some buffer solutions have been studied and recommended for electrode standardization. The results, tested by experimental work, show the importance of the incompleteness of dissociation of salts in these solvents, which decreases the pH of acid buffers and increases the buffer capacity.
In recent years the chemistry of non-aqueous solutions has been gaining in significance. Today the theory is developed to such an extent that it is possible with a reasonable degree of certainty to predict the behaviour of a substance in a given solvent, to explain theoretically the processes involved in the titration of different solutes, and to make quantitative calculations.‘” This paper deals with the study of ionic equilibria in some neutral amphiprotic non-aqueous solvents, in particular isopropyl and terf-butyl alcohols. These solvents are similar to water in some respects, the acid-base equilibria being mainly determined by the autoprotolysis of the solvent, and the pH scale by the autoprotolysis constant. Furthermore, the alcohols selected show the lowest autoprotolysis constants among the alcohols available’*9*‘0and thus are the most suitable for differentiating titrations. Moreover, they have the advantages of being commercially available in high purity, and having low volatility. However, isopropyl and tert-butyl alcohols have low dielectric constants, and ion-pair, and in some cases triple-ion formation, must be considered. This implies that salts are incompletely dissociated in these solvents, in contrast to the case for solutions in water, where the dissociation of the salt must rarely be taken into ac.;:ount. Also, the activity coefficients must be considered because of their exponential dependence on the inverse of the dielectric constant. In this work all the equilibria which should be considered in isopropyl and rert -butyl alcohols have been established, and equations to calculate the pH of solutions of an acid, a base, a salt or their mixtures have been developed. Also the effect of water on the autoprotolysis constant and in the dissociation of a base, such as tetrabutylammonium hydroxide, has TAL 3616-A
been considered. The pH values of some buffer solutions, as well as the buffer capacities, have been calculated. THEORY
Autoprotolysis equilibria in a solvent
Since the autoprotolysis of a solvent governs the pH scale of the solvent, it is important to know the value of this constant. The autoprotolysis equilibrium for a protic solvent HS can be written as: 2 SH=
HrS+ + S-;
Km = [HrS+][S-]y2
(1)
where KHs is the autoprotolysis constant and y the mean ionic molar activity coefficient. For simplicity, the activity coefficients of all the ions involved in the equilibria studies in this paper will be considered equal, despite their differences in size. For a pure solvent, equation (1) gives the pH scale, but in practice the observed pH scale is shorter than that expected from pK,, because of the presence of impurities, especially water. Water is dissociated to a greater or lesser extent, and produces H+ and OH- ions which act in the same way as the H+ and S- ions of the solvent. This is very similar to the case for mixtures of solvents with very similar acid-base properties (e.g., water-alcohol mixtures),3 but the water is considered as a solute because of its low concentration. The dissociation equilibrium of the water will be 2Hz0=H30+ KH~ = [Hjo+
+ OH-;
l[OH-Iv */[H201*
where KHp is the self-ionization in the given solvent.
constant
(2)
of water
616
ELISABETH EOXH
Two other equilibria water:
can be considered
H,O + HS=H$+ K a(HzO) =
for the
IfOH- IY~/[H~OI
2H,O + HS=HjO+
(3)
+ S-; (4)
where K(H~o) and &(H~o) are the acidity and basicity constants of water in relation to the main solvent. The apparent autoprotolysis constant of a solvent (KwIv,,,) containing a slight fixed quantity of water, can be defined as: K so~veot = (P-W+ I+
W2S+
HA=
KqHAj= [H+A-]/[HA]
H+A-;
The second is the dissociation
IY~/[H~OI
WP+IF
Solution equilibria of an acid
Because of ion-pair formation, the dissociation of an acid (HA) must be considered in two steps; the first is ionization of the acid:
+ OH-;
W2S+
K b(H20)=
and MARTYRods
H+A-z$H+ &HA) =
(7)
of the ion-pair:
+ A-;
[H+~[A-~Y~/[H+A-~
(8)
H+ being solvated by both HS and H20. Usually an overall acidity constant (K,) is defined as: K, = [H+][A-]y2/([HA]
I)WI + [OH-lb2 (5)
+ [H+A-I)
(9)
or
or K solvent=KHS +
+
(&(H~oJ
+
K, =
W201
KxH~o))
K~,o[H201*.
(6)
This equation shows that the presence of water narrows the pH scale of the solvent, and thus it must be reduced to the minimum. If [H,O] is constant, as in most solvents (usually 0.05-O. l%), Kaolwnt can be considered constant, and used for further calculations in the same way as KHs. Other ions more complex than HJOf or H2S+ can be formed in the medium by solvation of H+ ions with two or more molecules of solvent or water. More complex expressions for Kmlventwould be developed in this case but, in fact, for all of them KsolvEn, is constant if [H,O] is constant. Ksolvsnt is the “autoprotolysis constant” usually determined by potentiometric methods, because these measure the overall [H+]. For simplicity this overall proton concentration will be indicated as [H+], i.e., [H+] = [H,O+] + [H$+ I. If the presence of water is reduced so much that KHS
D
(K(H~oJ
+
Kb(H20))
W201+
KHS
a
K(H~o)
+
&(H20))
[Hz01+ KH~~K@~~~
then K so~vmt=K(H,OJ
•t KwH~oJ)[H~~I
+
KH~o[H~OI~
and the calculated constant is very dependent on the dissociation of water in the solvent, which really provides the acid-base behaviour of this solvent. The same considerations are applicable if another amphiprotic solvent, different from water, is present in low quantity: it also reduces the pH scale of the medium. Thus the presence of water or other solvents, such as the solvents added to the commercial titrants, should be controlled.
+
&HA))
(10)
which is constant for a given acid in a given solvent. For simplicity a concentration constant, K~~id, is defined: K: = 41~ 2
(11)
Because they refer only to dilute acid solutions in amphiprotic solvents with high hydrogen-bond acceptor characteristics,’ the homoconjugation effects are negligible and are not taken into account in this work. Solution equilibria of a salt
Because salts are constituted of ions, only the dissociation equilibrium must be taken into account in an amphiprotic solvent of low dielectric constant. A dissociation equilibrium has to be considered because of ion-pair formation in these solvents. The constant (KA,) can be defined as: B+A-=B+
&o[H2012,
then K&_, = KHs and the calculated constant is the real autoprotolysis constant of the solvent. On the other hand, if
K~(HA)K~(HA)/(~
+ A-;
Ksa,t= [B+~[A-~Y*/[B+A-~
(12)
K:,,, = L,,IY 2
(13)
and also
Solution equilibria of a base
The dissociation equilibrium of a base of type BS (lyate of the base) would be very similar to the equilibrium of a salt: B+S-=B+
+ S-;
&,,s, = [B’IP-ly2/[B+S-1
(14)
However, in non-aqueous titrations tetra-alkylammonium hydroxides are generally used as titrants. If it is considered that the OH- ion acts as the only base present in the medium, then B+OH-GB+
+ OH-; (15)
Buffers in neutral amphiprotic solvents
but OH- ions can also react with the solvent to give S- ions. The following equilibrium must then be taken into account: OH- + SH=
S- + H20;
D-WI is- I/W-i - 1 + &-ISM&~o[H~Ol+ Kq1.120) 1 (16)
= W,,,o,DWl
The last equilibrium must be considered even in the case of a base of type BS, because S- ions can react with any water present in the solvent to given OH- ions. Then, as in the case of the autoprotolysis equilibria, both S- and OH- ions must be considered, and an overall dissociation constant of the base (Kb) can be defined: ~~~~~+l~~~-l+~~~-I~y*
(17)
[B+S-] + [B+OH-] K;, = KJy=
(18)
From equations (14) and (15), however, ]B+S-I = P+lF-IY%,, P+OH-I
and substitution Kb
=
(20)
in equation (17) gives
Kd(as)Kd(ao~)([SI + IOH- I) Kdoo,,[s- 1 + &&OH
-1
+ KqH20j)P-401)
(22)
As in the case of autoprotolysis of the solvent, the presence of water affects the basicity of the base because both OH- and S- can act as a base. If KHS+ &~,o,[H,ol
B KHBWI*
Calculation of pH in amphiprotic solvents Solution of an acid. In a solution of an acid (HA) in an amphiprotic solvent, the pH is ruled by equation (9). As tert-butyl and isopropyl alcohols are solvents with very low Ktiya, values, the solvent contribution to total [H+] can be neglected for all except very dilute solutions, and the mass and charge balances are:
C, = [A-] + [H+A-] + [HA]
+ KqH20jH@l,
then Kb = Kd(ss), but if Ku, + K~(H~oJ[H@~<< K~,oWz01~ + KqH~o#Wlr then Kb = Kdu,oHj. Triple -ion formation
In solvents of low dielectric constant, formation of triple ions by union of an ion-pair (B+A-) with an ion (A- or B+) is observed. The energy of BzA+ and BA; ions differs only according to the size of these ions, and usually no difference can be discerned.” In a solvent such as tert-butyl alcohol the overall constants of triple-ion formation are about 100 or less, and K4, is 10-5-10-4.12~13With constants of this size, the effect of triple ions in the dissociation equilibria of the electrolyte can be neglected for
(23) (24)
where C, is the analytical concentration of the acid. Putting equations (23) and (24) into equations (9) and (1 I), and solving for [H+ 1, gives [H+] = - K;/2 + [(K;/2)* + K;C,]“*
(21)
Multiplying the numerator and denominator of equation (19) by ([H,O+] + [H$+]) and taking into account equations (l)-(6) yields the following equation:
+ &ces&,o[H#
solution concentrations up to approximately lo-*M. In the case of acids and bases, K. and Kb are lower than Kti, ,‘2*‘3and the formation of triple ions can be neglected at any concentration. In a solvent of dielectric constant sufficiently higher than that of tert-butyl alcohol, such as isopropyl alcohol (12.5 and 19.9 respectively at 25”),14 formation of triple ions is very low and should seldom be considered.
[H+] = [A-] (19)
= P+IW-IY~/&~,,,
617
(25)
This equation can be solved by an iterative procedure, starting with y = 1 and computing [H+], which is equal to the ionic strength of the solution; then activity coefficients can be calculated by means of the Debye-Hiickel equation and [H+] and the ionic strength recalculated. The procedure converges quickly to a constant value of [H+]. The pH is calculated from pH = -log[H+]y
(26)
Solution of a base. In this case, both S- and OH-
can act as bases, so C,, = [B+] + [B+S-] + [B+OH-] [B+]=[S-]+[OH-]
(27) (28)
where Cb is the analytical concentration of the base. Putting these two expressions into equations (17) and (18) gives [S-] + [OH-] = - K;/2 + [(K;/2)* + K;C,]“*
(29)
which can be solved in the same way as equation (25), and the pH calculated from equation (5): PH = P&M
+ WP-
I+ [OH- 1)~
(30)
Solution of a salt. Similar expressions to those for an acid or a base can be written for a salt (of analytical concentration Cd,) dissolved in an amphiprotic solvent. The mass and charge balances are:
Ctit = [B+] + [B+A-] [B+] = [A-]
(31) (32)
EL~BETHB~~~H and MARTLRO&
618
and from equations (12) and (13):
[A-l=P+l = - K&J2 + [(K&,,/2)’ + K&,&,J1’2 (33) For computing pH it is assumed that a few ions A- and B+ can react with the solvent to give undissociated acid (HA) and base (BS or BOH). The mass balance for the solvent is then [H+] + [H+A-] + [HA] = [S-l + [OH-] + [B+S-] + [B+OH-]
(34)
(46) (47)
[B+]=[A-]+[S-]+[OH-I
+ [A-I/K:) = ([S-l + [OH-Ml
and substitution
C,=[S-]+[OH-]+[B+S-] Cd, = [A-] + [B+A-]
From equations (9), (1 1), (17) and (18): [H+I(l
ionic strength (which is equal to [A-]) by means of equation (43). The new value of y is calculated by the Debye-Hiickel equation, and [H+] recalculated. The procedure converges quickly to a value of [H+]. The pH can then be calculated by means of equation (26). Solution of a base and its salt. This case is very similar to that of an acid and its salt, but expressions (12) and (17) must be considered. The mass and charge balances are:
+ [B+IIK;)
(35)
(48)
Considering equations (12), (13), (17) and (18) in the same way as for mixture of an acid and its salt gives:
of equation (5) in this gives (K;,--KL,,)([S-l+]OH-D3 (36)
- K&,,Csa,,IWl+
The pH can be computed by means of: PH = f ~Kao,vent - f log
1 + [A-]/K:
(37)
K,= Kb. Solution of an acid and its salt. In a mixture of
an acid and its salt, the equations which have to be considered are (9) and (12). The mass and charge balances are: C, = [H+] + [H+A-] + [HA] C,,,=[B+l+[B+A-I
(38) (39)
[B+] + [H+] = [A-].
(4)
Putting equations (9) and (11) into (38), and (12) and (13) into (39), yields C, - [H+] = [H+][A-I/K’,
Rearranging gives IA-1
(41) and substituting
x ([S-l + [OH-]) + (C,,K;)* =0
(40) into
(42) (42)
Buffered solutions
In a buffer solution of an acid and its salt, [H+] <<[A-] and [H+]c< C,, so equations (43) and (44) can be written as: W-1 = C,K,/W+IY~
PO)
G,,=W-IU +[A-IIKa,t)
(51)
and from these: LH+ly = CaK# + (1 + 4CdKL1t)“~l 2 G,,Y
(43)
C,,=([A-I-[H+I)(l+[A-IIK~,,) Putting (43) into (44) and rearranging the expression
(44
terms yields
PH = PK, + log C,,/C, + log Y (53)
In the same way the following expression can be obtained for buffer solutions of a base and its salt: PH = ~Kro,vsn,- PKb - log
cs.alt/cb -
1%
Y
+ log[l/2 + (l/4 + C,,JK&,d1'21 (54)
KL,tW+13 + (K;’- K:C,- K:K&,, - K&,C,,) [H+12
(K: -
+ (K:K:,,,C, - 2C,K;2)W+l + (C,K:)’ = 0.
(52)
The pH will be equal to:
- lo&l/2 + (l/4 + C,,/K;,)“‘]
=(Ca-W+IKIW+l
(49)
which can be solved for ([S-l + [OH-]) in the same way as equation (45) for [H+]. With ([S-l + [OH-]) known, pH can be computed by equation (30).
(41)
P+I(l + [A-I/K,,,)
[OH-I)’
+ [KiKh,,C, - 2 CdK;)21
1 + [B+]/K;,
As expected, pH is equal to ~PK~,,,, when the acid and the base have the same strength, i.e., when
C,,, =
+ [(K;)2-KG,-K;KI,,
(45)
This equation can be solved by an iterative procedure (e.g., the Newton-Raphson method), taking the starting value y = 1, computing [H+ ] and from this the
Expressions (53) and (54) differ in two terms from the usual expressions used for computing the pH of buffers in water. (1) The term log y is due to the activity coefficients of the acid or base; in water the activity coefficients in dilute solutions tend to unity and this term need not be considered, but in solvents of low dielectric constant, the activity coefficients are less than unity in dilute solutions and their effect on pH should
ButTen in neutral amphiprotic solvents
619
Table 1. Effect of activity coefficients and salt association in alcohols* I c Snh,
M
i-PrGH
10-S 10-4 IO-’ 10-2 10-I
1.0 x 9.9 x 9.5 x 7.9 x 5.3 x
10-J 10-s IO-’ 10-x 10-2
-logy
t -BuOH 9.2 x 6.7 x 3.5 x 1.6 x 7.9 x
i-PrGH
t-BuOH
i-PrGH
t-BuOH
0.01 0.04 0.10 0.23 0.39
0.03 0.06 0.14 0.25 0.41
0.03 0.18 0.45 0.79 1.11
lO-6 lo-5 lo-’ lo-’ lo-’
*For a monoprotic acid or base, taking pK,,,, = 2 for isopropyl alcohol (i-PrGH) or pK,,, = 4 for rert-butyl alcohol (t-BuOH). he considered. Thus, the higher the ionic strength, the bigger the decrease in the pH value for an acid or the increase for a base. (2) The term log[1/2 + (l/4 + C,JK&#] is due to the ionic association of the salt, which favours the dissociation of the acid or the base. If &, is very high, as in water, or C,, very low, this term tends to zero, but for isopropyl and terf-butyI alcohol solutions it should be considered.
As can be seen in Table 1, both terms favour the decrease of pH for an acid or increase for a base. At a given CJC,, ratio, a given acid will seem to be more acidic the higher C,, and the lower K&t are. This can be observed in Table 2, where some equimolar mixtures of acids with their corresponding tetrabutylammonium salts are proposed as buffers in tert-butyl alcohol. The pH values of these mixtures have been calculated from the proposed equation (53) and the pK values of the acids and salts.i3 It can be observed that pH < pK,; the higher C,,, the lower the pH value. The activity coefficient and salt effect terms also modify the buffer capacity. In Fig. 1 the buffer capacity (jI) of acetic acid in tert-butyl alcohol at various pH values is presented (A) together with the buffer capacity calculated by neglecting the activity coefficients and salt effect (B), i.e., using pH = pK, + log C,,JC, instead of equation (53). Both curves are presented for Cd, + C, = lo-‘M. If the activity coefficients and salt effect are neglected the curve is symmetrical and centred at pH = pK, = 14.60, as it would be in water (curve B). If both effects are considered (curve A) the curve is Table 2. Calculated
slightly unsymmetrical, with its maximum near the pH value corresponding to C, = C,, = 5 x lo-‘M @H = 13.58), owing to the change in the salt concentration with pH, which modifies the values of log y and lod l/2 + (l/4 + Cti,/K~#12] and consequently the shape of the curve. The maximum of curve A is higher than the maximum of curve B because the salt dissociation contributes to buffering the solution. The buffer solutions described allow easy electrode standardization, especially in the concentration range 10-3-10-2M, which gives adequate buffer capacity and avoids triple-ion formation. EXPERIMENTAL
Apparatus A Crison Digilab 517 pH-meter was used, with a Radiometer G202B glass electrode, a Radiometer K401 calomel electrode and the salt bridge described previou~ly.‘~ Chemicals Tert-butyl alcohol, Merck, GR grade. The water content was found to be 0.073%, by tlte Karl Fischer method. Tetrabutylammoniumhydroxide, O.lM stock solution in isopropyl alcohol; Carlo Erba, RPE grade. The methyl alcohol content was 8%, determined by gas chromatographic analysis. Acidr. Picric acid, Doesder, AR-ACS grade, vacuum dried. Acetic acid, Carlo Erba, RS grade. Monocbloroacetic acid, Scltarlau. Dichloroacetic acid, Carlo Erba, RPE grade. Trichloroacetic acid, Merck, GR grade. Barbital, Merck, GR grade. Determinationof the standardpotentials The electrode system was standardized by titration of solutions of picric acid (PK, = 5.35) with the tetra-
pH values of buffers in ferr-butyl alcohol
C,,=C,, M 1x 5x 1x 5x 1x
10-2 lo-’ lo-’ 10-4 lo-’
TCAA
DCAA
MCAA
AA
B
7.56 7.70 8.03 8.17 8.46
9.08 9.23 9.56 9.69 9.98
11.03 11.18 11.50 11.63 11.91
13.44 13.58 13.90 14.03 14.29
15.01 15.52 15.84 15.98 16.25
12.30 8.90 10.41 14.60 16.60 PK, 4.62 4.50 4.27 4.40 4.65 P&h TCAA = trichloroacetic acid, DCAA = dichloroacetic acid, MCAA = monocbloroacetic acid, AA = acetic acid, B = barbital.
PH
Fig. 1. (A) Buffer capacity of 10W2Macetic acid in tert-butyl alcohol [calculated by using equation (5311. (B) Buffer capacity of an acid at the same concentration and the same pX, value (14.60) in a solvent of bigb dieleotric constant (calculated by using pH = pK, + log C,,,,/C.).
ELISABETHBOSCHand MARIARosh
620
butylammonium hydroxide solution @Kb = 4.91, p&, = 4.36).‘” The glass electrode was stored in water, then ioaked for 15 min in pure tert-butyl alcohol, rinsed and cleaned before use. The electrode pair was kept in the test solution for half an hour before titration. The potential was measured at 5-min intervals for each point of the titration. Stable and reproducible potentials were usually obtained in 5-10 min. The pH was computed from the promsed equations (37), (45) and (54), by means of the ioiputer program ACETERISO. ” In this program the activity coefficients were calculated by means of the limiting Debye-Hilckel equation, taking A = 8.51 for L = 10.9,” and T = 303.15 K. The standard notentials were 657 mV
in acid medium and -981 mV in basic medium. Procedure
Ten ml of W3-5 x 10m3Msolutions of acids in terr-butyl alcohol were titrated with 0.02M solution of tetrabutylammonium hydroxide (prepared from the stock solution in isopropyl alcohol by dilution with fert -butyl alcohol), with Thymol Blue as indicator. I6 Twenty ml of the same acid solution were exactly half-neutralized with the 0.02M tetrabutylammonium solution, and diluted to 50 ml with tertbutyl alcohol, and the potential of this last solution was measured. Because the m.p. of tert-butyl alcohol is about 25.5”, all measurements were taken in a closed vessel placed in a thermostat at 30 f 0.2”. The vessel was kept in an atmosphere of dried nitrogen saturated with tert-butyl alcohol.
RESULTS
AND DLSCUSSlON
The computation of pK,,,,,, from acid and basic standard potentials in tert-butyl alcohol gives 27.2 i- 0.9 for the 95% confidence limits (10 determinations). A great variety of pK values is given in the literature: Sane” and Kreshkov et aLI give a value of about 22.2. Bykova and PetrovZOpoint out that this value is very low, probably because of the ionization of the water present in the solvent, which, as has been shown in the theoretical part of this paper, can notably decrease the pKsolventvalue. In other work*l these authors verified that removal of the water and methanol increases the pKaolvcntvalue and they obtained a value of 26.8, very close to the one reported here. Kolthoff and Chantoonil” gave a value of 28.5, which was obtained by measuring the proton activity potentiometrically with a hydrogen electrode, and the tert-butanolate activity conductimetrically by means of a solution of potassium tert-butanolate, to which crown-ethers or cryptands were added to complex the potassium ions and increase the solute dissociation. Therefore this result must be considered to be closer to pKHs than to pKW,,,,, (as defined here), which would be lower. The decrease of pKaolventby the presence of other solvents in the medium was tested by standardizing the electrode system with more concentrated solutions of picric acid in tert-butyl alcohol and titrating with 0.1 M tetrabutylammonium hydroxide solution in isopropyl alcohol. The addition of isopropyl alcohol with the titrant does not significantly affect the standard potential in acid medium, but remarkably
Table 3. pH values of buffers in tert-butyl alcohol PH c,, M
Acid TCAA DCAA CAA AA B
increases
1.37 x 5.95 x 6.47 x 7.17 x 8.60 x
Calculated Observed lO-3 10-d lO-4 10-d lO-4
the standard
7.97 9.66 11.58 13.96 15.87
potential
7.99 9.65 11.58 13.91 15.87
in basic
medium
(pK,,,_, of -25.7 was obtained” for N 3 : 1 tert-butyl alcohol: isopropyl alcohol mixtures). These results agree with the studies of Marple and F&s3 who found that the addition of solvents to solutions of acids and bases in tert-butyl alcohol affects solutions of bases very much more than solutions of acids. As the glass electrode measures proton activity, in acid medium the addition of a solvent does directly affect this activity (it can only affect it indirectly by changing the dissociation constants of the acid and salt),” but in basic medium an increase in the concentration of water (or another solvent) increases Kwlvcnt [see equation (6)], whereas K,, is only slightly modified, so [S-l and [OH-] are not very much increased (if the added solvent increases the dielectric constant), but [H + ] increases and less basic potentials are obtained. The theoretical equations developed have been tested by preparing equimolar buffer solutions of barbital, acetic, monochloroacetic, dichloroacetic and trichloroacetic acids and their tetrabutylammonium salts in tert-butyl alcohol. The results presented in Table 3 show good concordance between the pH values calculated by the proposed equation (53) and those obtained experimentally.
REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
I. M. Kolthoff and P. J. Elving (eds.), Treatise on Analytical Chemistry, 2nd Ed., Part I, Vol. 2, Wiley, New York, 1987. J. S. Fritz, Acid-Base Titrations in Nonaqueous Solvents, Allyn and Bacon. Boston. 1973. B. ?r&millon, L.a.quimica en 10s disolventes no acuosos, Bellaterra, Barcelona, 1973. A. P. Kreshkov, Talanta, 1970, 17, 1029. C. Vermesse-Jacquinot, R. Schaal and P. Rumpf, Bull. Sot. Chim. France, 1960, 2003. G. A. Harlow, C. M. Noble and G. E. A. Wyld, Anal. Chem., 1956, 28, 787. J. Hine and M. Hine, J. Am. Chem. Sot., 1952,74,5266. N. A. Izmailov and V. V. Alexandrov, Zh. Fiz. Khim., 1957, 31, 2619. E. P. Serjeant, Potentiometry and Potentiometric Titrations, Wiley, New York, 1984. I. M. Kolthoff and M. K. Chantooni, Anal. Chem., 1979, 51, 1301. R. M. Fuoss and C. A. Kraus, J. Am. Chem. Sot., 1933, 55, 2387. M. K. Chantooni and I. M. Kolthoff, Anal. Chem., 1979, Sl, 133. E. Bosch and M. Rosbs, Talanta, 1989, 36, 627.
Buffers in neutral amphiprotic solvents 14. I. M. Kolthoff and M. K. Chantooni, J. Whys. Chem., 1979, 83, 468. 15. L. W. Marple and J. S. Fritz, Anal. Chem., 1963, 35, 1431. 16. J. Barbosa, E. Bosch and M. Roses, Analyst, 1987, 112, 179. 17. R. C. Weast (ed.), Handbook of Chemistry and Physics, 59th Ed., CRC, Boca Raton, Florida, 1979. 18. H. Sano, Bull. Osaka Ind. Res. Inst., 1959, 10, 121.
621
19. A. P. Kreshkov, N. T. Smolova, N. Aldarova and N. A. Gabidulina, Zh. Analit. Khim., 1971, 26, 2456. 20. L. N. Bykova and S. I. Petrov, J. Anal. Chem. USSR, 1970, 25, 1. 21. I&m, Zh. Analit. Khim., 1972, 27, 1076. 22. M. Roses, Ph.D. Thesis, University of Barcelona, 1986. 23. L. W. Marple and J. S. Fritz, Anal. Chem., 1962, 34, 796. 24. E. Bosch and M. Roses, ibid., 1988, 60, 2008.
0039-9140/89 $3.00+ 0.00 Copyright 0 1989 Pergamon Press plc
IONIC EQUILIBRIA IN NEUTRAL AMPHIPROTIC SOLVENTS OF LOW DIELECTRIC CONSTANT: BUFFER SOLUTIONS ELISABETH BOSCH and
MARLRo&
Departament de Quimica Analitica, Universitat de Barcelona, Barcelona, Spain (Received 10 February 1988. Revised 11 November 1988. Accepted 17 January 1989) Summary-The ionic equilibria in neutral amphiprotic solvents (isopropyl and rerr-butyl alcohols) have been established, and equations to calculate pH values in solutions of acids, bases, salts or their mixtures, developed. The effect, on the dissociation equilibria, of the presence of small quantities of water or other solvents in the bulk solvent used has been taken into account in the proposed equations. On the basis of these equations some buffer solutions have been studied and recommended for electrode standardization. The results, tested by experimental work, show the importance of the incompleteness of dissociation of salts in these solvents, which decreases the pH of acid buffers and increases the buffer capacity.
In recent years the chemistry of non-aqueous solutions has been gaining in significance. Today the theory is developed to such an extent that it is possible with a reasonable degree of certainty to predict the behaviour of a substance in a given solvent, to explain theoretically the processes involved in the titration of different solutes, and to make quantitative calculations.‘” This paper deals with the study of ionic equilibria in some neutral amphiprotic non-aqueous solvents, in particular isopropyl and terf-butyl alcohols. These solvents are similar to water in some respects, the acid-base equilibria being mainly determined by the autoprotolysis of the solvent, and the pH scale by the autoprotolysis constant. Furthermore, the alcohols selected show the lowest autoprotolysis constants among the alcohols available’*9*‘0and thus are the most suitable for differentiating titrations. Moreover, they have the advantages of being commercially available in high purity, and having low volatility. However, isopropyl and tert-butyl alcohols have low dielectric constants, and ion-pair, and in some cases triple-ion formation, must be considered. This implies that salts are incompletely dissociated in these solvents, in contrast to the case for solutions in water, where the dissociation of the salt must rarely be taken into ac.;:ount. Also, the activity coefficients must be considered because of their exponential dependence on the inverse of the dielectric constant. In this work all the equilibria which should be considered in isopropyl and rert -butyl alcohols have been established, and equations to calculate the pH of solutions of an acid, a base, a salt or their mixtures have been developed. Also the effect of water on the autoprotolysis constant and in the dissociation of a base, such as tetrabutylammonium hydroxide, has TAL 3616-A
been considered. The pH values of some buffer solutions, as well as the buffer capacities, have been calculated. THEORY
Autoprotolysis equilibria in a solvent
Since the autoprotolysis of a solvent governs the pH scale of the solvent, it is important to know the value of this constant. The autoprotolysis equilibrium for a protic solvent HS can be written as: 2 SH=
HrS+ + S-;
Km = [HrS+][S-]y2
(1)
where KHs is the autoprotolysis constant and y the mean ionic molar activity coefficient. For simplicity, the activity coefficients of all the ions involved in the equilibria studies in this paper will be considered equal, despite their differences in size. For a pure solvent, equation (1) gives the pH scale, but in practice the observed pH scale is shorter than that expected from pK,, because of the presence of impurities, especially water. Water is dissociated to a greater or lesser extent, and produces H+ and OH- ions which act in the same way as the H+ and S- ions of the solvent. This is very similar to the case for mixtures of solvents with very similar acid-base properties (e.g., water-alcohol mixtures),3 but the water is considered as a solute because of its low concentration. The dissociation equilibrium of the water will be 2Hz0=H30+ KH~ = [Hjo+
+ OH-;
l[OH-Iv */[H201*
where KHp is the self-ionization in the given solvent.
constant
(2)
of water
616
ELISABETH EOXH
Two other equilibria water:
can be considered
H,O + HS=H$+ K a(HzO) =
for the
IfOH- IY~/[H~OI
2H,O + HS=HjO+
(3)
+ S-; (4)
where K(H~o) and &(H~o) are the acidity and basicity constants of water in relation to the main solvent. The apparent autoprotolysis constant of a solvent (KwIv,,,) containing a slight fixed quantity of water, can be defined as: K so~veot = (P-W+ I+
W2S+
HA=
KqHAj= [H+A-]/[HA]
H+A-;
The second is the dissociation
IY~/[H~OI
WP+IF
Solution equilibria of an acid
Because of ion-pair formation, the dissociation of an acid (HA) must be considered in two steps; the first is ionization of the acid:
+ OH-;
W2S+
K b(H20)=
and MARTYRods
H+A-z$H+ &HA) =
(7)
of the ion-pair:
+ A-;
[H+~[A-~Y~/[H+A-~
(8)
H+ being solvated by both HS and H20. Usually an overall acidity constant (K,) is defined as: K, = [H+][A-]y2/([HA]
I)WI + [OH-lb2 (5)
+ [H+A-I)
(9)
or
or K solvent=KHS +
+
(&(H~oJ
+
K, =
W201
KxH~o))
K~,o[H201*.
(6)
This equation shows that the presence of water narrows the pH scale of the solvent, and thus it must be reduced to the minimum. If [H,O] is constant, as in most solvents (usually 0.05-O. l%), Kaolwnt can be considered constant, and used for further calculations in the same way as KHs. Other ions more complex than HJOf or H2S+ can be formed in the medium by solvation of H+ ions with two or more molecules of solvent or water. More complex expressions for Kmlventwould be developed in this case but, in fact, for all of them KsolvEn, is constant if [H,O] is constant. Ksolvsnt is the “autoprotolysis constant” usually determined by potentiometric methods, because these measure the overall [H+]. For simplicity this overall proton concentration will be indicated as [H+], i.e., [H+] = [H,O+] + [H$+ I. If the presence of water is reduced so much that KHS
D
(K(H~oJ
+
Kb(H20))
W201+
KHS
a
K(H~o)
+
&(H20))
[Hz01+ KH~~K@~~~
then K so~vmt=K(H,OJ
•t KwH~oJ)[H~~I
+
KH~o[H~OI~
and the calculated constant is very dependent on the dissociation of water in the solvent, which really provides the acid-base behaviour of this solvent. The same considerations are applicable if another amphiprotic solvent, different from water, is present in low quantity: it also reduces the pH scale of the medium. Thus the presence of water or other solvents, such as the solvents added to the commercial titrants, should be controlled.
+
&HA))
(10)
which is constant for a given acid in a given solvent. For simplicity a concentration constant, K~~id, is defined: K: = 41~ 2
(11)
Because they refer only to dilute acid solutions in amphiprotic solvents with high hydrogen-bond acceptor characteristics,’ the homoconjugation effects are negligible and are not taken into account in this work. Solution equilibria of a salt
Because salts are constituted of ions, only the dissociation equilibrium must be taken into account in an amphiprotic solvent of low dielectric constant. A dissociation equilibrium has to be considered because of ion-pair formation in these solvents. The constant (KA,) can be defined as: B+A-=B+
&o[H2012,
then K&_, = KHs and the calculated constant is the real autoprotolysis constant of the solvent. On the other hand, if
K~(HA)K~(HA)/(~
+ A-;
Ksa,t= [B+~[A-~Y*/[B+A-~
(12)
K:,,, = L,,IY 2
(13)
and also
Solution equilibria of a base
The dissociation equilibrium of a base of type BS (lyate of the base) would be very similar to the equilibrium of a salt: B+S-=B+
+ S-;
&,,s, = [B’IP-ly2/[B+S-1
(14)
However, in non-aqueous titrations tetra-alkylammonium hydroxides are generally used as titrants. If it is considered that the OH- ion acts as the only base present in the medium, then B+OH-GB+
+ OH-; (15)
Buffers in neutral amphiprotic solvents
but OH- ions can also react with the solvent to give S- ions. The following equilibrium must then be taken into account: OH- + SH=
S- + H20;
D-WI is- I/W-i - 1 + &-ISM&~o[H~Ol+ Kq1.120) 1 (16)
= W,,,o,DWl
The last equilibrium must be considered even in the case of a base of type BS, because S- ions can react with any water present in the solvent to given OH- ions. Then, as in the case of the autoprotolysis equilibria, both S- and OH- ions must be considered, and an overall dissociation constant of the base (Kb) can be defined: ~~~~~+l~~~-l+~~~-I~y*
(17)
[B+S-] + [B+OH-] K;, = KJy=
(18)
From equations (14) and (15), however, ]B+S-I = P+lF-IY%,, P+OH-I
and substitution Kb
=
(20)
in equation (17) gives
Kd(as)Kd(ao~)([SI + IOH- I) Kdoo,,[s- 1 + &&OH
-1
+ KqH20j)P-401)
(22)
As in the case of autoprotolysis of the solvent, the presence of water affects the basicity of the base because both OH- and S- can act as a base. If KHS+ &~,o,[H,ol
B KHBWI*
Calculation of pH in amphiprotic solvents Solution of an acid. In a solution of an acid (HA) in an amphiprotic solvent, the pH is ruled by equation (9). As tert-butyl and isopropyl alcohols are solvents with very low Ktiya, values, the solvent contribution to total [H+] can be neglected for all except very dilute solutions, and the mass and charge balances are:
C, = [A-] + [H+A-] + [HA]
+ KqH20jH@l,
then Kb = Kd(ss), but if Ku, + K~(H~oJ[H@~<< K~,oWz01~ + KqH~o#Wlr then Kb = Kdu,oHj. Triple -ion formation
In solvents of low dielectric constant, formation of triple ions by union of an ion-pair (B+A-) with an ion (A- or B+) is observed. The energy of BzA+ and BA; ions differs only according to the size of these ions, and usually no difference can be discerned.” In a solvent such as tert-butyl alcohol the overall constants of triple-ion formation are about 100 or less, and K4, is 10-5-10-4.12~13With constants of this size, the effect of triple ions in the dissociation equilibria of the electrolyte can be neglected for
(23) (24)
where C, is the analytical concentration of the acid. Putting equations (23) and (24) into equations (9) and (1 I), and solving for [H+ 1, gives [H+] = - K;/2 + [(K;/2)* + K;C,]“*
(21)
Multiplying the numerator and denominator of equation (19) by ([H,O+] + [H$+]) and taking into account equations (l)-(6) yields the following equation:
+ &ces&,o[H#
solution concentrations up to approximately lo-*M. In the case of acids and bases, K. and Kb are lower than Kti, ,‘2*‘3and the formation of triple ions can be neglected at any concentration. In a solvent of dielectric constant sufficiently higher than that of tert-butyl alcohol, such as isopropyl alcohol (12.5 and 19.9 respectively at 25”),14 formation of triple ions is very low and should seldom be considered.
[H+] = [A-] (19)
= P+IW-IY~/&~,,,
617
(25)
This equation can be solved by an iterative procedure, starting with y = 1 and computing [H+], which is equal to the ionic strength of the solution; then activity coefficients can be calculated by means of the Debye-Hiickel equation and [H+] and the ionic strength recalculated. The procedure converges quickly to a constant value of [H+]. The pH is calculated from pH = -log[H+]y
(26)
Solution of a base. In this case, both S- and OH-
can act as bases, so C,, = [B+] + [B+S-] + [B+OH-] [B+]=[S-]+[OH-]
(27) (28)
where Cb is the analytical concentration of the base. Putting these two expressions into equations (17) and (18) gives [S-] + [OH-] = - K;/2 + [(K;/2)* + K;C,]“*
(29)
which can be solved in the same way as equation (25), and the pH calculated from equation (5): PH = P&M
+ WP-
I+ [OH- 1)~
(30)
Solution of a salt. Similar expressions to those for an acid or a base can be written for a salt (of analytical concentration Cd,) dissolved in an amphiprotic solvent. The mass and charge balances are:
Ctit = [B+] + [B+A-] [B+] = [A-]
(31) (32)
EL~BETHB~~~H and MARTLRO&
618
and from equations (12) and (13):
[A-l=P+l = - K&J2 + [(K&,,/2)’ + K&,&,J1’2 (33) For computing pH it is assumed that a few ions A- and B+ can react with the solvent to give undissociated acid (HA) and base (BS or BOH). The mass balance for the solvent is then [H+] + [H+A-] + [HA] = [S-l + [OH-] + [B+S-] + [B+OH-]
(34)
(46) (47)
[B+]=[A-]+[S-]+[OH-I
+ [A-I/K:) = ([S-l + [OH-Ml
and substitution
C,=[S-]+[OH-]+[B+S-] Cd, = [A-] + [B+A-]
From equations (9), (1 1), (17) and (18): [H+I(l
ionic strength (which is equal to [A-]) by means of equation (43). The new value of y is calculated by the Debye-Hiickel equation, and [H+] recalculated. The procedure converges quickly to a value of [H+]. The pH can then be calculated by means of equation (26). Solution of a base and its salt. This case is very similar to that of an acid and its salt, but expressions (12) and (17) must be considered. The mass and charge balances are:
+ [B+IIK;)
(35)
(48)
Considering equations (12), (13), (17) and (18) in the same way as for mixture of an acid and its salt gives:
of equation (5) in this gives (K;,--KL,,)([S-l+]OH-D3 (36)
- K&,,Csa,,IWl+
The pH can be computed by means of: PH = f ~Kao,vent - f log
1 + [A-]/K:
(37)
K,= Kb. Solution of an acid and its salt. In a mixture of
an acid and its salt, the equations which have to be considered are (9) and (12). The mass and charge balances are: C, = [H+] + [H+A-] + [HA] C,,,=[B+l+[B+A-I
(38) (39)
[B+] + [H+] = [A-].
(4)
Putting equations (9) and (11) into (38), and (12) and (13) into (39), yields C, - [H+] = [H+][A-I/K’,
Rearranging gives IA-1
(41) and substituting
x ([S-l + [OH-]) + (C,,K;)* =0
(40) into
(42) (42)
Buffered solutions
In a buffer solution of an acid and its salt, [H+] <<[A-] and [H+]c< C,, so equations (43) and (44) can be written as: W-1 = C,K,/W+IY~
PO)
G,,=W-IU +[A-IIKa,t)
(51)
and from these: LH+ly = CaK# + (1 + 4CdKL1t)“~l 2 G,,Y
(43)
C,,=([A-I-[H+I)(l+[A-IIK~,,) Putting (43) into (44) and rearranging the expression
(44
terms yields
PH = PK, + log C,,/C, + log Y (53)
In the same way the following expression can be obtained for buffer solutions of a base and its salt: PH = ~Kro,vsn,- PKb - log
cs.alt/cb -
1%
Y
+ log[l/2 + (l/4 + C,,JK&,d1'21 (54)
KL,tW+13 + (K;’- K:C,- K:K&,, - K&,C,,) [H+12
(K: -
+ (K:K:,,,C, - 2C,K;2)W+l + (C,K:)’ = 0.
(52)
The pH will be equal to:
- lo&l/2 + (l/4 + C,,/K;,)“‘]
=(Ca-W+IKIW+l
(49)
which can be solved for ([S-l + [OH-]) in the same way as equation (45) for [H+]. With ([S-l + [OH-]) known, pH can be computed by equation (30).
(41)
P+I(l + [A-I/K,,,)
[OH-I)’
+ [KiKh,,C, - 2 CdK;)21
1 + [B+]/K;,
As expected, pH is equal to ~PK~,,,, when the acid and the base have the same strength, i.e., when
C,,, =
+ [(K;)2-KG,-K;KI,,
(45)
This equation can be solved by an iterative procedure (e.g., the Newton-Raphson method), taking the starting value y = 1, computing [H+ ] and from this the
Expressions (53) and (54) differ in two terms from the usual expressions used for computing the pH of buffers in water. (1) The term log y is due to the activity coefficients of the acid or base; in water the activity coefficients in dilute solutions tend to unity and this term need not be considered, but in solvents of low dielectric constant, the activity coefficients are less than unity in dilute solutions and their effect on pH should
ButTen in neutral amphiprotic solvents
619
Table 1. Effect of activity coefficients and salt association in alcohols* I c Snh,
M
i-PrGH
10-S 10-4 IO-’ 10-2 10-I
1.0 x 9.9 x 9.5 x 7.9 x 5.3 x
10-J 10-s IO-’ 10-x 10-2
-logy
t -BuOH 9.2 x 6.7 x 3.5 x 1.6 x 7.9 x
i-PrGH
t-BuOH
i-PrGH
t-BuOH
0.01 0.04 0.10 0.23 0.39
0.03 0.06 0.14 0.25 0.41
0.03 0.18 0.45 0.79 1.11
lO-6 lo-5 lo-’ lo-’ lo-’
*For a monoprotic acid or base, taking pK,,,, = 2 for isopropyl alcohol (i-PrGH) or pK,,, = 4 for rert-butyl alcohol (t-BuOH). he considered. Thus, the higher the ionic strength, the bigger the decrease in the pH value for an acid or the increase for a base. (2) The term log[1/2 + (l/4 + C,JK&#] is due to the ionic association of the salt, which favours the dissociation of the acid or the base. If &, is very high, as in water, or C,, very low, this term tends to zero, but for isopropyl and terf-butyI alcohol solutions it should be considered.
As can be seen in Table 1, both terms favour the decrease of pH for an acid or increase for a base. At a given CJC,, ratio, a given acid will seem to be more acidic the higher C,, and the lower K&t are. This can be observed in Table 2, where some equimolar mixtures of acids with their corresponding tetrabutylammonium salts are proposed as buffers in tert-butyl alcohol. The pH values of these mixtures have been calculated from the proposed equation (53) and the pK values of the acids and salts.i3 It can be observed that pH < pK,; the higher C,,, the lower the pH value. The activity coefficient and salt effect terms also modify the buffer capacity. In Fig. 1 the buffer capacity (jI) of acetic acid in tert-butyl alcohol at various pH values is presented (A) together with the buffer capacity calculated by neglecting the activity coefficients and salt effect (B), i.e., using pH = pK, + log C,,JC, instead of equation (53). Both curves are presented for Cd, + C, = lo-‘M. If the activity coefficients and salt effect are neglected the curve is symmetrical and centred at pH = pK, = 14.60, as it would be in water (curve B). If both effects are considered (curve A) the curve is Table 2. Calculated
slightly unsymmetrical, with its maximum near the pH value corresponding to C, = C,, = 5 x lo-‘M @H = 13.58), owing to the change in the salt concentration with pH, which modifies the values of log y and lod l/2 + (l/4 + Cti,/K~#12] and consequently the shape of the curve. The maximum of curve A is higher than the maximum of curve B because the salt dissociation contributes to buffering the solution. The buffer solutions described allow easy electrode standardization, especially in the concentration range 10-3-10-2M, which gives adequate buffer capacity and avoids triple-ion formation. EXPERIMENTAL
Apparatus A Crison Digilab 517 pH-meter was used, with a Radiometer G202B glass electrode, a Radiometer K401 calomel electrode and the salt bridge described previou~ly.‘~ Chemicals Tert-butyl alcohol, Merck, GR grade. The water content was found to be 0.073%, by tlte Karl Fischer method. Tetrabutylammoniumhydroxide, O.lM stock solution in isopropyl alcohol; Carlo Erba, RPE grade. The methyl alcohol content was 8%, determined by gas chromatographic analysis. Acidr. Picric acid, Doesder, AR-ACS grade, vacuum dried. Acetic acid, Carlo Erba, RS grade. Monocbloroacetic acid, Scltarlau. Dichloroacetic acid, Carlo Erba, RPE grade. Trichloroacetic acid, Merck, GR grade. Barbital, Merck, GR grade. Determinationof the standardpotentials The electrode system was standardized by titration of solutions of picric acid (PK, = 5.35) with the tetra-
pH values of buffers in ferr-butyl alcohol
C,,=C,, M 1x 5x 1x 5x 1x
10-2 lo-’ lo-’ 10-4 lo-’
TCAA
DCAA
MCAA
AA
B
7.56 7.70 8.03 8.17 8.46
9.08 9.23 9.56 9.69 9.98
11.03 11.18 11.50 11.63 11.91
13.44 13.58 13.90 14.03 14.29
15.01 15.52 15.84 15.98 16.25
12.30 8.90 10.41 14.60 16.60 PK, 4.62 4.50 4.27 4.40 4.65 P&h TCAA = trichloroacetic acid, DCAA = dichloroacetic acid, MCAA = monocbloroacetic acid, AA = acetic acid, B = barbital.
PH
Fig. 1. (A) Buffer capacity of 10W2Macetic acid in tert-butyl alcohol [calculated by using equation (5311. (B) Buffer capacity of an acid at the same concentration and the same pX, value (14.60) in a solvent of bigb dieleotric constant (calculated by using pH = pK, + log C,,,,/C.).
ELISABETHBOSCHand MARIARosh
620
butylammonium hydroxide solution @Kb = 4.91, p&, = 4.36).‘” The glass electrode was stored in water, then ioaked for 15 min in pure tert-butyl alcohol, rinsed and cleaned before use. The electrode pair was kept in the test solution for half an hour before titration. The potential was measured at 5-min intervals for each point of the titration. Stable and reproducible potentials were usually obtained in 5-10 min. The pH was computed from the promsed equations (37), (45) and (54), by means of the ioiputer program ACETERISO. ” In this program the activity coefficients were calculated by means of the limiting Debye-Hilckel equation, taking A = 8.51 for L = 10.9,” and T = 303.15 K. The standard notentials were 657 mV
in acid medium and -981 mV in basic medium. Procedure
Ten ml of W3-5 x 10m3Msolutions of acids in terr-butyl alcohol were titrated with 0.02M solution of tetrabutylammonium hydroxide (prepared from the stock solution in isopropyl alcohol by dilution with fert -butyl alcohol), with Thymol Blue as indicator. I6 Twenty ml of the same acid solution were exactly half-neutralized with the 0.02M tetrabutylammonium solution, and diluted to 50 ml with tertbutyl alcohol, and the potential of this last solution was measured. Because the m.p. of tert-butyl alcohol is about 25.5”, all measurements were taken in a closed vessel placed in a thermostat at 30 f 0.2”. The vessel was kept in an atmosphere of dried nitrogen saturated with tert-butyl alcohol.
RESULTS
AND DLSCUSSlON
The computation of pK,,,,,, from acid and basic standard potentials in tert-butyl alcohol gives 27.2 i- 0.9 for the 95% confidence limits (10 determinations). A great variety of pK values is given in the literature: Sane” and Kreshkov et aLI give a value of about 22.2. Bykova and PetrovZOpoint out that this value is very low, probably because of the ionization of the water present in the solvent, which, as has been shown in the theoretical part of this paper, can notably decrease the pKsolventvalue. In other work*l these authors verified that removal of the water and methanol increases the pKaolvcntvalue and they obtained a value of 26.8, very close to the one reported here. Kolthoff and Chantoonil” gave a value of 28.5, which was obtained by measuring the proton activity potentiometrically with a hydrogen electrode, and the tert-butanolate activity conductimetrically by means of a solution of potassium tert-butanolate, to which crown-ethers or cryptands were added to complex the potassium ions and increase the solute dissociation. Therefore this result must be considered to be closer to pKHs than to pKW,,,,, (as defined here), which would be lower. The decrease of pKaolventby the presence of other solvents in the medium was tested by standardizing the electrode system with more concentrated solutions of picric acid in tert-butyl alcohol and titrating with 0.1 M tetrabutylammonium hydroxide solution in isopropyl alcohol. The addition of isopropyl alcohol with the titrant does not significantly affect the standard potential in acid medium, but remarkably
Table 3. pH values of buffers in tert-butyl alcohol PH c,, M
Acid TCAA DCAA CAA AA B
increases
1.37 x 5.95 x 6.47 x 7.17 x 8.60 x
Calculated Observed lO-3 10-d lO-4 10-d lO-4
the standard
7.97 9.66 11.58 13.96 15.87
potential
7.99 9.65 11.58 13.91 15.87
in basic
medium
(pK,,,_, of -25.7 was obtained” for N 3 : 1 tert-butyl alcohol: isopropyl alcohol mixtures). These results agree with the studies of Marple and F&s3 who found that the addition of solvents to solutions of acids and bases in tert-butyl alcohol affects solutions of bases very much more than solutions of acids. As the glass electrode measures proton activity, in acid medium the addition of a solvent does directly affect this activity (it can only affect it indirectly by changing the dissociation constants of the acid and salt),” but in basic medium an increase in the concentration of water (or another solvent) increases Kwlvcnt [see equation (6)], whereas K,, is only slightly modified, so [S-l and [OH-] are not very much increased (if the added solvent increases the dielectric constant), but [H + ] increases and less basic potentials are obtained. The theoretical equations developed have been tested by preparing equimolar buffer solutions of barbital, acetic, monochloroacetic, dichloroacetic and trichloroacetic acids and their tetrabutylammonium salts in tert-butyl alcohol. The results presented in Table 3 show good concordance between the pH values calculated by the proposed equation (53) and those obtained experimentally.
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