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Potentiometric determination of the dissociation constants of itaconic acid
ELECTROANALYTICAL CHEMISTRY AND INTERFACIAL ELECTROCHEMISTRY Elsevier Sequoia S.A., Lausanne Printed in The Netherlands
299
POTENTIOMETRIC DETERMINATION OF THE DISSOCIATION CONSTANTS OF ITACONIC ACID
H. SCHURMANS, H. THUN AND F. VERBEEK
Laboratory for Analytical Chemistry, University of Ghent, 9000 Ghent (Belgium) (Received January 31st, 1970)
In connection with a potentiometric investigation of the complex formation between itaconate and various lanthanide ions an accurate determination of the dissociation constants of itaconic acid, under the conditions of ionic strength (I = 1 in NaC104) and temperature (25°C) used in the complex formation, was required. By employing this appropriate ionic medium it is possible to control the activity coefficients of the various species participating in the reaction, and the various liquid junction potentials a. The dissociation constants of itaconic acid have already been investigated at different ionic strengths or temperatures 2-4, but none of these determinations refers to the authors' conditions. In the present paper a potentiometric investigation and calculation procedure of the dissociation constants of itaconic acid are discussed and constants reported over a certain concentration range of itaconate in water. CALCULATION PROCEDURE
Several methods are reported in the literature for calculating the dissociation constants of dibasic acids 5- 9. The treatment of the specific data depends upon the ratio of the dissociation constants. With a favourable ratio ( > 1000) the acid is generally treated as a mixture of monobasic acids. In all other cases, such as for itaconic acid, graphical treatment of the equations is necessary. As this is a laborious and time-consuming work, especially for polybasic acids, and as computers have become more readily available, Dunning and Martin 9 have reported a general computational method for mono- and polybasic acids and mixtures of acids, based upon the least squares method. Thus it becomes possible to calculate dissociation constants without making simplifying assumptions, and with full consideration of all available data. In a later paper, Thun e t al. 1° reported a computer version of Fronaeus' graphical integration method for calculating stability constants of complexes. The author indicated that there had already been some attempts to calculate the dissociation constants of dibasic acids with the aid of this new computer method, which gave entirely good agreement with other methods. Moreover, in this kind of problem, this method seems to enable individual constants to be calculated more rapidly than with the least squares ,treatment, without losing the advantages of the latter. If one considers the undissociated acid form H2L of a dibasic acid as a complex of the anion L 2 -, acting as central group, and protons, acting as ligands, the following relationships J. Eleetroanal. Chem., 26 (1970) 299-305
300
H. SCHURMANS, H. THUN, F. VERBEEK
exist between the dissociation constants KA1 and KA2 of the acid and the stability constants fin and f12 n flU_
[HL] 1 [H] [El - KA~ [H2L]
(1) 1
flu _ [ H ] 2 [ L ] _ KAIKA2
(2)
It is now convenient to introduce these stability constants, from which the acid dissociation constants can be found, in the equation of Bjerrum's formation function hn, here defined as the number of protons bound to a central group L. Thus [HE] + 2 [HEL] n" = [L] + [HL] + [H2L]
(3)
or combined with eqns. (1) and (2) fill[H] + 2fi~[H] e n" = 1 +fill[H] +fl~[H] a
(4)
Thus, fin and fizn can be deduced from a set of known nit and [H] values obtained by the usual methods for the determination of stability constants 11. For example, in the method of Speakman v eqn. (4) was transformed into eqn. (5) 1
(nu-- 1)[H] fl~
(2-hH)[H]2
(5)
Plots of the right term ofeqn. (5) vs. the left term yield fly and fin. The computer version of Fronaeus' graphical integration method especially seems to be applicable as the computations are based upon eqn. (4), while all data can be treated simultaneously. EXPERIMENTAL
Reagents Deionizised water was distilled twice before making up all solutions. Sodium perchlorate. Sodium perchlorate (Fluka, crystallised analytical grade) was used for adjusting the ionic strength of the various solutions to unity. Perchloric acid (U.C.B., p.a. 70~o). The diluted solutions were determined by potentiometric titrations, employing Gran plots 12, with carbonate-free sodium hydroxide. Sodium hydroxide (U.C.B., p.a.). Carbonate-free sodium hydroxide solutions were prepared by diluting a filtered 50~oo N a O H solution with CO2-free water. The solutions were standardised titrimetrically against standard oxalic acid under a nitrogen atmosphere. Itaconic acid (Fluka purum) H2L : CH2=C CH2 • The purity of the acid I L COOH COOH used in the experiments was found titrimetrically to be 99.90 +_0.06~ as an average for 10 determinations. After recrystallisation the purity of the acid remained unchanged. The solutions required for each titration were prepared from a stock soluJ. Electroanal. Chem., 26 (1970} 299-305
301
DISSOCIATION CONSTANTS OF ITACONIC ACID
tion by appropriate dilution.
Disodium itaconate" Na2L. A weighed amount of itaconic acid was brought into solution and a calculated quantity of sodium hydroxide was added in slight excess. After careful evaporation of the solution the salt was dried at + 60°C and afterwards pulverised. The small excess of sodium hydroxide was removed by stirring the salt for some time in ethyl alcohol in which disodium itaconate is practically insoluble. After drying the salt at 120°C (because of its hygroscopic character), the purity was checked by converting a weighed amount of salt into its acid form over a cation exchange column (Amberlite IR) and titration with carbonate-free sodium hydroxide under a nitrogen atmosphere. The purity of the salt was found to be 100.0~o. The solutions necessary for each titration were prepared from a stock solution by appropriate dilution. Apparatus The electrodes used for determinations of hydrogen ion concentration were an Ingold glass electrode (type LOT-201 NS) and silver-silver chloride electrodes prepared according to Brown 13. The e.m.f, during the titrations was measured on a Radiometer PHM4c potentiometer. For the determination of the Eo value of the electrode system the e.m.f, was measured on a Dynamco digital voltmeter, type DM 2022S. The temperature of the titration vessel and the reference electrode system was maintained at 25.00 +0.02°C by pumping thermostatted water through the mantle of the vessels, by means of a Lauda Thermostat, connected with an electronic relaybox R 10. The titrant was added from a 10 ml piston burette (Metrohm) and magnetic stirring was employed.
Procedure In order to measure hydrogen ion concentrations during the titrations; the Eo value of the electrode system has to be determined. Therefore the e.m.f., E, of perchloric acid solutions with known hydrogen ion concentration and with I = 1 in NaC10 4 was measured with galvanic cells of the type described by Grenthe 14. The reference solution had the composition CNaC1= 10.0 mM
and
CNaC104= 990 mM
A few results are given in Table 1. E o + Ej has been calculated from E = Eo+ 59.15 log [H +] +Ej where Ej represents the liquid junction potential. When E o + Ej is plotted as a function of the hydrogen ion concentration [H +] it is clear that all plots lie on a straight line. Thus Ej is only a function of [H +] and is given by the slope, while E o can be evaluated by linear extrapolation. In this way TABLE 1 C A L I B R A T I O N OF T H E E L E C T R O D E SYSTEM
E/mV log(H +) (Eo+Ej)/mV 59.15
6.76 159.65 166.41
24.51 141.72 166.23
65.44 99.67 165.11
81.96 81.86 163.82
91.08 71.45 162.53
97.21 64.06 16L27
101.66 58.32 159.98
J. Electroanal. Chern., 26 (1970) 299-305
302
H. SCHURMANS,H. THUN, F. VERBEEK
Eo was found to be 166.5_+0.1 mV and Ej= - 6 4 [H+]. The latter value is in good agreement with those of other authors 1'15,16 who worked at I = 1. The dissociation constants ofitaconic acid were determined potentiometrically by measuring the variation of the hydrogen ion concentration using galvanic cells similar to those used for the determination of E o and Ej L) glass Ag, AgC1 ref. soln. 1.00 M CHzL(X CNa2L(ymM mM H2 Na2L) NaC104 NaC104 ( I - 1) electrode CIt2Land CNa2Lare respectively the total concentrations of itaconic acid and itaconate. Their sum, CL, was kept constant during the whole titration. The concentrations CH2L and CNa2Lin the right half-cell were changed systematically by titration of 25.00 ml of a solution of itaconic acid with known volumes of itaconate of the same concentration for the high nH values, and vice versa for the low hn values. After each addition the e.m.f, was measured after 5 min, when stable and reproducible potentials are reached. The reproducibility was usually within 0.1 mV. CO2 was expelled from the cell solutions by nitrogen which had previously been passed through a 1 M NaC104 solution. Titrations were performed at three different total concentrations of itaconic acid and itaconate (10, 20 and 50 mM). Eo was checked before and after each titration by measuring the e.m.f, of a solution with a known hydrogen ion concentration. RESULTSAND DISCUSSION The results of the titrations are summarised in Table 2; ~n and - log [H +] are listed for each concentration CL as a function of the quantity of H2L or Na2L added. The values of - l o g [H +] were calculated from the E and Eo values measured. - l o g [H +] = (Eo-E)/59.15
(6)
Ej was not taken into account because - l o g [H +] values below 3 were not used in the calculations. The values exceeding 3 are very little influenced by E j, as stated above. The hn values were calculated from
nn = (cn- [H +])/CL
(7)
where cH is given by Cn = 2 CH~L"Vo/(Vo + Vx)
(8)
for titration of H2L with Na2L (Vo= initial volume, Vx---volume of titrant added) and
cH = 2 CH~L"Vx/(Vo + vx)
(9)
for titrations of NaEL with HzL For each eL the corresponding nn and [H +] values were supplied to an IBM 1620 digital computer, and the stability constants fin and fin calculated with the com-
J. Electroanal. Chem., 26 (1970) 299-305
303
DISSOCIATION CONSTANTS OF ITACONIC ACID TABLE 2 hi.F-log [ H + ] DATA FOR THE PROTON ITACONATE SYSTEM AT VARIOUS TOTAL ITACONATE CONCENTRATIONS
Volume added /ml
CL ~- 10 m M
CL=20 m M
CL= 50 m M
HzL
nn
- l o g [H+]/ mol 1-1
fin
--log [H+]/ mol l- ~
~.
- l o g [H+]/ mol l- 1
0.0768 0.1480 0.2755 0.3865 0.4840 0.5702 0.6471 0.7160 0.7670 0.8344 0.8740 0.9322 ff9950 0.9950 1.0577 1.1155 1.1543 1.2204 1.2699 1.3362 1.4093 1.4900 1.5785 1.6742 1.7737
6.051 5.746 5A22 5.217 5.060 4.935 4.820 4.725 4.647 4.556 4.495 4.407 ~309 4.312 4.218 4.140 4.075 3.988 3.914 3.819 3.716 3.599 3.464 3.302 3.107
0.0769 0.1481 0.2757 0.3868 0.4844 ~5708 0.6479 0.7170 0.7681 0.8358 0.8756 0.9342 ff9975 0.9975 1.0607 1.1191 1.1585 •.2255 1.2758 1.3435 1.4186 1.5020 1.5945 1.6965 1.8044
6.051 5.745 5.422 5.217 5.060 4.935 4.820 4.725 4.647 4.555 4.494 4.401 &306 4.308 4.215 4.130 4.073 3.980 3.905 3.809 3.701 3.581 3.433 3.258 3.023
0.0769 0.1481 0.2758 0.3870 0.4847 ~5712 0.6483 0.7176 0.7688 0.8366 0.8765 0.9354 ~9990 0.9990 1.0626 1.1213 1.1611 •.2286 1.2795 1.3482 1.4245 1.5097 1.6051 1.7121 1.8287
6.057 5.751 5.422 5.217 5.062 4.930 4.822 4.723 4.646 4.553 4.492 4.399 4.304 4.304 4.210 4.128 4.068 3.975 3.899 3.799 3.689 3.562 3.410 3.219 2.937
Na2 L
1.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 40.00 18.00 32.00 22.00 25.00 25.00 22.00 32.00 18.00 40.00 14.00 12.00 10.00 8.00 6.00 4.00 2.00
puter version of Fronaeus' graphical integration method. The resUlts with their standard deviations are given in Table 3. Use was also made of Speakman's graphical method to evaluate the stability constants of itaconic acid. The values of (~I~= 1)[H+]/hr~ and (2-~n)[H+]2/~ n in eqn. 5 were calculated with the data for nn and - l o g [-H +] of Table 2. An example of the TABLE 3 STABILITY CONSTANTS OF THE PROTON ITACONATE SYSTEM
CUmM
10 20 50 Mean values
Computer
Speakman's 9raphical method
lO-~ffi
10-~/3~/ l mol-1
10-sflg/ 12tool-2
109(fl~)- a/ molZ l 2
104(fi~/flg)/ mol l- X
10'-' fix/n i mol- a
12 mol- 2
9.729_+0.004 9.721 -+0.005 9.713-+0.008 9.721-+0.006
4.144-+0.005 4.156_+0.005 4.120_+0.010 4.140-+0.008
2.45-+0.01 2.43_+0.02 2.44_+0.01 2.44 _+0.01
2.39 ~0.01 2.40__+0.01 2.38_+0.01 2.39 -+0.01
9.75-+0.08 9.87_+0.11 9.75_+0.08 9.79 + 0.09
4.08 '+ 0.02' 4.12__+0.04 4A0+0.02 4.10_+0.02
J. Electroanal. Chem., 26 0970)299-305
304
H. SCHURMANS, H. THUN, F. VERBEEK
(2-fill)(H)2 xlO 9
-lo
I
-~
~
I
~
i
lo
1'5 (~.-O(H) ~1oe n H
Fig. 1. Graphical evaluation of the stability constants of the proton itaconate system according to the method of Speakman.
graphical evaluation of the constants is given in Fig. 1 (cL = 50 mM). The results for each cL are also given in Table 3. As can be seen from Table 3, the results of the computer method for the three concentrations are in very good mutual agreement which shows that in the eL range of our experiments only the mononuclear forms L 2-, H L - and H2L of itaconic acid exist in solution. The agreement between the two different methods is remarkable and better than 1~ , but it can be seen that the uncertainty on the values obtained graphically is much greater than with the computer values. This is probably due to the limitation of the number of data that Can be treated simultaneously in Speakman's method which emphasizes that, whenever possible, computer methods must be used for the determination of equilibria constants, although graphical methods can be used as an additional control. From the stability constants obtained, the two dissociation constants ofitaconic acid were calculated with eqns. (1) and (2) KA, ----2.349_+0.006 x 1 0 - 4 ;
KA2 =
1.029_+0.001 x 10 -s and KA,/KA2 -----23
and pKA1 =
3.629+0.002;
pKA2 = 4.988_+0.001
In connection with this investigation, it is of interest to note that similar experiments have been performed in the eL range above 50 mM. It seems that in this range, besides the mononuclear forms, polynuclear complexes do exist in solution. The identification of these proton itaconate complexes and their corresponding stability constants will be published in a second paper. ACKNOWLEDGEMENT
One of the authors (H.S.) wishes to thank the I.W.O.N.U for a grant. J. Electroanal. Chem., 26 (1970) 299-305
DISSOCIATION CONSTANTS OF ITACONIC ACID
305
SUMMARY
The dissociation of itaconic acid was investigated potentiometrically at ionic strength / = 1 in NaC104 at 25.000 +_0.02°C in the concentration range 0-50 mM. The two dissociation constants were calculated by both a graphical and a computer method. The values reported are pKAI = 3.629 +_0.002 and PKA2=4.988 +0.001. For concentrations > 50 mM, polynuclear proton itaconate complexes are observed. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
G. BIEDERMANNAND L. G. SILLEN,Arkiv Kemi, 5 (1953) 425. M. YASUDA,K. YAMASAKIAND H. OHTAKI,Bull. Chem. Soc. Japan, 33 (1960) 8, 1067. S. RAMAMOORTHyAND M. SANTAPPA,Current Sci. India, 35 (1966) 6, 145. H. W. ASHTONAND J. R. PARTINGTON, Trans. Faraday Soc., 30 (1934) 598. A. NOYES,Z. Physik. Chem., 11 (1893) 495. G. SWARZENBACH,A. WILLI AND R. O. BACH, Helv. Chim. Acta, 30 (1947) 1303. J. C. SPEAKMAN,J. Chem. Soc., (1940) 855. H. T. S. BRITTON, Hydrogen Ions, Vol. 1, Chapman and Hall, London, 4th ed., 1955, p. 217. W. S. DUNNINGAND D. S. MARTIN,Report IS-822 (1964). H. THUN, F. VERBEEKAND W. VANDERLEEN,J. Inorg. Nucl. Chem., 29 (1967) 2109. F. J. C. ROSSOTTIAND H. ROSSOTTI, The Determination of Stability Constants, McGraw-Hill, London, 1961, p. 89. G. GRAN, Acta Chem. Scand., 4 (1950) 559; Analyst, 77 (1952) 661. A. S. BROWN, J. Am. Chem. Soc., 56 (1934) 646. I. GRENTHEAND D. R. WILLIAMS,Acta Chem. Scand., 21 (1967) 341. F. J. C. ROSSOT'rIAND H. S. ROSSOTTI,Acta Chem. Scand., 10 (1956) 957. W. KRAFT,Monatsh. Chem., 5 (1967) 1979.
J. Electroanal. Chem., 26 (1970) 299-305
299
POTENTIOMETRIC DETERMINATION OF THE DISSOCIATION CONSTANTS OF ITACONIC ACID
H. SCHURMANS, H. THUN AND F. VERBEEK
Laboratory for Analytical Chemistry, University of Ghent, 9000 Ghent (Belgium) (Received January 31st, 1970)
In connection with a potentiometric investigation of the complex formation between itaconate and various lanthanide ions an accurate determination of the dissociation constants of itaconic acid, under the conditions of ionic strength (I = 1 in NaC104) and temperature (25°C) used in the complex formation, was required. By employing this appropriate ionic medium it is possible to control the activity coefficients of the various species participating in the reaction, and the various liquid junction potentials a. The dissociation constants of itaconic acid have already been investigated at different ionic strengths or temperatures 2-4, but none of these determinations refers to the authors' conditions. In the present paper a potentiometric investigation and calculation procedure of the dissociation constants of itaconic acid are discussed and constants reported over a certain concentration range of itaconate in water. CALCULATION PROCEDURE
Several methods are reported in the literature for calculating the dissociation constants of dibasic acids 5- 9. The treatment of the specific data depends upon the ratio of the dissociation constants. With a favourable ratio ( > 1000) the acid is generally treated as a mixture of monobasic acids. In all other cases, such as for itaconic acid, graphical treatment of the equations is necessary. As this is a laborious and time-consuming work, especially for polybasic acids, and as computers have become more readily available, Dunning and Martin 9 have reported a general computational method for mono- and polybasic acids and mixtures of acids, based upon the least squares method. Thus it becomes possible to calculate dissociation constants without making simplifying assumptions, and with full consideration of all available data. In a later paper, Thun e t al. 1° reported a computer version of Fronaeus' graphical integration method for calculating stability constants of complexes. The author indicated that there had already been some attempts to calculate the dissociation constants of dibasic acids with the aid of this new computer method, which gave entirely good agreement with other methods. Moreover, in this kind of problem, this method seems to enable individual constants to be calculated more rapidly than with the least squares ,treatment, without losing the advantages of the latter. If one considers the undissociated acid form H2L of a dibasic acid as a complex of the anion L 2 -, acting as central group, and protons, acting as ligands, the following relationships J. Eleetroanal. Chem., 26 (1970) 299-305
300
H. SCHURMANS, H. THUN, F. VERBEEK
exist between the dissociation constants KA1 and KA2 of the acid and the stability constants fin and f12 n flU_
[HL] 1 [H] [El - KA~ [H2L]
(1) 1
flu _ [ H ] 2 [ L ] _ KAIKA2
(2)
It is now convenient to introduce these stability constants, from which the acid dissociation constants can be found, in the equation of Bjerrum's formation function hn, here defined as the number of protons bound to a central group L. Thus [HE] + 2 [HEL] n" = [L] + [HL] + [H2L]
(3)
or combined with eqns. (1) and (2) fill[H] + 2fi~[H] e n" = 1 +fill[H] +fl~[H] a
(4)
Thus, fin and fizn can be deduced from a set of known nit and [H] values obtained by the usual methods for the determination of stability constants 11. For example, in the method of Speakman v eqn. (4) was transformed into eqn. (5) 1
(nu-- 1)[H] fl~
(2-hH)[H]2
(5)
Plots of the right term ofeqn. (5) vs. the left term yield fly and fin. The computer version of Fronaeus' graphical integration method especially seems to be applicable as the computations are based upon eqn. (4), while all data can be treated simultaneously. EXPERIMENTAL
Reagents Deionizised water was distilled twice before making up all solutions. Sodium perchlorate. Sodium perchlorate (Fluka, crystallised analytical grade) was used for adjusting the ionic strength of the various solutions to unity. Perchloric acid (U.C.B., p.a. 70~o). The diluted solutions were determined by potentiometric titrations, employing Gran plots 12, with carbonate-free sodium hydroxide. Sodium hydroxide (U.C.B., p.a.). Carbonate-free sodium hydroxide solutions were prepared by diluting a filtered 50~oo N a O H solution with CO2-free water. The solutions were standardised titrimetrically against standard oxalic acid under a nitrogen atmosphere. Itaconic acid (Fluka purum) H2L : CH2=C CH2 • The purity of the acid I L COOH COOH used in the experiments was found titrimetrically to be 99.90 +_0.06~ as an average for 10 determinations. After recrystallisation the purity of the acid remained unchanged. The solutions required for each titration were prepared from a stock soluJ. Electroanal. Chem., 26 (1970} 299-305
301
DISSOCIATION CONSTANTS OF ITACONIC ACID
tion by appropriate dilution.
Disodium itaconate" Na2L. A weighed amount of itaconic acid was brought into solution and a calculated quantity of sodium hydroxide was added in slight excess. After careful evaporation of the solution the salt was dried at + 60°C and afterwards pulverised. The small excess of sodium hydroxide was removed by stirring the salt for some time in ethyl alcohol in which disodium itaconate is practically insoluble. After drying the salt at 120°C (because of its hygroscopic character), the purity was checked by converting a weighed amount of salt into its acid form over a cation exchange column (Amberlite IR) and titration with carbonate-free sodium hydroxide under a nitrogen atmosphere. The purity of the salt was found to be 100.0~o. The solutions necessary for each titration were prepared from a stock solution by appropriate dilution. Apparatus The electrodes used for determinations of hydrogen ion concentration were an Ingold glass electrode (type LOT-201 NS) and silver-silver chloride electrodes prepared according to Brown 13. The e.m.f, during the titrations was measured on a Radiometer PHM4c potentiometer. For the determination of the Eo value of the electrode system the e.m.f, was measured on a Dynamco digital voltmeter, type DM 2022S. The temperature of the titration vessel and the reference electrode system was maintained at 25.00 +0.02°C by pumping thermostatted water through the mantle of the vessels, by means of a Lauda Thermostat, connected with an electronic relaybox R 10. The titrant was added from a 10 ml piston burette (Metrohm) and magnetic stirring was employed.
Procedure In order to measure hydrogen ion concentrations during the titrations; the Eo value of the electrode system has to be determined. Therefore the e.m.f., E, of perchloric acid solutions with known hydrogen ion concentration and with I = 1 in NaC10 4 was measured with galvanic cells of the type described by Grenthe 14. The reference solution had the composition CNaC1= 10.0 mM
and
CNaC104= 990 mM
A few results are given in Table 1. E o + Ej has been calculated from E = Eo+ 59.15 log [H +] +Ej where Ej represents the liquid junction potential. When E o + Ej is plotted as a function of the hydrogen ion concentration [H +] it is clear that all plots lie on a straight line. Thus Ej is only a function of [H +] and is given by the slope, while E o can be evaluated by linear extrapolation. In this way TABLE 1 C A L I B R A T I O N OF T H E E L E C T R O D E SYSTEM
E/mV log(H +) (Eo+Ej)/mV 59.15
6.76 159.65 166.41
24.51 141.72 166.23
65.44 99.67 165.11
81.96 81.86 163.82
91.08 71.45 162.53
97.21 64.06 16L27
101.66 58.32 159.98
J. Electroanal. Chern., 26 (1970) 299-305
302
H. SCHURMANS,H. THUN, F. VERBEEK
Eo was found to be 166.5_+0.1 mV and Ej= - 6 4 [H+]. The latter value is in good agreement with those of other authors 1'15,16 who worked at I = 1. The dissociation constants ofitaconic acid were determined potentiometrically by measuring the variation of the hydrogen ion concentration using galvanic cells similar to those used for the determination of E o and Ej L) glass Ag, AgC1 ref. soln. 1.00 M CHzL(X CNa2L(ymM mM H2 Na2L) NaC104 NaC104 ( I - 1) electrode CIt2Land CNa2Lare respectively the total concentrations of itaconic acid and itaconate. Their sum, CL, was kept constant during the whole titration. The concentrations CH2L and CNa2Lin the right half-cell were changed systematically by titration of 25.00 ml of a solution of itaconic acid with known volumes of itaconate of the same concentration for the high nH values, and vice versa for the low hn values. After each addition the e.m.f, was measured after 5 min, when stable and reproducible potentials are reached. The reproducibility was usually within 0.1 mV. CO2 was expelled from the cell solutions by nitrogen which had previously been passed through a 1 M NaC104 solution. Titrations were performed at three different total concentrations of itaconic acid and itaconate (10, 20 and 50 mM). Eo was checked before and after each titration by measuring the e.m.f, of a solution with a known hydrogen ion concentration. RESULTSAND DISCUSSION The results of the titrations are summarised in Table 2; ~n and - log [H +] are listed for each concentration CL as a function of the quantity of H2L or Na2L added. The values of - l o g [H +] were calculated from the E and Eo values measured. - l o g [H +] = (Eo-E)/59.15
(6)
Ej was not taken into account because - l o g [H +] values below 3 were not used in the calculations. The values exceeding 3 are very little influenced by E j, as stated above. The hn values were calculated from
nn = (cn- [H +])/CL
(7)
where cH is given by Cn = 2 CH~L"Vo/(Vo + Vx)
(8)
for titration of H2L with Na2L (Vo= initial volume, Vx---volume of titrant added) and
cH = 2 CH~L"Vx/(Vo + vx)
(9)
for titrations of NaEL with HzL For each eL the corresponding nn and [H +] values were supplied to an IBM 1620 digital computer, and the stability constants fin and fin calculated with the com-
J. Electroanal. Chem., 26 (1970) 299-305
303
DISSOCIATION CONSTANTS OF ITACONIC ACID TABLE 2 hi.F-log [ H + ] DATA FOR THE PROTON ITACONATE SYSTEM AT VARIOUS TOTAL ITACONATE CONCENTRATIONS
Volume added /ml
CL ~- 10 m M
CL=20 m M
CL= 50 m M
HzL
nn
- l o g [H+]/ mol 1-1
fin
--log [H+]/ mol l- ~
~.
- l o g [H+]/ mol l- 1
0.0768 0.1480 0.2755 0.3865 0.4840 0.5702 0.6471 0.7160 0.7670 0.8344 0.8740 0.9322 ff9950 0.9950 1.0577 1.1155 1.1543 1.2204 1.2699 1.3362 1.4093 1.4900 1.5785 1.6742 1.7737
6.051 5.746 5A22 5.217 5.060 4.935 4.820 4.725 4.647 4.556 4.495 4.407 ~309 4.312 4.218 4.140 4.075 3.988 3.914 3.819 3.716 3.599 3.464 3.302 3.107
0.0769 0.1481 0.2757 0.3868 0.4844 ~5708 0.6479 0.7170 0.7681 0.8358 0.8756 0.9342 ff9975 0.9975 1.0607 1.1191 1.1585 •.2255 1.2758 1.3435 1.4186 1.5020 1.5945 1.6965 1.8044
6.051 5.745 5.422 5.217 5.060 4.935 4.820 4.725 4.647 4.555 4.494 4.401 &306 4.308 4.215 4.130 4.073 3.980 3.905 3.809 3.701 3.581 3.433 3.258 3.023
0.0769 0.1481 0.2758 0.3870 0.4847 ~5712 0.6483 0.7176 0.7688 0.8366 0.8765 0.9354 ~9990 0.9990 1.0626 1.1213 1.1611 •.2286 1.2795 1.3482 1.4245 1.5097 1.6051 1.7121 1.8287
6.057 5.751 5.422 5.217 5.062 4.930 4.822 4.723 4.646 4.553 4.492 4.399 4.304 4.304 4.210 4.128 4.068 3.975 3.899 3.799 3.689 3.562 3.410 3.219 2.937
Na2 L
1.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 40.00 18.00 32.00 22.00 25.00 25.00 22.00 32.00 18.00 40.00 14.00 12.00 10.00 8.00 6.00 4.00 2.00
puter version of Fronaeus' graphical integration method. The resUlts with their standard deviations are given in Table 3. Use was also made of Speakman's graphical method to evaluate the stability constants of itaconic acid. The values of (~I~= 1)[H+]/hr~ and (2-~n)[H+]2/~ n in eqn. 5 were calculated with the data for nn and - l o g [-H +] of Table 2. An example of the TABLE 3 STABILITY CONSTANTS OF THE PROTON ITACONATE SYSTEM
CUmM
10 20 50 Mean values
Computer
Speakman's 9raphical method
lO-~ffi
10-~/3~/ l mol-1
10-sflg/ 12tool-2
109(fl~)- a/ molZ l 2
104(fi~/flg)/ mol l- X
10'-' fix/n i mol- a
12 mol- 2
9.729_+0.004 9.721 -+0.005 9.713-+0.008 9.721-+0.006
4.144-+0.005 4.156_+0.005 4.120_+0.010 4.140-+0.008
2.45-+0.01 2.43_+0.02 2.44_+0.01 2.44 _+0.01
2.39 ~0.01 2.40__+0.01 2.38_+0.01 2.39 -+0.01
9.75-+0.08 9.87_+0.11 9.75_+0.08 9.79 + 0.09
4.08 '+ 0.02' 4.12__+0.04 4A0+0.02 4.10_+0.02
J. Electroanal. Chem., 26 0970)299-305
304
H. SCHURMANS, H. THUN, F. VERBEEK
(2-fill)(H)2 xlO 9
-lo
I
-~
~
I
~
i
lo
1'5 (~.-O(H) ~1oe n H
Fig. 1. Graphical evaluation of the stability constants of the proton itaconate system according to the method of Speakman.
graphical evaluation of the constants is given in Fig. 1 (cL = 50 mM). The results for each cL are also given in Table 3. As can be seen from Table 3, the results of the computer method for the three concentrations are in very good mutual agreement which shows that in the eL range of our experiments only the mononuclear forms L 2-, H L - and H2L of itaconic acid exist in solution. The agreement between the two different methods is remarkable and better than 1~ , but it can be seen that the uncertainty on the values obtained graphically is much greater than with the computer values. This is probably due to the limitation of the number of data that Can be treated simultaneously in Speakman's method which emphasizes that, whenever possible, computer methods must be used for the determination of equilibria constants, although graphical methods can be used as an additional control. From the stability constants obtained, the two dissociation constants ofitaconic acid were calculated with eqns. (1) and (2) KA, ----2.349_+0.006 x 1 0 - 4 ;
KA2 =
1.029_+0.001 x 10 -s and KA,/KA2 -----23
and pKA1 =
3.629+0.002;
pKA2 = 4.988_+0.001
In connection with this investigation, it is of interest to note that similar experiments have been performed in the eL range above 50 mM. It seems that in this range, besides the mononuclear forms, polynuclear complexes do exist in solution. The identification of these proton itaconate complexes and their corresponding stability constants will be published in a second paper. ACKNOWLEDGEMENT
One of the authors (H.S.) wishes to thank the I.W.O.N.U for a grant. J. Electroanal. Chem., 26 (1970) 299-305
DISSOCIATION CONSTANTS OF ITACONIC ACID
305
SUMMARY
The dissociation of itaconic acid was investigated potentiometrically at ionic strength / = 1 in NaC104 at 25.000 +_0.02°C in the concentration range 0-50 mM. The two dissociation constants were calculated by both a graphical and a computer method. The values reported are pKAI = 3.629 +_0.002 and PKA2=4.988 +0.001. For concentrations > 50 mM, polynuclear proton itaconate complexes are observed. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
G. BIEDERMANNAND L. G. SILLEN,Arkiv Kemi, 5 (1953) 425. M. YASUDA,K. YAMASAKIAND H. OHTAKI,Bull. Chem. Soc. Japan, 33 (1960) 8, 1067. S. RAMAMOORTHyAND M. SANTAPPA,Current Sci. India, 35 (1966) 6, 145. H. W. ASHTONAND J. R. PARTINGTON, Trans. Faraday Soc., 30 (1934) 598. A. NOYES,Z. Physik. Chem., 11 (1893) 495. G. SWARZENBACH,A. WILLI AND R. O. BACH, Helv. Chim. Acta, 30 (1947) 1303. J. C. SPEAKMAN,J. Chem. Soc., (1940) 855. H. T. S. BRITTON, Hydrogen Ions, Vol. 1, Chapman and Hall, London, 4th ed., 1955, p. 217. W. S. DUNNINGAND D. S. MARTIN,Report IS-822 (1964). H. THUN, F. VERBEEKAND W. VANDERLEEN,J. Inorg. Nucl. Chem., 29 (1967) 2109. F. J. C. ROSSOTTIAND H. ROSSOTTI, The Determination of Stability Constants, McGraw-Hill, London, 1961, p. 89. G. GRAN, Acta Chem. Scand., 4 (1950) 559; Analyst, 77 (1952) 661. A. S. BROWN, J. Am. Chem. Soc., 56 (1934) 646. I. GRENTHEAND D. R. WILLIAMS,Acta Chem. Scand., 21 (1967) 341. F. J. C. ROSSOT'rIAND H. S. ROSSOTTI,Acta Chem. Scand., 10 (1956) 957. W. KRAFT,Monatsh. Chem., 5 (1967) 1979.
J. Electroanal. Chem., 26 (1970) 299-305