Titration in Dipolar Aprotic Solvents of Diprotic Acids as Monoprotic Acids 1. M. Kolthoff and M. K. Chantoonl, Jr. Department of Chemistry, University of Minnesota, Minneapolis, Minn. 55455
The break In pH at the flrst equlvalence polnt In the absence of an amphlprotlc solute In the tltratlon of a dlprotlc acid, wlth pK2 - pK, > 6 In acetonltrlle Is some 4 pH units greater In thls solvent than In DMSO. In practlce, an amphlprotlc solute Is always present whlch decreases the break In pH, but when the lnltlal concentratlon of acid Is taken of the order of 0.005M and a tltrant In a suitable solvent Is used, the break In pH at the equivalence polnt remalns greater In A N than In DMSO. The solvation constants of water, methanol, Isopropanol, and ted-butanol wlth succinic acld, blsucclnate, and succinate In A N and DMSO have been determined, and equatlons are presented whlch allow the calculatlon of the effect of these addltlves on titration curves. A s solutes, they are equally strong hydrogen bond acceptors towards succinic acld In AN. The effects of a change of temperature between 0 and 50 O C In A N and of a decrease of the dlelectrlc constant of DMSO to one half of Its value wlth carbon tetrachlorlde are negllglbly small.
DMSO (13), values of K‘ of these acids have been found to be large, except for bioxalate and bifumarate in which intramolecular hydrogen bonding is sterically impossible. Values of K’ decrease with increasing distance (number of CH2 groups) between the two carboxyl groups. The COOgroup in HA- is a strong hydrogen bond acceptor (15) and is strongly hydrogen bonded to the donors water (W) or methanol (M). On the other hand, dipolar aprotic solvents, like AN and DMSO, are extremely weak hydrogen bond donors and hardly solvate the COO- group by hydrogen bonding. This difference mainly accounts for the fact that the equilibrium in Equation 1 is shifted to the right in AN and DMSO as compared to that in W or M. DMSO is a stronger hydrogen bond acceptor (15) than W, M, or AN, and it stabilizes by hydrogen bonding the COOH group in HA- (but not in RA-). As a result, values of K’ are about 40 times smaller in DMSO than in AN (13). Intramolecular hydrogen bonding in RA- stabilizes this anion and makes it a weaker base as well as a weaker acid than HA-. For this reason alone, K l becomes (K’ + 1) times greater, and K2 (K’ 1) times smaller than when the monoanion is only in the form HA-, since ZHA- = [HA-] [HA-] = [HA-] (K’ + 1). In addition, (PKP - P K ~ A N , D M S O(PKZ- PKdw, denoted by AN,DMsoAWpK:,is to a considerable extent determined by the transfer activity coefficients WyANpDMSO of H2A and particularly of HA- and A2-. As a rule AN,DMSOAWpK:is larger than 2 log(K’ + 1) and is of the same sign. The combined effects of larger values of K’ and of smaller electrostatic free energies of solvation of A2(large negative values of pWyANyDMSoA2-)in AN and DMSO than in M or W result in large values of ANsDMSOAWpK:.Therefore in titrations of diprotic acids with a strong base, the break at the first equivalence point is much larger in aprotic solvents than in W or M. For reasons presented in a review paper (15), we had concluded that, in general, a protophilic solvent is preferable to a protophobic one for the titration of an uncharged monoprotic acid with a strong base. In the present paper, it is demonstrated that a protophobic aprotic solvent is preferable to a protophilic one in the titration of a diprotic acid to the first equivalence point, provided the concentration of amphiprotic solvent added with the titrant is kept small and homoconjugation is minimized by taking dilute solutions of the diacid. No information in the literature is available on the effect of temperature on pK1 and pK2 of diprotic acids in aprotic solvents. For this reason, a brief study has been made of this temperature effect on succinic acid. Also, a few exploratory experiments have been made on the effect of the dielectric constant on pK2 - pK1 of succinic acid in a mixture of DMSO and carbon tetrachloride. Calculation of Titration Curves of Diprotic Acids with a Strong Base in Presence of Additives. Representing C H ~ ACHA-, , and (2.42- as the analytical concentration of diacid, monoanion, and dianion, respectively, in mixtures of the three, we may write
+
In the titration of the first proton in diprotic acids, use has been made for many years of the fact that, for a given acid, the ratio K1/K2 of the first to the second dissociation constant is very much greater in dipolar aprotic solvents than in water (or methanol). Experimental conditions of titrations of diprotic acids in dipolar aprotic solvents have been presented in several books (1-3). Solvents which have been used are acetone ( 4 , 5 ) ,acetonitrile (6),methyl isobutyl ketone (7), sulfolane (8),pyridine (5, 9, IO), N,N’-dimethylformamide (9), and dimethylsulfoxide (11). The present paper deals with two important aspects of such titrations, first, the break in potential at the first end point in dipolar aprotic protophobic solvents (e.g., acetonitrile) as compared with that in protophilic solvents (e.g., dimethylsulfoxide) and, second, a quantitative interpretation of the effect on the titration curves of amphiprotic compounds, like alcohols and water, which are usually present in the titrants and which arise as a reaction product in the titration. Recently (12, 13), we have made extensive studies in acetonitrile (AN), dimethylsulfoxide (DMSO), and methanol (M) of the various constants which determine acid-base equilibria in these solvents of the homologous series of oxalic acid, and of o-phthalic and fumaric acids. A factor which can have a major effect on (pK2 - pK1) is intramolecular hydrogen bonding in the monoanion HA-: COOH
COOH,
/
/
\coo-
\
HA-
HA-
K’
i I’
COO--’
=
[FIA-]/[HA-I
Of the diprotic acids mentioned above, the value of K’ in water (W) has been found by Westheimer and Benfy (14) to be virtually equal to zero. However, in AN (12) and
+
CH~A + CHA- + ( 2 ~ 2 - = [H2A]t + Z[HA-]t
+ [A2-]t (2)
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
1921
Table I. First and Second Dissociation Constants of Diprotic Acids in Acetonitrile and Dimethylsulfoxide, log K ’ and Homoconjugation Constant, Khomo,of H2A.ZHA- in Acetonitrile AN
DMSO
(CHZ), n
Acid
Oxalic Malonic Succinic Glutaric Adipic Azelaic 0-Phthalic a A = pK2 - pK1.
0 1
PKi
PK2
6.2 7.2 9.5 10.9 11.9 12 .o 6.2
14.9 18.6 16.7 15.3 14.1 13.6 16.0
A5
8.7 11.4 2 7.2 3 4.4 4 2.2 7 1.6 9.8 log K’ in DMSO z (log K’ in AN) - 1.6.
+ CHA- + 2c~2-= Z[HA-]t + 2[A2-]t
pK.1
PKZ
An
14.5 15.3 17.6 19.2 20.4 20.8 14.2
27.7 30.5 29 .O 28 .O 26.9 24.8 29.8
13.2 15.2 11.4 8.8 6.5 4 .O 15.6
Khomo
4 x 0.9 0.2 0.6 1.4 2.7 0.9
log K ‘
0 4.4 3.7 2.8 1.6 1.2 5.5
103 x 103 x 103 x 103 x 103 x 103 x 102
products used previously (12). Tetramethylammonium hydroxide (1.1M) in methanol was prepared from the bromide by the silver oxide method (11, omitting the ion exchange procedure. where the subscript t denotes the sum of the solvated and Salts. The sample of tetraethylammonium bisuccinate used for unsolvated forms and Z[HA-] = [HA-] [HA-]. As exthe determination of pK1 and pK2 of succinic acid had been preplained previously (12), we define w E 1 KB.H*A[B]+ pared in this laboratory (19). It was further recrystallized from an , . . , v 31 KB.HA-[B] . . . , and U E 1 KB.A~-[B]+ ethanol-ethyl acetate mixture. The crop of crystals which first . . . , B denoting the additive and KB.H~A,KB.HA-,KB.A~- separated out was rejected. The purified product appeared to be practically free of basic or acidic impurities. Tetraethylammonium the formation constants of the solvates BeHzA, B-HA-, and succinate was a product used previously (12). B.A2-, respectively. Therefore, [H2AIt = W[HzA], Z[HA-It Instrumentation. The glass electrode was used for pH mea= VZ[HA-], and [A2-]t = .[A2-]. Substituting the definisurements. Details of the cell and pH meter are found elsewhere tion just given and the expressions for the first and second (20). A t 0 and 50 “C, 1-2 hr were required to attain a steady potendissociation constants of the diacid, K1 and K2, respectivetial in the bisuccinate-succinate mixture. ly, into Equations 2 and 3, Equation 4 results RESULTS AND DISCUSSION a 2 ~(1 + WZ[HA-]f*/Kl) fH+aH+(CA2-Table I presents values (13) of pK1 and pK2 in AN and C H ~ A-) uK2Z[HA-]f-’/f2- = 0 (4) DMSO of the homologous series of oxalic acid and o phthalic acid. In the next to the last column are listed hoWhen K2
