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Thermodynamic stabilities of copper(II)-ethyl α-(phenyl)phenylpropioloyl-acetato complexes in dioxane-water media
J. inorg, nucl. Chem., 1973, Vol. 35, pp. 4199 4206. Pergamon Press. Printed in Great Britain.
THERMODYNAMIC STABILITIES OF COPPER(II)-ETHYL ~-(PHENYL) PHENYLPROPIOLOYLACETATO COMPLEXES IN DIOXANE-WATER MEDIA N. S. A L - N I A I M I and B. M. A L - S A A D I Department of Chemistry, Nuclear Research Institute, Tuwaitha, Baghdad, lraq
(Received 4 December 1972)
Abstract--The acid dissociation constant, K~, of ethyl ~-(phenyl)phenylpropioloylacetate is determined potentiometrically in 75 vol ~ dioxane-water solution at 30°C as a function of ionic strength (/~) in the range 0.02-0.10 in a sodium perchlorate medium. A value of pKo(# ~ 0) of 11.66 is calculated with the aid of an extended form of the Debye-Hiickel equation while a recalculation using reported values of 7 + gives a value of 11.85. This is in agreement with the value calculated from results obtained in very dilute solution. The stoichiometric stability constants of the complexes formed with copper(II) are determined as a function of # in the same range. Calculation of "thermodynamic" stability constants from these values using the Debye-Hiickel equation or using reported values of 7 + does not give consistent results. It is concluded that it is incorrect to perform such calculations on results obtained in such a medium having an ionic strength p >~ 0"02. The "thermodynamic" stability constants calculated from titration results in very dilute solution are log K~ = 11'69 and log K 2 = 8'95.
INTRODUCTION
STABILITYconstants of metal chelates are frequently determined in dioxane-water mixtures. "Thermodynamic" stability constants are often calculated from stoichiometric stability constants determined in 75 vol ~ dioxane-water solution of a fixed ionic strength[i-3]. Such interconversion can, in theory, be easily made provided that the activity coefficient (~) of each species is known throughout a series of measurements. Two approaches are used for the determination of a set of meaningful and comparable stability constants. The first is to keep the activity coefficient (?) of each species constant, which is done by carrying out all the measurements in a constant ionic medium made by the addition of a "neutral electrolyte". The second approach is to make all the measurements in solutions of low ionic strength for which the activity corrections can be calculated. The question as to which of the two approaches should be adopted in a particular study has received some attention[4, 5]. The constant ionic medium method is invaluable where a number of complicated equilibria R. M. Izzat, C. G. Haas, B. P. Block and W. C. Fernelius, J. phys. Chem. 58, 133 (1954). I. D. Chawla and C. R. Spillert, J. inorg, nucl. Chem. 30, 2717 (1968). B. R a o and H. B. Mathur, J. inorg, nucl. Chem. 33, 2919 (1971). F. J. C. Rossotti and H. Rossotti, The Determination o f Stability Constants, Chapter 2. McGraw-Hill, New York (1961). 5. C. H. Nancollas, Interactions in Electrolyte Solution. Elsevier, A m s t e r d a m (1960).
1. 2. 3. 4.
4199
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N.S. AL-NIAIMI and B. M. AL-SAADI
are involved, and different schools have tended to choose different media for their studies of metal complex formation[4]. It must be emphasized, however, that the calculated stability constants are directly comparable for different systems only when obtained in the same medium. For this reason there continues to be great interest in the calculation of activity coefficients in order that "thermodynamic" s'mbility constants can be obtained. The derivation of "thermodynamic" stability constants is made possible by suitable choice of the concentrations of the reactants, so that the number of complexes can be limited to one or two. The "thermodynamic" stability constants can be derived from a series of constants calculated for media of different ionic strengths with the aid of one of the extended forms of the Debye-Hiickel equation. The object of the present work was to investigate critically the determination of the "thermodynamic" acid dissociation constant of ethyl ct-(phenyl)phenylpropioloylacetate and of the "thermodynamic" stability constants of its complexes with copper(II). Potentiometric titration in 75 vol ~ dioxane-water solution at 30 _ 0.1°C was used. The two approaches mentioned above for the determination of "thermodynamic" constants have been adopted and the results are critically examined. The ligand chosen is one of a number of fl-keto-esters whose complexing abilities have been studied; those results will be published elsewhere. EXPERIMENTAL Chemicals Ethyl ~t-(Phenyl)phenylpropioloylacetate was prepared as described in the literature[6] Dioxane was purified as described by Vogel[7] and freshly used. Carbonate-free sodium hydroxide solution was prepared according to the method described by Vogel[8]. Copper perchlorate was prepared by dissolving spectroscopically pure copper metal in an excess of perchloric acid, which was evaporated to near dryness several times over a steam-bath. The product was recrystallized from water. A stock solution was prepared by dissolving the salt in doubly-distilled and boiled-out water with slight acidification by perchloric acid to suppress hydrolysis.
Titrations Titrations were performed using a Radiometer (PHM26C) pH-meter equipped with a glass electrode (G202B) and a saturated calomel electrode. The thermostated vessel of 50 ml capacity was tightly covered with a special electrode head through which passed the glass and calomel electrodes, the polyethylene stirrer rod, the nitrogen inlet tube and the delivery tube from the auto-burette. The auto-burette was a Radiometer instrument (ABUIb) connected with a burette unit (B150) of 2.5 ml capacity capable of delivering 0.001 ml of the titrant. The burette readings were checked by weighing the mercury delivered. In a typical titration 15 ml of dioxane solution of the ligand was transferred to the titration vessel, to which was added 5 ml of an aqueous solution of copper perchlorate containing the appropriate concentration of sodium perchlorate. The contraction upon mixing was experimentally determined and found to be 1'56 vol ~. The solution was mechanically stirred and a stream of nitrogen gas, purified from oxygen and carbon dioxide by the method of Albert and Serjeant[9], was bubbled through at such a rate that the bubbles could just be counted. A complete titration consisted of successive additions of 0'01 ml of the titrant. One minute after each addition the stirring motor was stopped and the pH-meter reading was taken. The titration was continued until the pH-meter reading could not be kept steady or the solution became 6. H. N. A1-Jallo and F. H. A1-Hajjar, J. chem. Soc. (C), 2056 (1970). 7. A. I. Vogel, Practical Organic Chemistry, 3rd Edn, p. 177. Longmans, London (1957). 8. A. I. Vogel, A Text-book of Quantitative Inorganic Chemistry, 3rd Edn, p. 239. Longmans, London (1964). 9. A. Albert and E. P. Serjeant, Ionization Constants of Weak Acids and Bases, p. 20. John Wiley, New York (1962).
Thermodynamic stability of copper(II) complexes
4201
heterogeneous. Each titration was repeated at least twice giving a reproducibility of + 0.01 pH units along the titration. The pH-meter readings were calibrated before, and checked after, each titration with 0.05 M potassium hydrogen phthalate aqueous solution and 0.01 M borax solution. RESULTS AND DISCUSSION
The pH-meter readings (B) in 75 vol ~ dioxane-water solution are converted to hydrogen ion concentrations [H + ] by means of the widely used empirical relationships of Van Uitert and Haas[10], namely: - l o g [ H +] = B + log U .
(1)
- l o g [ H + ] = B + log U ° + logT+
(2)
and
where Un is the correction factor, U ° is the correction factor at zero ionic strength and y + is the mean activity coefficient for the solvent composition and ionic strength for which B is read. The activity coefficients used are interpolated from the values of 7+ for hydrochloric acid[ill. In a thorough investigation values of Un were determined as a function of solvent composition and ionic medium and a value of log U ° = 1.08 ___0.01 was obtained for 75 vol ~ dioxane-water medium at 30°C[12]. For the acid dissociation constant of the ligand HA,
pK~ = -Iog[H +] + log [HA] [A-]
(3)
p r K a = pK a - 2 log 7___
(4)
and
where Ka and r K a are the stoichiometric and "thermodynamic" dissociation constants. At any point during the titration of a solution of the acid of an initial concentration [HA], with a base, [HA]
[A-]
[ H A J t - Con --
COH
,
(5)
where COH is the equivalent concentration of the base added. Combination of Eqs (1) and (3) gives, pK a = B +
[HA] [A-]
log UH + l o g - -
(6)
Values of p K a were determined in aqueous-dioxane solutions adjusted to have an ionic strength (#) of 0"02, 0.04, 0"06, 0"08 or 0.10 by addition of appropriate concentrations of sodium perchlorate by titrating the solution with a 0.294 M standard aqueous solution of sodium hydroxide. Values of pK, were computed from the experimental results of the titrations using Eqn (6). The results are given in Table I. 10. k. G. Van Uitert and C. G. Haas, J. Am. chem. Soe. 75, 45 (1953). 11. H. S. Harned and B. B. Owen, The Physical Chemistry oJ Electrolytic Solutions, p. 717. Reinhold. New York (1958). 12. B. M. A1-Saadi, M.Sc. Thesis, University of Baghdad, 1972.
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N. S. A L - N I A I M I and B. M. A L - S A A D I Table 1. p K , values of ethyl ct-(phenyl)phenylpropioloylacetate at various ionic strengths (#) in 75 vol ~ dioxa n e - w a t e r mixture at 30°C #
--
pK a
0"02 0"04 0"06 0'08 0"10
10"50 10"30 10"16 10"05 9'99
+ 0-03 + 0"04 + 0"03 + 0-03 __+0"04
The calculation of p r K a from these values of p K a was performed by two different methods. The first was by using Eqn (4) and the values of 7 - given in Table 2, as read from a curve drawn for interpolation from Harned and Owen's data. The value of prKa thus calculated is 11"86 _ 0"03. The second method was by using the extended Debye-Hiickel equation, namely log7+
I Z I Z E I A # 1/2 1 + BCII.t1/2 + cl't
=
(7)
2 A # 1/2
p K a + 1 + Ba]21/2 - p T K a -- C~
(8)
where A and B are functions of temperature and the dielectric constant of the medium, d is the minimum distance of approach of the oppositely charged ions without association. The constants A and B can be evaluated from the expressions given for nonaqueous media[13], viz., 1"82455 × 106 50.2904 x 108 A= ;B= ( D T ) 3/2
( D T ) 1/2
where D is the dielectric constant of the medium and T is the temperature in degrees Kelvin. For a 75 vol ~o dioxane-water medium, the value of D interpolated from the data of Harned and Owen* is 13.50 at 30°C, giving A = 6.969 and B = 0.7859. Equation (8) becomes, 13.938/./1/2 pK~ + 1 + 0"7859 d/~1/2 = P r K ~ - ct~,
(9)
which can be rewritten as W = p r K a - c1~. Table 2. Values ofT_+ as a function of/~ in 75 vol ~ dioxane-water at 30°C as interpolated from Harned and Owen's data[11]
- log 7 ___
0"02 0'68
0"04 0-78
0"06 0"85
0-08 t>90
*Ref. [11], p. 718. 13. W. J. H a m e r and S. F. Acree, J. Res. natn. Bur. Stand. 35, 381 (1945).
0" 10 0'93
T h e r m o d y n a m i c stability of copper(I1) complexes
4203
A plot of Wvs ~t should give a straight line with a slope of - c and an intercept of pT"K a at p -~ 0. The function W depends upon the value chosen for ~. A value of 10 )~ has been chosen for ~ in 75 vol ~o dioxane-water medium in similar studies [1 3]. In the present work several values for d have been chosen ranging from 5-10 A, and the corresponding plots of Wvs # are shown in Fig. 1. The results are best fitted to Eqn (8) when d = 6"5 ~ and c = 0 giving pK,(# --* 0) = 11-66. The possible range is 11.66_o. +o.11. This value is 0.2log unit different from the value calculated above according to Eqn (4) employing 7-+ values of Table 2. As pointed out by Guggenheim[14], there is a conceptual difficulty about the extrapolation to infinite dilution, so the above value of pK~(# ~ 0) should be accepted as an empirical fit to the results. Moreover, in 75 vol '~o dioxane-water medium, ionic association occurs in relatively dilute solutions* and consequently the value of 7 +- predicted by simple forms of Debye-Hfickel equation would deviate from the true values even at electrolyte concentrations much below the maximum value (0.1 M) taken in the present investigation. The acid dissociation constant of HA was also determined by titrating its solution with 0.294 M aqueous sodium hydroxide. At each point of the titration the mean ionic molarity was estimated and the corresponding value of log 7 + was read from the curve drawn for interpolation from Harned and Owen's data. The values of pTK, were calculated for each point of the titration and the average value of p r K , thus calculated was found to be 11.85 _+ 0.04. This value agrees remarkably well with that obtained by titrating solutions of constant ionic strength and computing prK a by means of values of log 7 ± interpolated from Harned and Owen's data. 12-2
12.0
j
o"
t l.8
oo=6.5 ~, 11.6 W 11.4 -
"
11-2
I1.0
I
0-02
I
0.04
I
0.06
J
0.08 ,U.
J
0.10
Fig. 1. Variation of Wwith the ionic strength. *Ref. [11], p. 472. 14. E. A. Guggenheim, Trans. Faraday Soc. 62, 2750 (1966).
I 0.12
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N. S. A L - N I A I M I a n d B. M. A L - S A A D I
The determination of the stoichiometric and "thermodynamic" stability constants of the complexes formed between the ligand HA and Cu(II) was investigated along the lines discussed above. For these complexes, log K 1 = log qa - 4 log y ±
(10)
and log K 2 =
log q2
--
2 log y__
(11)
where K a and K 2 a r e the "thermodynamic" and qa and q2 are the stoichiometric stepwise formation constants of the complexes CuA + and CuA2. To compute the values of the stability constants consider: h =
concentration of the ligand bound to the metal total concentration of the metal
For the present study where only the first two complexes have been shown to be important, [MA +] + 2[MA2J h = [M2+ ] + [MA+ ] + [MA2]
(12)
or
ill[A-] + 2f12[A-] 2 = 1 + flaEA-] + fl2EA-] 2
(13)
where fll = ql and
qlq2.
f12 =
Also, =
[ H A ] t - [HA] CM
-
[A-]
(14)
but, [HA] = bound hydrogen = total hydrogen--reacted hydrogen--dissociated hydrogen = [HAl t
+
CHCIO . -- Coil
--
[H +] + [ O H - ]
(15)
where Cnoo, is the concentration of perchloric acid present initially. Combining Eqns (14) and (15) we have, COH -- CHCIO4+ [H +] - [OH-] - [A-] CM
T h e r m o d y n a m i c stability of copper(II) complexes
4205
and since [ O H - ] and [A-] are very small compared to the other terms in the numerator, we have h = C°H - CHCIO4+ [H+] CM
(16)
Similarly, [A-] =
[HAIr +
CHCIO 4 -- COIl +
Ka_I[H+ ]
[H+]
(17)
The quantities [HA]t, Cnclo,, Con and CM were calculated taking into account the 1-56 vol ~ contraction upon mixing 75 volumes of dioxane with 25 volumes of water. Rearranging Eqn (13) we have, h --- f l , ( l - h ) [ A
] + fl2(2 - h ) [ A - ] 2.
(18)
Computation of the values of/~1 and f12 from the experimental values of h and [A-] was made from Eqn (18) using a modified least squares technique and a computer programme[12]. In the first method used the solution titrated with 0.294 M N a O H solution had initial concentrations of Cu(II) = 1"025 × 10-3 M, of HC10 4 = 0.44 × 10-3 M and of HA = 4 x 10-3 M. The ionic strength (#) was initially adjusted to the required fixed values of 0'02, 0.04, 0.06, 0-08 or 0.10 using sodium perchlorate. During the titration the ionic strength remains almost constant. The computed values of the stoichiometric stability constants are given in Table 3. Rao and Mathur[3] have calculated the "thermodynamic" stability constants of 3-diketonato complexes of Cu(II) and Ni(II) from stoichiometric constants ql and q2 determined in 75 vol ~ dioxane-water solution of ionic strength # = 0.02, using equations similar to (10) and (11). In their calculation of log 7-+ they used the Debye Hiickel equation of the form shown in Eqn (7) and by choosing a value of d = 10 ~. and c = 0. Other earlier workers have adopted similar approximations[l, 2]. In the present investigation values of K 1 and K 2 are calculated from the values of ql and q2 using Eqns (10) and (11) and values of log 7 + either interpolated from Harned and Owen's data or calculated from the Debye-Htickel equation as shown in Eqn (7) with values of d = 10 A and c = 0. The results of such calculations are shown in Table 4. The calculated values of log K~ and log K 2 are not constant but vary with the ionic strength, although the variation in the calculated values of log K 2 is not great. The use of the extended form of the Debye-Htickel equation in the same way as discussed in the calculation o f p r K , did not give meaningful results either. Consequently these methods of calculating "thermodynamic" stability constants are not accurate Table 3. Stoichiometric stability constants of the complexes Cu(ll)-ethyl ~-Iphenyl)phenylpropioloylacetate at various ionic strengths (/~) in 75 vol % dioxane water at 30°C # log q 1 log q2
0"02 9" 14 7"26
0.04 9"06 7"18
0"06 8"94 7'12
0"08 8"82 7"08
0" 10 8"74 6'93
N. S. AL-NIA1MI and B. M. AL-SAADI
4206
Table 4. Calculations of the "thermodynamic" stability constants K~ and K 2 from the stoichiometric constants ql and q2 measured at various ionic strengths (#) of the complexes Cu(II)-ethyl ~-(phenyl)phenyipropioloylacetatein 75 vol ~ dioxane at 30°C p
log ql
log K*
log KI"~
log q2
log K~
log K2"~
0"02 0-04 0'06 0"08 0"10
9"14 9"06 8"94 8-82 8"74
11"86 12"18 12'34 12"42 12"46
11"06 11"26 11'30 11"42 11"46
7.26 7"18 7"12 7-08 6.93
8"62 8.74 8.82 8-88 8"79
8"22 8-22 8"30 8'31 8"30
* log y_+ read from a curve drawn from an interpolation of Harned and Owen's data. t log y _+ calculated using the extended Debye-Hiickel equations with a° = 10 A and c = 0. and do not give acceptable results. The reason for this is that in a medium of low dielectric constant, such as the d i o x a n e - w a t e r mixture used, the higher order terms of the inter-ionic attraction theory given by La Mer's et al.[15] extension of the Debye-HiJckel theory must be taken into consideration in the extrapolation even at electrolyte concentration as low as 0-002 M.* The assumption made by many workers that log y + (2 : 1) electrolyte = 2 log y ___ (1 : 1) electrolyte,
(19)
which is deduced from the simple D e b y e - H i i c k e l equation, can therefore only be valid at very low concentrations of the electrolyte. Also, since Eqn (19) is the basis of deducing Eqn (10), then the latter cannot be truly valid at electrolyte concentrations much greater than 0.002 M. This explains the inconsistency in the calculated results of log K1 given in Table 4. On the other hand, Eqn (19) is not utilized in the derivation of Eqn (11). This may explain the lesser variation in the calculated values of log K 2 given in Table 4. One may conclude that it is incorrect to calculate "thermodynamic" stability constants from stoichiometric values determined in 75 vol ~ d i o x a n e water media from data at ionic strengths of 0-02 or above as has been done by some workers. It is better to report the stoichiometric stability constants together with concentration and the nature of the salt background. An alternative method for the determination of "thermodynamic" stability constants was the titration of 20 ml solution containing an exact initial concentration of copper perchlorate of about 1 x 1 0 - 3 M and an initial concentration of 4 x 1 0 - 3 M of the ligand with no supporting electrolyte. It was found that for the first few points in the titration, # = 0.0026 and log V+ = -0"33 as read from the curve of Harned and Owen's data, followed by p = 0.002 and l o g T + = -0.34. Throughout the rest of the titration the variation in the value of log 7 + was very small. Consequently one could assume that the solutions were of very low ionic strength in the range # = 0.0020-0.0026 and that log 7-+ had an almost fixed value. The stoichiometric stability constants determined in such a medium could then be confidently converted to "thermodynamic" constants using Eqns (10) and (11) and the fixed known value of log 7 - . This was done and the values determined are log ql = 10.23, log K 1 = 11.69, log q2 = 8-27 and log K2 = 8.95. *Ref. [11], p. 458. 15. V. K. La Mer, T. H. Gronwall and L. J. Grieff,J. phys. Chem. 35, 2245 (1931).
THERMODYNAMIC STABILITIES OF COPPER(II)-ETHYL ~-(PHENYL) PHENYLPROPIOLOYLACETATO COMPLEXES IN DIOXANE-WATER MEDIA N. S. A L - N I A I M I and B. M. A L - S A A D I Department of Chemistry, Nuclear Research Institute, Tuwaitha, Baghdad, lraq
(Received 4 December 1972)
Abstract--The acid dissociation constant, K~, of ethyl ~-(phenyl)phenylpropioloylacetate is determined potentiometrically in 75 vol ~ dioxane-water solution at 30°C as a function of ionic strength (/~) in the range 0.02-0.10 in a sodium perchlorate medium. A value of pKo(# ~ 0) of 11.66 is calculated with the aid of an extended form of the Debye-Hiickel equation while a recalculation using reported values of 7 + gives a value of 11.85. This is in agreement with the value calculated from results obtained in very dilute solution. The stoichiometric stability constants of the complexes formed with copper(II) are determined as a function of # in the same range. Calculation of "thermodynamic" stability constants from these values using the Debye-Hiickel equation or using reported values of 7 + does not give consistent results. It is concluded that it is incorrect to perform such calculations on results obtained in such a medium having an ionic strength p >~ 0"02. The "thermodynamic" stability constants calculated from titration results in very dilute solution are log K~ = 11'69 and log K 2 = 8'95.
INTRODUCTION
STABILITYconstants of metal chelates are frequently determined in dioxane-water mixtures. "Thermodynamic" stability constants are often calculated from stoichiometric stability constants determined in 75 vol ~ dioxane-water solution of a fixed ionic strength[i-3]. Such interconversion can, in theory, be easily made provided that the activity coefficient (~) of each species is known throughout a series of measurements. Two approaches are used for the determination of a set of meaningful and comparable stability constants. The first is to keep the activity coefficient (?) of each species constant, which is done by carrying out all the measurements in a constant ionic medium made by the addition of a "neutral electrolyte". The second approach is to make all the measurements in solutions of low ionic strength for which the activity corrections can be calculated. The question as to which of the two approaches should be adopted in a particular study has received some attention[4, 5]. The constant ionic medium method is invaluable where a number of complicated equilibria R. M. Izzat, C. G. Haas, B. P. Block and W. C. Fernelius, J. phys. Chem. 58, 133 (1954). I. D. Chawla and C. R. Spillert, J. inorg, nucl. Chem. 30, 2717 (1968). B. R a o and H. B. Mathur, J. inorg, nucl. Chem. 33, 2919 (1971). F. J. C. Rossotti and H. Rossotti, The Determination o f Stability Constants, Chapter 2. McGraw-Hill, New York (1961). 5. C. H. Nancollas, Interactions in Electrolyte Solution. Elsevier, A m s t e r d a m (1960).
1. 2. 3. 4.
4199
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N.S. AL-NIAIMI and B. M. AL-SAADI
are involved, and different schools have tended to choose different media for their studies of metal complex formation[4]. It must be emphasized, however, that the calculated stability constants are directly comparable for different systems only when obtained in the same medium. For this reason there continues to be great interest in the calculation of activity coefficients in order that "thermodynamic" s'mbility constants can be obtained. The derivation of "thermodynamic" stability constants is made possible by suitable choice of the concentrations of the reactants, so that the number of complexes can be limited to one or two. The "thermodynamic" stability constants can be derived from a series of constants calculated for media of different ionic strengths with the aid of one of the extended forms of the Debye-Hiickel equation. The object of the present work was to investigate critically the determination of the "thermodynamic" acid dissociation constant of ethyl ct-(phenyl)phenylpropioloylacetate and of the "thermodynamic" stability constants of its complexes with copper(II). Potentiometric titration in 75 vol ~ dioxane-water solution at 30 _ 0.1°C was used. The two approaches mentioned above for the determination of "thermodynamic" constants have been adopted and the results are critically examined. The ligand chosen is one of a number of fl-keto-esters whose complexing abilities have been studied; those results will be published elsewhere. EXPERIMENTAL Chemicals Ethyl ~t-(Phenyl)phenylpropioloylacetate was prepared as described in the literature[6] Dioxane was purified as described by Vogel[7] and freshly used. Carbonate-free sodium hydroxide solution was prepared according to the method described by Vogel[8]. Copper perchlorate was prepared by dissolving spectroscopically pure copper metal in an excess of perchloric acid, which was evaporated to near dryness several times over a steam-bath. The product was recrystallized from water. A stock solution was prepared by dissolving the salt in doubly-distilled and boiled-out water with slight acidification by perchloric acid to suppress hydrolysis.
Titrations Titrations were performed using a Radiometer (PHM26C) pH-meter equipped with a glass electrode (G202B) and a saturated calomel electrode. The thermostated vessel of 50 ml capacity was tightly covered with a special electrode head through which passed the glass and calomel electrodes, the polyethylene stirrer rod, the nitrogen inlet tube and the delivery tube from the auto-burette. The auto-burette was a Radiometer instrument (ABUIb) connected with a burette unit (B150) of 2.5 ml capacity capable of delivering 0.001 ml of the titrant. The burette readings were checked by weighing the mercury delivered. In a typical titration 15 ml of dioxane solution of the ligand was transferred to the titration vessel, to which was added 5 ml of an aqueous solution of copper perchlorate containing the appropriate concentration of sodium perchlorate. The contraction upon mixing was experimentally determined and found to be 1'56 vol ~. The solution was mechanically stirred and a stream of nitrogen gas, purified from oxygen and carbon dioxide by the method of Albert and Serjeant[9], was bubbled through at such a rate that the bubbles could just be counted. A complete titration consisted of successive additions of 0'01 ml of the titrant. One minute after each addition the stirring motor was stopped and the pH-meter reading was taken. The titration was continued until the pH-meter reading could not be kept steady or the solution became 6. H. N. A1-Jallo and F. H. A1-Hajjar, J. chem. Soc. (C), 2056 (1970). 7. A. I. Vogel, Practical Organic Chemistry, 3rd Edn, p. 177. Longmans, London (1957). 8. A. I. Vogel, A Text-book of Quantitative Inorganic Chemistry, 3rd Edn, p. 239. Longmans, London (1964). 9. A. Albert and E. P. Serjeant, Ionization Constants of Weak Acids and Bases, p. 20. John Wiley, New York (1962).
Thermodynamic stability of copper(II) complexes
4201
heterogeneous. Each titration was repeated at least twice giving a reproducibility of + 0.01 pH units along the titration. The pH-meter readings were calibrated before, and checked after, each titration with 0.05 M potassium hydrogen phthalate aqueous solution and 0.01 M borax solution. RESULTS AND DISCUSSION
The pH-meter readings (B) in 75 vol ~ dioxane-water solution are converted to hydrogen ion concentrations [H + ] by means of the widely used empirical relationships of Van Uitert and Haas[10], namely: - l o g [ H +] = B + log U .
(1)
- l o g [ H + ] = B + log U ° + logT+
(2)
and
where Un is the correction factor, U ° is the correction factor at zero ionic strength and y + is the mean activity coefficient for the solvent composition and ionic strength for which B is read. The activity coefficients used are interpolated from the values of 7+ for hydrochloric acid[ill. In a thorough investigation values of Un were determined as a function of solvent composition and ionic medium and a value of log U ° = 1.08 ___0.01 was obtained for 75 vol ~ dioxane-water medium at 30°C[12]. For the acid dissociation constant of the ligand HA,
pK~ = -Iog[H +] + log [HA] [A-]
(3)
p r K a = pK a - 2 log 7___
(4)
and
where Ka and r K a are the stoichiometric and "thermodynamic" dissociation constants. At any point during the titration of a solution of the acid of an initial concentration [HA], with a base, [HA]
[A-]
[ H A J t - Con --
COH
,
(5)
where COH is the equivalent concentration of the base added. Combination of Eqs (1) and (3) gives, pK a = B +
[HA] [A-]
log UH + l o g - -
(6)
Values of p K a were determined in aqueous-dioxane solutions adjusted to have an ionic strength (#) of 0"02, 0.04, 0"06, 0"08 or 0.10 by addition of appropriate concentrations of sodium perchlorate by titrating the solution with a 0.294 M standard aqueous solution of sodium hydroxide. Values of pK, were computed from the experimental results of the titrations using Eqn (6). The results are given in Table I. 10. k. G. Van Uitert and C. G. Haas, J. Am. chem. Soe. 75, 45 (1953). 11. H. S. Harned and B. B. Owen, The Physical Chemistry oJ Electrolytic Solutions, p. 717. Reinhold. New York (1958). 12. B. M. A1-Saadi, M.Sc. Thesis, University of Baghdad, 1972.
4202
N. S. A L - N I A I M I and B. M. A L - S A A D I Table 1. p K , values of ethyl ct-(phenyl)phenylpropioloylacetate at various ionic strengths (#) in 75 vol ~ dioxa n e - w a t e r mixture at 30°C #
--
pK a
0"02 0"04 0"06 0'08 0"10
10"50 10"30 10"16 10"05 9'99
+ 0-03 + 0"04 + 0"03 + 0-03 __+0"04
The calculation of p r K a from these values of p K a was performed by two different methods. The first was by using Eqn (4) and the values of 7 - given in Table 2, as read from a curve drawn for interpolation from Harned and Owen's data. The value of prKa thus calculated is 11"86 _ 0"03. The second method was by using the extended Debye-Hiickel equation, namely log7+
I Z I Z E I A # 1/2 1 + BCII.t1/2 + cl't
=
(7)
2 A # 1/2
p K a + 1 + Ba]21/2 - p T K a -- C~
(8)
where A and B are functions of temperature and the dielectric constant of the medium, d is the minimum distance of approach of the oppositely charged ions without association. The constants A and B can be evaluated from the expressions given for nonaqueous media[13], viz., 1"82455 × 106 50.2904 x 108 A= ;B= ( D T ) 3/2
( D T ) 1/2
where D is the dielectric constant of the medium and T is the temperature in degrees Kelvin. For a 75 vol ~o dioxane-water medium, the value of D interpolated from the data of Harned and Owen* is 13.50 at 30°C, giving A = 6.969 and B = 0.7859. Equation (8) becomes, 13.938/./1/2 pK~ + 1 + 0"7859 d/~1/2 = P r K ~ - ct~,
(9)
which can be rewritten as W = p r K a - c1~. Table 2. Values ofT_+ as a function of/~ in 75 vol ~ dioxane-water at 30°C as interpolated from Harned and Owen's data[11]
- log 7 ___
0"02 0'68
0"04 0-78
0"06 0"85
0-08 t>90
*Ref. [11], p. 718. 13. W. J. H a m e r and S. F. Acree, J. Res. natn. Bur. Stand. 35, 381 (1945).
0" 10 0'93
T h e r m o d y n a m i c stability of copper(I1) complexes
4203
A plot of Wvs ~t should give a straight line with a slope of - c and an intercept of pT"K a at p -~ 0. The function W depends upon the value chosen for ~. A value of 10 )~ has been chosen for ~ in 75 vol ~o dioxane-water medium in similar studies [1 3]. In the present work several values for d have been chosen ranging from 5-10 A, and the corresponding plots of Wvs # are shown in Fig. 1. The results are best fitted to Eqn (8) when d = 6"5 ~ and c = 0 giving pK,(# --* 0) = 11-66. The possible range is 11.66_o. +o.11. This value is 0.2log unit different from the value calculated above according to Eqn (4) employing 7-+ values of Table 2. As pointed out by Guggenheim[14], there is a conceptual difficulty about the extrapolation to infinite dilution, so the above value of pK~(# ~ 0) should be accepted as an empirical fit to the results. Moreover, in 75 vol '~o dioxane-water medium, ionic association occurs in relatively dilute solutions* and consequently the value of 7 +- predicted by simple forms of Debye-Hfickel equation would deviate from the true values even at electrolyte concentrations much below the maximum value (0.1 M) taken in the present investigation. The acid dissociation constant of HA was also determined by titrating its solution with 0.294 M aqueous sodium hydroxide. At each point of the titration the mean ionic molarity was estimated and the corresponding value of log 7 + was read from the curve drawn for interpolation from Harned and Owen's data. The values of pTK, were calculated for each point of the titration and the average value of p r K , thus calculated was found to be 11.85 _+ 0.04. This value agrees remarkably well with that obtained by titrating solutions of constant ionic strength and computing prK a by means of values of log 7 ± interpolated from Harned and Owen's data. 12-2
12.0
j
o"
t l.8
oo=6.5 ~, 11.6 W 11.4 -
"
11-2
I1.0
I
0-02
I
0.04
I
0.06
J
0.08 ,U.
J
0.10
Fig. 1. Variation of Wwith the ionic strength. *Ref. [11], p. 472. 14. E. A. Guggenheim, Trans. Faraday Soc. 62, 2750 (1966).
I 0.12
4204
N. S. A L - N I A I M I a n d B. M. A L - S A A D I
The determination of the stoichiometric and "thermodynamic" stability constants of the complexes formed between the ligand HA and Cu(II) was investigated along the lines discussed above. For these complexes, log K 1 = log qa - 4 log y ±
(10)
and log K 2 =
log q2
--
2 log y__
(11)
where K a and K 2 a r e the "thermodynamic" and qa and q2 are the stoichiometric stepwise formation constants of the complexes CuA + and CuA2. To compute the values of the stability constants consider: h =
concentration of the ligand bound to the metal total concentration of the metal
For the present study where only the first two complexes have been shown to be important, [MA +] + 2[MA2J h = [M2+ ] + [MA+ ] + [MA2]
(12)
or
ill[A-] + 2f12[A-] 2 = 1 + flaEA-] + fl2EA-] 2
(13)
where fll = ql and
qlq2.
f12 =
Also, =
[ H A ] t - [HA] CM
-
[A-]
(14)
but, [HA] = bound hydrogen = total hydrogen--reacted hydrogen--dissociated hydrogen = [HAl t
+
CHCIO . -- Coil
--
[H +] + [ O H - ]
(15)
where Cnoo, is the concentration of perchloric acid present initially. Combining Eqns (14) and (15) we have, COH -- CHCIO4+ [H +] - [OH-] - [A-] CM
T h e r m o d y n a m i c stability of copper(II) complexes
4205
and since [ O H - ] and [A-] are very small compared to the other terms in the numerator, we have h = C°H - CHCIO4+ [H+] CM
(16)
Similarly, [A-] =
[HAIr +
CHCIO 4 -- COIl +
Ka_I[H+ ]
[H+]
(17)
The quantities [HA]t, Cnclo,, Con and CM were calculated taking into account the 1-56 vol ~ contraction upon mixing 75 volumes of dioxane with 25 volumes of water. Rearranging Eqn (13) we have, h --- f l , ( l - h ) [ A
] + fl2(2 - h ) [ A - ] 2.
(18)
Computation of the values of/~1 and f12 from the experimental values of h and [A-] was made from Eqn (18) using a modified least squares technique and a computer programme[12]. In the first method used the solution titrated with 0.294 M N a O H solution had initial concentrations of Cu(II) = 1"025 × 10-3 M, of HC10 4 = 0.44 × 10-3 M and of HA = 4 x 10-3 M. The ionic strength (#) was initially adjusted to the required fixed values of 0'02, 0.04, 0.06, 0-08 or 0.10 using sodium perchlorate. During the titration the ionic strength remains almost constant. The computed values of the stoichiometric stability constants are given in Table 3. Rao and Mathur[3] have calculated the "thermodynamic" stability constants of 3-diketonato complexes of Cu(II) and Ni(II) from stoichiometric constants ql and q2 determined in 75 vol ~ dioxane-water solution of ionic strength # = 0.02, using equations similar to (10) and (11). In their calculation of log 7-+ they used the Debye Hiickel equation of the form shown in Eqn (7) and by choosing a value of d = 10 ~. and c = 0. Other earlier workers have adopted similar approximations[l, 2]. In the present investigation values of K 1 and K 2 are calculated from the values of ql and q2 using Eqns (10) and (11) and values of log 7 + either interpolated from Harned and Owen's data or calculated from the Debye-Htickel equation as shown in Eqn (7) with values of d = 10 A and c = 0. The results of such calculations are shown in Table 4. The calculated values of log K~ and log K 2 are not constant but vary with the ionic strength, although the variation in the calculated values of log K 2 is not great. The use of the extended form of the Debye-Htickel equation in the same way as discussed in the calculation o f p r K , did not give meaningful results either. Consequently these methods of calculating "thermodynamic" stability constants are not accurate Table 3. Stoichiometric stability constants of the complexes Cu(ll)-ethyl ~-Iphenyl)phenylpropioloylacetate at various ionic strengths (/~) in 75 vol % dioxane water at 30°C # log q 1 log q2
0"02 9" 14 7"26
0.04 9"06 7"18
0"06 8"94 7'12
0"08 8"82 7"08
0" 10 8"74 6'93
N. S. AL-NIA1MI and B. M. AL-SAADI
4206
Table 4. Calculations of the "thermodynamic" stability constants K~ and K 2 from the stoichiometric constants ql and q2 measured at various ionic strengths (#) of the complexes Cu(II)-ethyl ~-(phenyl)phenyipropioloylacetatein 75 vol ~ dioxane at 30°C p
log ql
log K*
log KI"~
log q2
log K~
log K2"~
0"02 0-04 0'06 0"08 0"10
9"14 9"06 8"94 8-82 8"74
11"86 12"18 12'34 12"42 12"46
11"06 11"26 11'30 11"42 11"46
7.26 7"18 7"12 7-08 6.93
8"62 8.74 8.82 8-88 8"79
8"22 8-22 8"30 8'31 8"30
* log y_+ read from a curve drawn from an interpolation of Harned and Owen's data. t log y _+ calculated using the extended Debye-Hiickel equations with a° = 10 A and c = 0. and do not give acceptable results. The reason for this is that in a medium of low dielectric constant, such as the d i o x a n e - w a t e r mixture used, the higher order terms of the inter-ionic attraction theory given by La Mer's et al.[15] extension of the Debye-HiJckel theory must be taken into consideration in the extrapolation even at electrolyte concentration as low as 0-002 M.* The assumption made by many workers that log y + (2 : 1) electrolyte = 2 log y ___ (1 : 1) electrolyte,
(19)
which is deduced from the simple D e b y e - H i i c k e l equation, can therefore only be valid at very low concentrations of the electrolyte. Also, since Eqn (19) is the basis of deducing Eqn (10), then the latter cannot be truly valid at electrolyte concentrations much greater than 0.002 M. This explains the inconsistency in the calculated results of log K1 given in Table 4. On the other hand, Eqn (19) is not utilized in the derivation of Eqn (11). This may explain the lesser variation in the calculated values of log K 2 given in Table 4. One may conclude that it is incorrect to calculate "thermodynamic" stability constants from stoichiometric values determined in 75 vol ~ d i o x a n e water media from data at ionic strengths of 0-02 or above as has been done by some workers. It is better to report the stoichiometric stability constants together with concentration and the nature of the salt background. An alternative method for the determination of "thermodynamic" stability constants was the titration of 20 ml solution containing an exact initial concentration of copper perchlorate of about 1 x 1 0 - 3 M and an initial concentration of 4 x 1 0 - 3 M of the ligand with no supporting electrolyte. It was found that for the first few points in the titration, # = 0.0026 and log V+ = -0"33 as read from the curve of Harned and Owen's data, followed by p = 0.002 and l o g T + = -0.34. Throughout the rest of the titration the variation in the value of log 7 + was very small. Consequently one could assume that the solutions were of very low ionic strength in the range # = 0.0020-0.0026 and that log 7-+ had an almost fixed value. The stoichiometric stability constants determined in such a medium could then be confidently converted to "thermodynamic" constants using Eqns (10) and (11) and the fixed known value of log 7 - . This was done and the values determined are log ql = 10.23, log K 1 = 11.69, log q2 = 8-27 and log K2 = 8.95. *Ref. [11], p. 458. 15. V. K. La Mer, T. H. Gronwall and L. J. Grieff,J. phys. Chem. 35, 2245 (1931).