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Acid-base equilibria in aqueous solution of cis-bis(trimethylphosphine)platinum(II) dinitrate at 25 °C, 0.2 M ionic strength. A potentiometric study
Talanta ELSEVIER
Talanta 43 ( 1996) 99 I 1000
Acid-base equilibria in aqueous solution of cis-bis(trimethylphosphine)platinum(II) dinitrate at 25”C, 0.2 M ionic strength. A potentiometric study Carlo Mac&*, Depnrtnw~r
of lnorganic~.
Bruno Longato,
Mrrullor~c~rri~~
mrci .4nulyti~ul
Guendalina C/wmtr~~.
Trovb,
G. Giorgio
C~~~irer.sit~ of’ Pudo~cr,
Via Marsolo
Bombi
I, I-35131
Pcrdocu. IIUIJ,
Received I August 1995; revised 18 October 1995: accepted I4 November 1995
Abstract
Acid-base equilibria in aqueoussolutionsof ci.\-bis(trimethylphosphine)platinum(II)dinitrate at 25°C. 0.2 M ionic strength (KNO,), have beeninvestigatedby potentiometry with a glass electrode. The procedure consisted of multiple addition of the investigatedanalyte to a supportingelectrolyte solution (“multiple sampleaddition”) and subsequent titration with strong base.For the treatment of potentiometric multiple sampleaddition data, a new linearization procedure. suitablefor an acid dissociationequilibrium whoseproduct dimerizes.has beendevisedand tested,The potentiometric results have been interpreted with the support of NMR data. By dissociationof the first acidic function of the solute diaquo cation. ci.s-[(PMe,)2Pt(OH2),]1 ’ . a dimeric amphoiite. cis-[(PMe,)2Pt(Lc-OH)],’A . is quantitatively formed which. in turn. can be converted into the di-hydroxo derivative ci.c-(PMe,),Pt(OH)2. The two acid dissociationstepsinvolving two molecules of solute and condensation of ampholyte have PK,,,~, = 3.89 and pK;,:,,, = 22.17. K~JWJJ~Y:
Cisplatin complexes:Acidity constant: Potentiometry: Linearized an&e addition __~~___________
I. Introduction
water molecules:
The study of the aqueous chemistry of platinum complexes has been stimulated by its relevance to the anticancer properties of cisplatin, cis(NH,),PtCl,. When the removal of the halide ligands with silver salts from L,PtCl, (L = Ndonor ligand) is carried out in water, the diaquo complex c*is-[L,Pt( H,O),]’ + is formed, which behaves as a diprotic acid through the coordinated
cis-[L,Pt(H,O),]‘+
* Correspondq
author
$ cis-[L,Pt(OH)(H,O)] ck-[L,Pt(OH)(
++ H+
H,O)] + G+ck-[L,Pt(OH),]
(1) ++ H+ (2)
The values of the relative acidity constants have been determined for a number of N-donor ligands, L, such as ammonia [l], ethylenediamine (en) [2.3], and 1.2-diaminocyclohexene [4].
0039-9130/96 $15.00 C 1996 Elsevier Science B.V. ,411right5 reserved SSDI 00?9-914Ol95)01822-0
The aquohydroxo species resulting from reaction (I) can undergo the oligomerization reaction 11cis-[LZPt(OH)(H,O)]
+
+ L.iS-[L2Pt(/l-OH)],,”
- + 12H,O
(3)
with the formation of polynuclear hydroxocomplexes. Generally the dinuclear and trinuclear derivatives (n = 2 and 3) are formed [5-81 but, in the case of the Pt(en) system, even the tetranuclear complex has been structurally characterized [91. In contrast, despite the huge number of phosphino complexes of platinum(II). to our knowledge no data on the acidity of water molecules in systems of the type [L,Pt(H20),,,]’ + , where L is a P-donor atom of a tertiary phosphine, have been reported. We have shown that the water soluble cis-( PMe,),Pt( NO,), (Me = CH,) complex. by neutralization of the diaquo complex, yields quantitatively the dinuclear species with bridging hydroxo ligands, cis-[(PMe,)2Pt(p-OH)]&NOi)Z (determined from X-ray analysis of an isolated single-crystal) [lo] which, by further addition of strong base, can be converted into the dihydroxo derivative cis-(PMe,)zPt(OH), [l 11. In this paper, the constants of the proton dissociation equilibrium of the solute diaquo cation with formation of the dimeric conjugate base 2cis-[( PMel),Pt(OH,),]’
+
Z$ cir-[(PMe,),Pt(jl-OH)],‘+
+ 3H + + 2H,O (4)
and of the further
deprotonation
cis-[(PMe,)zPt(p-OH)],’ $2
2. Experimental
cis-(PMe,&Pt(OH)?
equibilrium
+ + 2H10 + 2H *
(5)
have been determined at 25”C, 0.2 M ionic strength, by potentiometric multiple analyte addition and subsequent titration with strong base. For this purpose, a new procedure for the treatment of the analyte addition data using linear functions has been devised and tested. The potentiometric findings have been interpreted with the support of NMR measurements.
C’is-bis( trimethylphosphine)platinum(II) dinitrate was prepared as previously reported [lo]. The {‘H; “P NMR data were obtained with a Jeol 90Q instrument operating at 36.23 MHz, using 5 mm tubes with a coaxial capillary for the lock (D,O). The chemical shifts, in ppm, are referred to external H,PO, (85%). Different amounts of standard HNO, or NaOH solutions were added to 0.3 ml aliquots of 0.135 M aqueous solution of c-is-(PMe,),Pt(NO,), in an NMR tube at room temperature. The tube was quickly transferred into the NMR probe at 27°C and the spectrum was obtained within 10 min.
A glass cell (IO ml total volume), provided with a thermostatic jacket and a tight cover for inserting the electrodes, temperature probe and nitrogen inlet. was used as the container for the measured solution, which was magnetically stirred. Motor-driven microburettes (MicroBUR 2030, Crison, Barcelona) equipped with 1 ml Hamilton syringes (0.4 /ll resolution) were used for the additions of reactants. The additions were managed with a potentiometric titrator Crison MicroTT 2050. The e.m.f. of a cell composed of a pH glass electrode (Ingold type 10 265 3042) and a Ag: AgCl reference electrode in 3 M KC1 with 1 M KNO, salt bridge and sleeve junction (Ingold type 10 373 3145) was measured with 0.1 mV resolution during the additions. A data file was created by the titrator on a PC for each part of an experiment. 2.22. Retrgrnts Analytical or higher grade (e.g. Merck Suprapur) reagents and freshly prepared ultrapure water (MilliQ-Plus” grade) were used in all potentiometric experiments.
993
22.3. Proceduw 10 ml of 0.20 M potassium nitrate were used as the supporting solution in each experiment. The electrode was firstly calibrated in the acidic pH range of principal interest (pH 4.1-3.4) by multiple constant addition (10 x 100.0 itl) of standard 0.01 M strong acid in 0.19 M potassium nitrate; the calibration was completed in the basic range by titration via multiple constant addition (20 x 50.0 /tl) of standard 0.02 M sodium hydroxide in 0.18 M potassium nitrate. After careful washing, the cell was again filled with 10 ml of supporting electrolyte solution and multiple addition was performed via 14 additions (increasing in four steps from 20.0 to 100.0 ~1, for a total added volume of 0.8 ml) of 7.62 x 10e3 M solution prepared by dissolving a weighed amount of cis-bis(trimethylphosphine)platinum(II) dinitrate in ultrapure water. Thereafter. the acid was titrated by multiple constant addition of standard 0.02 M sodium hydroxide in 0.18 M potassium nitrate. The cell was thermostated at 25 k O.l”C throughout all experiments.
2.2.4. Culculutions Calibration allowed the experimental e.m.f. data of the additiontitration experiments to be converted to values of hydronium ion concentration. Thereby, concentration constants at constant ionic strength were calculated. The analyte addition data were initially linearized using Eq. (11) (see Section 3) for the determination of a first-approximation value of the first acidity constant at known analyte concentration C; Eq. (15) was also tested for the simultaneous determination of C. The data from the subsequent titration were used, together with the analyte addition data. to refine the value of the first acidity constant and to obtain the value of the second one via generalized (non-linear) leastsquares fitting, using a home computer program based on the pit-mapping method
1121.
3. Theory 3.1. Liiwurizution of’potmtiometric multiple addition qf’u tceuk ucid dinzerizing ujier dissociution Acidity constants are most commonly determined by pH-metric titration. By treatment of the titration data with existing generalized leastsquares computer programs, other experimental parameters (such as titrated acid concentration, solvent autoprotolysis constant, glass electrode calibration parameters) can be optimized simultaneously with the target acidity constant(s) [12171. For weak monoprotic acids. it has been shown [18] that pH-metric multiple analyte addition provides a very useful complement to titration data. If the concentration of acid to be titrated with strong base is built-up by multiple addition of relatively concentrated analyte, the number of measurements in each experiment is increased in a more significant way than by crowding the titration points. This opportunity can be particularly appreciated when only a small amount of analyte is available, as it was in the present research. For the separate or simultaneous determination of acidity constant and analyte concentration, the general titration equation relating the measured pH to the added titrant volume can be transformed into several forms of linear equations, each one making use of different auxiliary variables and including in the linear parameters either or both of the analytical parameters [19]. However, the linear transformation may produce a strong correlation between the relevant auxiliary variables and, in general. it destroys the Gaussian distribution (if any) of random error. Therefore, such equations are not suitable for a rigorous statistical evaluation of the desired quantities. However. with good experimental data, they yield values of acidity constant in agreement with those of rigorous methods, and are acceptable at least for preliminary studies [20]. It has been shown that pH-metric linearized multiple analyte addition can also be profitably used for the determination of acidity constants of moderately weak monoprotic acids [ 18,201.A very
994
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et ul.
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good accuracy, comparable with that obtained by titration, is obtained by linearized multiple addition of acid at known concentration. The simultaneous determination of the acidity constant and acid concentration by linear equations is more subject to the adverse effects of acidic or basic contaminants in the analyte or supporting electrolyte solutions [18]. However, this higher sensitivity to chemical interferences makes this technique particularly suitable for a preliminary evaluation of the reliability of experimental data by comparison of the deviations from linearity with the theoretical expectations for contaminated systems [ 181. In solutions of diprotic acids with sharply separated dissociation steps, the second dissociation step can be neglected; therefore, the first dissociation can be studied with the linearized multiple analyte addition procedure for monoprotic acids. In the case under study, however, dimerization of the ampholyte makes the equations previously developed [20] unsuitable. Appropriate linear equations are presented in the following. For simplicity, the equations for a monoprotic acid with dimerizing conjugated base are obtained. On the above assumption. these equations have been applied to the first dissociation step of the investigated diprotic system. 3.2. The general equations for wudtiple anol?ste addition of \i,eak rnonoprotic acid dimerizhg tljitv dissociation For a monoprotic dissociation, 2HB$B,‘-
+2H+
the acidity constant conjugate base is
K , JB? d(C)
acid that dimerizes
after
(6) involving
condensation
I[H+l’
of the
(7)
[HB]’
When a volume V of a solution containing HB at a concentration C is added to an initial volume V” of supporting electrolyte, the mass balance of the solute is CL’= ( I”’ + V))([HB]
+ 2[B,‘~
1)
18)
4.7 (1996)
991-1000
The electroneutrality [H+]=2[B,’
condition
]+[OH-
]-“2[B,‘-
is ]
(9)
(the concentration of hydroxide ion is negligible at the acidic pH values of practical interest). By combining the above equations. one obtains the general equation relating the hydronium ion concentration (the measured variable) with the added volume of analyte solution (the controlled variable). For moderately weak acids at moderate dilution, the approximate form obtained by neglecting the hydroxide ion concentration in Eq. (9).
(10) can be used. Eq. (10) has the shape of the relevant Gran-type equation for multiple analyte addition, expressing the total amount (moles) of analyte in the measured solution as a functional relation of the hydronium ion concentration [ 19,201. 3.3. Linear equation jbr multiple addition of imil?‘te at known concentration Eq. ( 10) can be rearranged
to give
(11) an equation of the form lary variables
Y = hX. with
the auxil-
J’= [H-l”y=
&-
(12)
W’l
which can be calculated from the experimental data of each addition step if the concentration C of the added analyte solution is known. The acidity constant can be obtained from the parameter b either by linear least-squares optimization or graphically from the slope of the relevant plot:
3.4. Linear equation ,fkw nmltiple addition anal?.te at unknorvn concentration By a different
rearrangement
qf
of Eq. (lo), a
C. .Muc,c2 rf al.
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43 (1996)
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Table 1 “P NMR data for aqueous solutions of (,I.\-bis(trimethylphosphine)platinum(lI) (A: c,is-[(PMe,)2Pt(OH,)21~+: B: ~,is-[(PMe,),Pt(~c-OH)],‘i ; C: r.i.\-(PMe,),Pt(OH),) Neutralization
ratio
ii, (ppm) (‘J,,,
dinitrate
Fraction
B
c
n.d.
n.d.
0 0.154
n.d.
0.16
n.d.
0.49
n.d.
1.00
1.62
n.d. n.d.
-31.24 (3375) -31.30 (3323)
0.38
2.00
~ 15.57 (3401) -25.57 (3401) -15.57 ( 3400) - 25.56 ( 3400) -15.58 (3398) n.d.
n.d.
1.oo
-25.33 (3736) -25.31 (3735) -25.31 (3735) -25.33 (3735) n.d.
0.00 0.25 0.50
,’ Nitric
of Pt as B from
neutralization
the intensity
ratio
ratio
0.00
acid added.
linear equation of the form Y= LI+ bX is obtained:
(~“+;N~-l~c+
( V” + I’)[H + 1’ ’ (2K,,,,)’ 2v
(15)
and auxiliary variables x=W”+
y=(V”+
I’)[H+13’ V
VW+1 V
(16)
acidity constant, to be refined with a rigorous method; moreover, they have been used for the treatment of preliminary measurements performed to optimize the experiments. Titrations could not be used for the same purposes, because for the type of systems under study the general titration equation is not linearizable on the same principles.
(17)
From the relevant linear parameters. the analyte concentration in the added solution can be calculated together with the acidity constant: c=u
at variable
(Hz))
A -0.33”
995
(18)
The linearly transformed Eqs. (11) and (15) suffer the limitations pointed out in Section 3.1. Therefore they must be cautiously employed. In the present case, these equations have been found to be very convenient for verifying the validity of the chemical model assumed,reaction (4). as well as for obtaining first-approximation values of the
4. Results
The “P NMR spectrum of a 0.135 M solution of cis-(PMe,),Pt( NO,), shows two singlets, flanked by ‘95Pt satellites, centred at chemical shifts (d‘r) of -25.314 ppm (coupling constant ‘Jptp= 3735 Hz) and - 25.57 ppm (‘Jptp = 3401 Hz) which are attributable to cis-[(PMe,)z Pt(OHZ),]’ + and ci.s-[(PMe,)2Pt(/l-OH)]27respectively [lo], with an intensity ratio of about 5: 1. Accordingly, the addition of HNO, results in the decreaseand eventually the disappearance of the resonance at higher field, whereas that at
996
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rr al.
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lower field maintains its chemical shift and coupling constant values virtually unchanged (Table 1). Similarly, the addition of NaOH causes a progressive increase in the intensity of the singlet at -25.57 ppm, with the concomitant decrease of that at - 25.3 1, which becomes undetectable when the molar ratio PtjNaOH is 1: 1. Since the acid-base reactions are fast on the NMR time scale, only one set of resonances should be observable for the species involved in the straight dissociation equilibrium cis-[(PMe,),Pt(H,O)#
+
G cis-[(PMe,),Pt(OH)(H,0)]
+ + HT
H,O)J
+ cis-[( PMe,),Pt(p
i
-OH)],’
+ + 2H,O
991~-1000
K, = W,A,IW +I’ d(L) [H,A]’
(221
(where H,A = cis-[(PMe,),Pt(HzO)J2’) has the form of Eq. (7). The measurement of the equilibrium concentration ratio of cisand cis-[(PMe,),Pt [(PMe,)2Pt(H,0),]’ + (p - OH)lZ2 + in the solution of cis(PMe&Pt(NO,), through the integrals of the corresponding “P NMR resonances yields an approximate pK,,(,, value of 3.46. The formation of the dihydroxo complex cis(PMe,)?Pt(OH), according to Eq. (5) with the acidity constant expressed by
(20)
with chemical shift and coupling constants that should be the concentration-weighted averages for cis-[(PMe,),Pt(H,O),]‘+ and cis-[(PMe,)zPt(OH) (H,O)]+. Indeed, although the chemical shift difference (0.25 ppm) between the species ciscis-[(PMe,)zPt(Ll~H~Q$W-W~21‘ + and is rather small, the difference in their ’JRP’values (265 Hz) is remarkable. Thus, mixtures of cis-[(PMe,),Pt(HzO)$ + and cisNPMe3LPWWW20)l + are expected to exhibit a resonance whose coupling constant should change significantly with the molar ratio. In contrast. the data collected in Table 1, obtained within about 10 min after the mixing of the solutions, show that both the resonances maintain their chemical shift and ‘Jptp values unchanged (6, = + 0.01 ppm, ‘Jptr = + 1 Hz) during the titration of cis(PMe&Pt(NO,), with strong base. This result suggests that the equilibrium concentration of the mononuclear species cis-[( PMe&Pt(OH)( H,O)] + is not detectable as the consequence of the relatively fast and practically complete dimerization to cis-[(PMe,),Pt(p-OH)],‘+ : cis-[( PMe,),Pt(OH)(
43 (1996)
(21)
It can be concluded that the resonance at - 25.31 ppm is exclusively due to the diaquo complex and therefore the only equilibrium that can be studied under the prevailing experimental conditions is the one represented by Eq. (4). for which the acidity constant
(23) has also been monitored by 3’P NMR. The addition of NaOH to the solution of cis-[(PMe&Pt(pOH)12(N0,), causes the appearance of a new singlet at - 31.24 ppm, flanked by the 19’Pt satellites (‘J PtP= 3324 Hz), which is the only resonance detectable when the molar ratio NaOH/Pt is raised to one (as also occurs [l l] with an aqueous solution of an isolated sample of cisPMe,),WOH)). 4.2. PotentionletriL.
measurtwienls
The results obtained by treating, separately or together, the multiple addition and titration data of three experiments with different numerical procedures based on the model of complete dimerization (negligible concentration of HA) are summarized in Table 2. The plots of Eq. (11) for the determination of K,,(,, with known C are presented in Fig. 1. The linearity appears to be very good (the correlation coefficient is always larger than 0.9997); by inspection of the residuals of the linear least-squares fitting, only a very small downward convexity is detected in the very first part of the plot (closest to the origin, corresponding to the first additions). It is deduced that the data are only very slightly affected by some source of systematic error, possibly a limited validity of the model (see Section 5) and, in addition, the presence of a basic contaminant at very low concentrations in the supporting solution [ 181.
C. Macc~d
Table 2 Results of potentiometric
er ul.
Talanrtr
4.3 (1996)
991~
1000
997
measurements
Method
Parameter
Experiment I
Linearized
analyte
addition,
known
Linearized
analyte
addition.
unknown
Generalized
least-squares,
only
Generalized
least-squares,
analyte
concentration,
analyte
Eq. (1 I)
concentration,
Eq. (I 5)
additions
addition
+ titration
0
-I
“0 r -2
0
1
2
3
4
5
x .106
Fig. I. Potentiometric multiple additions of 7.50 x IO- ’ M cis-bis(trimethylphosphine)platinum(If) dinitrate (25”C, 0.2 M ionic strength) linearized with Eq. (I I) for the determination of K,,,,, at known concentration. Auxiliary variables. X, Eq. (12) Y. Eq. (13). r-1, experiment I: C. experiment 2. “. experiment 3 of Table 2.
3
PK.%,,4 s.d.
3.794 0.004
3.796 0.003
3.832 0.004
Ph;,,,, s.d. IO’ x C (mol s.d.
3.774 0.012 7.37 0.05
3.548 0.008 6.59 0.03
3.778 0.017 7.24 0.08
PK,?,,,, s.d.
3.814 0.004
3.866 0.022
3.863 0.010
P&W, s.d.
3.867 0.004 ‘3 171 k_.& 0.019
3.895 0.017 22.139 0.013
3.918 0.023 22.120 0.016
Pk:,,,,, s.d.
The final value of the first acidity constant. x 10PJ (pK,,,,, = 3.893 -t K~I,,, = (1.28~0.08) 0.025) as well as the value of the second one, (pK,,,,, = 22.17 + Ltc) = (6.7* 1.2) x 1O-‘3 0.07) were determined by generalized leastsquares fitting of the whole set of experimental
2
dm
‘)
points. Simultaneous optimization of the analyte concentration yielded a value of 7.50 mmol 1~ ‘, comparable with the nominal value of 7.63 ( - 1.7X1, possibly due to water impurity); for this purpose only two sets of experiments were used because in the third one drifting potentials near to the equivalence point of the titration resulted in a value affected by high uncertainty. For homogeneity, all the other results reported in Table 2 have been (re)calculated using the final concentration value; however, the difference between the mean values of Kalcc, calculated with Eq. (11) using the nominal concentration value, Kalcc, = (1.46kO.11) x IO- ‘, and using the final value, K,,,,,=(1.59*0.11) x 10 ’ (pK,,,,, =3.80+ 0.03). is small. These values of K,,(,, compare very well with those calculated from the same points by generalized least-squares fitting (Table 2). Eq. (15) was also tested. The plots of the linear function for the simultaneous determination of K a,icj and C from multiple addition of the analyte acid, Eq. (15) are shown in Fig. 2. The linearity is good (correlation coefficient IT/ > 0.998) in two experiments, while in the third (with 1~1= 0.995) an appreciable curvature is shown by the residuals. The calculated concentration of the analyte solution, although of the correct magnitude, is appreciably variable and systematically smaller
998
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991-1000
constants (mere dissociation); Kc is the equilibrium constant of the dimerization (condensation) reaction (2 1):
8
K, = WA1 ’
/
0
I
/
I
2
4 x,
I
I
6
IO5
Fig. 2. Potentlometric multiple additions linearized with Eq. (15) for the determination of K,,,,, at unknown concentration of added sample. Auxiliary variables X. Eq. (16). I’. Eq. (17). Symbols as in Fig. 1.
than the nominal value. The value of K,,,,, is also larger than that resulting from the other methods of data treatment (Table 2). However, the results are not far from the final values determined by generalized least-squares, showing that Eq. (15) can be used as first approximation values in the situation where there is little information on the real composition of the tested analyte solution. Advantage was also taken of the diagnostic value of deviations from linearity of this linear transformation [ 181: a pair of preliminary experiments was discarded after inspection of the respective plots of Eq. (15) because systematically large deviations from linearity at low acid concentration revealed the presence of too large a concentration ( > 10 ’ M) of basic contaminant in the supporting electrolyte solution. Deviations were strongly reduced in the final experiments after changing the supporting electrolyte solution for one of controlled purity.
5. Discussion The equilibria occurring in the investigated system are summarized in Scheme 1, in which the ionic charges have been omitted for simplicity. K,, [reaction (20)] and K,,z are the straight acidity
(24)
[H?A]’
The equilibrium constants K,,,,, and Kazcc, for the dissociation through the dimer, reactions (4) and (5) have been defined above (Eqs. (22) and (23)). The ratio of the concentrations of monomeric and dimeric forms of ampholyte, [HA]/[H,A,], depends on the total concentration of the amphoteric species. In solutions of cis-bis(trimethylphosphine)platinum(II) dinitrate, i.e. during analyte addition. it decreases with increasing concentration. During titration, it reaches a minimum at the first neutralization point. The NMR experiments, performed at relatively high concentration, give evidence of the absence of the monomeric form of the ampholyte within the sensitivity of the method. With the conservative assumption that this finding indicates a monomer fraction not greater than 5% of the total Pt in the ampholyte, a value of log Kc 2 4.0 is calculated. The potentiometric experiments have been performed at much lower concentration (1.5 x 10 ~ 555.6 x 10 ’ M); in consequence, the important presence of the amphoteric monomer HA could not be excluded on the basis of the NMR data. However. the validity of the complete dimerization model has been confirmed by the satisfactory linearity of the analyte addition data transformed according to Eq. (1 I) (Fig. l), with some systematic deviation only in the very first points. In contrast, transformation via the linear equation for monoprotic acid (20). ( V” + l’)[H +I’ =
Ka,(CL'- [H ‘1)
(25)
3 HA--A H2A \ tKc/ * K al@)
HZ& Scheme
Ka2(c) I
taken, because the few useful points were possibly affected by systematic and random deviations of different origins. i 6. Conclusions
0
I
2
3
x ,103 Fig. 3. Transformation of potentiometric multiple additions of 7.50 x IO ’ M c,i.s-bis(trimethylphosphine)platinum(II) dinitrate with the linear Eq. (25) for the determination of K,,. the first acidity constant. according to the straight dissociation model. reaction (20). Auxiliary variables X= (Cl.[H + 1). Y = ( C”’ + I ‘)[H +12. Symbols as in Fig. I.
on the assumption of complete formation of the monomeric ampholyte, yields a strongly curved plot (Fig. 3). This result confirms the predominance of the dimeric form at least at a concentration greater than 10PJ M. At higher dilution, with increasing monomeric ampholyte fraction. the slope of the plot of Eq. (25) should approach K,,; accordingly, the value pK<,, 3 4.0 was calculated from the initial slope of the plots of Fig. 3. A better guess can be made by considering that. according to the linearization results, at least 90% of the ampholyte must still be present in the dimeric form at 10 -’ M total concentration of solute; in this way, a value of log Kc in the range 6-6.5 is calculated, from which the value 5.0-5.2 is obtained as the lower limit for pK,, = (p&,,, + log Kc):2 and 8.1 -7.9 as the higher limit for pKdz = (pK,,,,,, - log K,);2. The difference between the literature values of pK,, and pK,, for other platinum diaquo complexes is in the range of 2-4 units. Assuming pK,, - pK,, = i.3 an’upper limit of 5.5 is obtained for pK,, and a lower limit of 7.5 for pK,, and thereafter an upper limit of 7.1 for pK,. A more accurate calculation of Kc from the experimental data was not under-
Cis-bis( trimethylphosphine)platinum( II) is a stronger acid (pK,, = 5.0-5.5) than complexes with N-donor atoms (pK,, > 5.9 [2]). Its strength, as well as the difference in strength between the two acidities, is strongly enhanced by the dimerization equilibrium in comparison with other platinum diaquo complexes. As assumed, the difference between the two acidity constants is large enough such that the first dissociation can be treated as that of a monoprotic acid. Dimerization of the ampholyte is also practically quantitative over a large concentration range. The results of potentiometric measurements confirm that linearized standard acid additions can be profitably used for the limited purposes for which they have been proposed. References [I] K..4. Jensen, Z. Anorg, Allg. Chem., 242 (1939) 87. [2] T.G. .4ppleton. J.R. Hall. S.R. Ralph and C.S.M. Thompson, Inorg. Chem., 28 (1989) 1989. [3] M.C. Lim and R.B. Martin, J. Inorg. Nucl. Chem.. 38 (1976) 1911. [4] D.S. Gill and B. Rosenberg. J. Am. Chem. Sot.. 104 (198’) 4598. [5] R. Faggiani. B. Lippert. C.J.L. Lock and B. Rosenberg, J. Am. Chem. Sot.. 99 (1977) 777. [6] R. Faggiani. B. Lippert, C.J.L. Lock and B. Rosenberg. Inorg. Chem.. 16 (1977) 1192. [7] B. Lippert. C.J.L. Lock, B. Rosenberg and M. Zvagulis, Inorg. Chem.. 17 (1978) 2971. [8] S. Wimmer. P. Castan. L.L. Wimmer and N.P. Johnson, J. Chem. Sot.. Dalton Trans.. (1989) 403. [9] F.D. Rochon. A. Morneau and R. Melanson, Inorg. Chem., 27 (1988) IO. [II)] G. Trovb. G. Bandoli. I;. Casellato. B. Corain. M. Nicolim and B. Longato. Inorg. Chem., 29 (1990) 4616. [I I] T.K. Miyamoto. Y. Suzuki and H. Ichida. Chem. Lett.. (1992) 839. [I?] L.G. Sill&x. Acta Chem. Stand., 16 (1962) 159; 18 (1964) 1803. [I.31 D.J. Legger (Ed.). Computational Methods for the Determination of Formation Constants. Plenum. New York, 1985.
[I41 A.E. Martell and R.J. Motekaitis, Determination and Use of Stability Constants. VCH, New York. 1988. [I51 A. Albert and E.P. Serjeant, The Determination of lonization Constants. 3rd edn., Chapman and Hall. New York, 1984. [I61 P. Cans. A. Sabatini and A. Vacca. J. Chem. Sot.. Dalton Trans., (1985) 1195.
[17] C. De Stefano, P. Princi, C. Rigano and S. Sanmartano. Ann. Chim. (Rome), 77 (1987) 643. [IX] C. Mac&. A. Merkoci and G.G. Bombi. Talanta. 42 (1995) 1433. [Is)] C. Mac&. Fresenius‘ J. Anal. Chem.. 336 (1990) 29. [10] C. Macca and A. Merkoci. Talanta, 41 (1994) 2033.
Talanta 43 ( 1996) 99 I 1000
Acid-base equilibria in aqueous solution of cis-bis(trimethylphosphine)platinum(II) dinitrate at 25”C, 0.2 M ionic strength. A potentiometric study Carlo Mac&*, Depnrtnw~r
of lnorganic~.
Bruno Longato,
Mrrullor~c~rri~~
mrci .4nulyti~ul
Guendalina C/wmtr~~.
Trovb,
G. Giorgio
C~~~irer.sit~ of’ Pudo~cr,
Via Marsolo
Bombi
I, I-35131
Pcrdocu. IIUIJ,
Received I August 1995; revised 18 October 1995: accepted I4 November 1995
Abstract
Acid-base equilibria in aqueoussolutionsof ci.\-bis(trimethylphosphine)platinum(II)dinitrate at 25°C. 0.2 M ionic strength (KNO,), have beeninvestigatedby potentiometry with a glass electrode. The procedure consisted of multiple addition of the investigatedanalyte to a supportingelectrolyte solution (“multiple sampleaddition”) and subsequent titration with strong base.For the treatment of potentiometric multiple sampleaddition data, a new linearization procedure. suitablefor an acid dissociationequilibrium whoseproduct dimerizes.has beendevisedand tested,The potentiometric results have been interpreted with the support of NMR data. By dissociationof the first acidic function of the solute diaquo cation. ci.s-[(PMe,)2Pt(OH2),]1 ’ . a dimeric amphoiite. cis-[(PMe,)2Pt(Lc-OH)],’A . is quantitatively formed which. in turn. can be converted into the di-hydroxo derivative ci.c-(PMe,),Pt(OH)2. The two acid dissociationstepsinvolving two molecules of solute and condensation of ampholyte have PK,,,~, = 3.89 and pK;,:,,, = 22.17. K~JWJJ~Y:
Cisplatin complexes:Acidity constant: Potentiometry: Linearized an&e addition __~~___________
I. Introduction
water molecules:
The study of the aqueous chemistry of platinum complexes has been stimulated by its relevance to the anticancer properties of cisplatin, cis(NH,),PtCl,. When the removal of the halide ligands with silver salts from L,PtCl, (L = Ndonor ligand) is carried out in water, the diaquo complex c*is-[L,Pt( H,O),]’ + is formed, which behaves as a diprotic acid through the coordinated
cis-[L,Pt(H,O),]‘+
* Correspondq
author
$ cis-[L,Pt(OH)(H,O)] ck-[L,Pt(OH)(
++ H+
H,O)] + G+ck-[L,Pt(OH),]
(1) ++ H+ (2)
The values of the relative acidity constants have been determined for a number of N-donor ligands, L, such as ammonia [l], ethylenediamine (en) [2.3], and 1.2-diaminocyclohexene [4].
0039-9130/96 $15.00 C 1996 Elsevier Science B.V. ,411right5 reserved SSDI 00?9-914Ol95)01822-0
The aquohydroxo species resulting from reaction (I) can undergo the oligomerization reaction 11cis-[LZPt(OH)(H,O)]
+
+ L.iS-[L2Pt(/l-OH)],,”
- + 12H,O
(3)
with the formation of polynuclear hydroxocomplexes. Generally the dinuclear and trinuclear derivatives (n = 2 and 3) are formed [5-81 but, in the case of the Pt(en) system, even the tetranuclear complex has been structurally characterized [91. In contrast, despite the huge number of phosphino complexes of platinum(II). to our knowledge no data on the acidity of water molecules in systems of the type [L,Pt(H20),,,]’ + , where L is a P-donor atom of a tertiary phosphine, have been reported. We have shown that the water soluble cis-( PMe,),Pt( NO,), (Me = CH,) complex. by neutralization of the diaquo complex, yields quantitatively the dinuclear species with bridging hydroxo ligands, cis-[(PMe,)2Pt(p-OH)]&NOi)Z (determined from X-ray analysis of an isolated single-crystal) [lo] which, by further addition of strong base, can be converted into the dihydroxo derivative cis-(PMe,)zPt(OH), [l 11. In this paper, the constants of the proton dissociation equilibrium of the solute diaquo cation with formation of the dimeric conjugate base 2cis-[( PMel),Pt(OH,),]’
+
Z$ cir-[(PMe,),Pt(jl-OH)],‘+
+ 3H + + 2H,O (4)
and of the further
deprotonation
cis-[(PMe,)zPt(p-OH)],’ $2
2. Experimental
cis-(PMe,&Pt(OH)?
equibilrium
+ + 2H10 + 2H *
(5)
have been determined at 25”C, 0.2 M ionic strength, by potentiometric multiple analyte addition and subsequent titration with strong base. For this purpose, a new procedure for the treatment of the analyte addition data using linear functions has been devised and tested. The potentiometric findings have been interpreted with the support of NMR measurements.
C’is-bis( trimethylphosphine)platinum(II) dinitrate was prepared as previously reported [lo]. The {‘H; “P NMR data were obtained with a Jeol 90Q instrument operating at 36.23 MHz, using 5 mm tubes with a coaxial capillary for the lock (D,O). The chemical shifts, in ppm, are referred to external H,PO, (85%). Different amounts of standard HNO, or NaOH solutions were added to 0.3 ml aliquots of 0.135 M aqueous solution of c-is-(PMe,),Pt(NO,), in an NMR tube at room temperature. The tube was quickly transferred into the NMR probe at 27°C and the spectrum was obtained within 10 min.
A glass cell (IO ml total volume), provided with a thermostatic jacket and a tight cover for inserting the electrodes, temperature probe and nitrogen inlet. was used as the container for the measured solution, which was magnetically stirred. Motor-driven microburettes (MicroBUR 2030, Crison, Barcelona) equipped with 1 ml Hamilton syringes (0.4 /ll resolution) were used for the additions of reactants. The additions were managed with a potentiometric titrator Crison MicroTT 2050. The e.m.f. of a cell composed of a pH glass electrode (Ingold type 10 265 3042) and a Ag: AgCl reference electrode in 3 M KC1 with 1 M KNO, salt bridge and sleeve junction (Ingold type 10 373 3145) was measured with 0.1 mV resolution during the additions. A data file was created by the titrator on a PC for each part of an experiment. 2.22. Retrgrnts Analytical or higher grade (e.g. Merck Suprapur) reagents and freshly prepared ultrapure water (MilliQ-Plus” grade) were used in all potentiometric experiments.
993
22.3. Proceduw 10 ml of 0.20 M potassium nitrate were used as the supporting solution in each experiment. The electrode was firstly calibrated in the acidic pH range of principal interest (pH 4.1-3.4) by multiple constant addition (10 x 100.0 itl) of standard 0.01 M strong acid in 0.19 M potassium nitrate; the calibration was completed in the basic range by titration via multiple constant addition (20 x 50.0 /tl) of standard 0.02 M sodium hydroxide in 0.18 M potassium nitrate. After careful washing, the cell was again filled with 10 ml of supporting electrolyte solution and multiple addition was performed via 14 additions (increasing in four steps from 20.0 to 100.0 ~1, for a total added volume of 0.8 ml) of 7.62 x 10e3 M solution prepared by dissolving a weighed amount of cis-bis(trimethylphosphine)platinum(II) dinitrate in ultrapure water. Thereafter. the acid was titrated by multiple constant addition of standard 0.02 M sodium hydroxide in 0.18 M potassium nitrate. The cell was thermostated at 25 k O.l”C throughout all experiments.
2.2.4. Culculutions Calibration allowed the experimental e.m.f. data of the additiontitration experiments to be converted to values of hydronium ion concentration. Thereby, concentration constants at constant ionic strength were calculated. The analyte addition data were initially linearized using Eq. (11) (see Section 3) for the determination of a first-approximation value of the first acidity constant at known analyte concentration C; Eq. (15) was also tested for the simultaneous determination of C. The data from the subsequent titration were used, together with the analyte addition data. to refine the value of the first acidity constant and to obtain the value of the second one via generalized (non-linear) leastsquares fitting, using a home computer program based on the pit-mapping method
1121.
3. Theory 3.1. Liiwurizution of’potmtiometric multiple addition qf’u tceuk ucid dinzerizing ujier dissociution Acidity constants are most commonly determined by pH-metric titration. By treatment of the titration data with existing generalized leastsquares computer programs, other experimental parameters (such as titrated acid concentration, solvent autoprotolysis constant, glass electrode calibration parameters) can be optimized simultaneously with the target acidity constant(s) [12171. For weak monoprotic acids. it has been shown [18] that pH-metric multiple analyte addition provides a very useful complement to titration data. If the concentration of acid to be titrated with strong base is built-up by multiple addition of relatively concentrated analyte, the number of measurements in each experiment is increased in a more significant way than by crowding the titration points. This opportunity can be particularly appreciated when only a small amount of analyte is available, as it was in the present research. For the separate or simultaneous determination of acidity constant and analyte concentration, the general titration equation relating the measured pH to the added titrant volume can be transformed into several forms of linear equations, each one making use of different auxiliary variables and including in the linear parameters either or both of the analytical parameters [19]. However, the linear transformation may produce a strong correlation between the relevant auxiliary variables and, in general. it destroys the Gaussian distribution (if any) of random error. Therefore, such equations are not suitable for a rigorous statistical evaluation of the desired quantities. However. with good experimental data, they yield values of acidity constant in agreement with those of rigorous methods, and are acceptable at least for preliminary studies [20]. It has been shown that pH-metric linearized multiple analyte addition can also be profitably used for the determination of acidity constants of moderately weak monoprotic acids [ 18,201.A very
994
C. Muccri
et ul.
Tulmta
good accuracy, comparable with that obtained by titration, is obtained by linearized multiple addition of acid at known concentration. The simultaneous determination of the acidity constant and acid concentration by linear equations is more subject to the adverse effects of acidic or basic contaminants in the analyte or supporting electrolyte solutions [18]. However, this higher sensitivity to chemical interferences makes this technique particularly suitable for a preliminary evaluation of the reliability of experimental data by comparison of the deviations from linearity with the theoretical expectations for contaminated systems [ 181. In solutions of diprotic acids with sharply separated dissociation steps, the second dissociation step can be neglected; therefore, the first dissociation can be studied with the linearized multiple analyte addition procedure for monoprotic acids. In the case under study, however, dimerization of the ampholyte makes the equations previously developed [20] unsuitable. Appropriate linear equations are presented in the following. For simplicity, the equations for a monoprotic acid with dimerizing conjugated base are obtained. On the above assumption. these equations have been applied to the first dissociation step of the investigated diprotic system. 3.2. The general equations for wudtiple anol?ste addition of \i,eak rnonoprotic acid dimerizhg tljitv dissociation For a monoprotic dissociation, 2HB$B,‘-
+2H+
the acidity constant conjugate base is
K , JB? d(C)
acid that dimerizes
after
(6) involving
condensation
I[H+l’
of the
(7)
[HB]’
When a volume V of a solution containing HB at a concentration C is added to an initial volume V” of supporting electrolyte, the mass balance of the solute is CL’= ( I”’ + V))([HB]
+ 2[B,‘~
1)
18)
4.7 (1996)
991-1000
The electroneutrality [H+]=2[B,’
condition
]+[OH-
]-“2[B,‘-
is ]
(9)
(the concentration of hydroxide ion is negligible at the acidic pH values of practical interest). By combining the above equations. one obtains the general equation relating the hydronium ion concentration (the measured variable) with the added volume of analyte solution (the controlled variable). For moderately weak acids at moderate dilution, the approximate form obtained by neglecting the hydroxide ion concentration in Eq. (9).
(10) can be used. Eq. (10) has the shape of the relevant Gran-type equation for multiple analyte addition, expressing the total amount (moles) of analyte in the measured solution as a functional relation of the hydronium ion concentration [ 19,201. 3.3. Linear equation jbr multiple addition of imil?‘te at known concentration Eq. ( 10) can be rearranged
to give
(11) an equation of the form lary variables
Y = hX. with
the auxil-
J’= [H-l”y=
&-
(12)
W’l
which can be calculated from the experimental data of each addition step if the concentration C of the added analyte solution is known. The acidity constant can be obtained from the parameter b either by linear least-squares optimization or graphically from the slope of the relevant plot:
3.4. Linear equation ,fkw nmltiple addition anal?.te at unknorvn concentration By a different
rearrangement
qf
of Eq. (lo), a
C. .Muc,c2 rf al.
Trrhta
43 (1996)
991-1000
Table 1 “P NMR data for aqueous solutions of (,I.\-bis(trimethylphosphine)platinum(lI) (A: c,is-[(PMe,)2Pt(OH,)21~+: B: ~,is-[(PMe,),Pt(~c-OH)],‘i ; C: r.i.\-(PMe,),Pt(OH),) Neutralization
ratio
ii, (ppm) (‘J,,,
dinitrate
Fraction
B
c
n.d.
n.d.
0 0.154
n.d.
0.16
n.d.
0.49
n.d.
1.00
1.62
n.d. n.d.
-31.24 (3375) -31.30 (3323)
0.38
2.00
~ 15.57 (3401) -25.57 (3401) -15.57 ( 3400) - 25.56 ( 3400) -15.58 (3398) n.d.
n.d.
1.oo
-25.33 (3736) -25.31 (3735) -25.31 (3735) -25.33 (3735) n.d.
0.00 0.25 0.50
,’ Nitric
of Pt as B from
neutralization
the intensity
ratio
ratio
0.00
acid added.
linear equation of the form Y= LI+ bX is obtained:
(~“+;N~-l~c+
( V” + I’)[H + 1’ ’ (2K,,,,)’ 2v
(15)
and auxiliary variables x=W”+
y=(V”+
I’)[H+13’ V
VW+1 V
(16)
acidity constant, to be refined with a rigorous method; moreover, they have been used for the treatment of preliminary measurements performed to optimize the experiments. Titrations could not be used for the same purposes, because for the type of systems under study the general titration equation is not linearizable on the same principles.
(17)
From the relevant linear parameters. the analyte concentration in the added solution can be calculated together with the acidity constant: c=u
at variable
(Hz))
A -0.33”
995
(18)
The linearly transformed Eqs. (11) and (15) suffer the limitations pointed out in Section 3.1. Therefore they must be cautiously employed. In the present case, these equations have been found to be very convenient for verifying the validity of the chemical model assumed,reaction (4). as well as for obtaining first-approximation values of the
4. Results
The “P NMR spectrum of a 0.135 M solution of cis-(PMe,),Pt( NO,), shows two singlets, flanked by ‘95Pt satellites, centred at chemical shifts (d‘r) of -25.314 ppm (coupling constant ‘Jptp= 3735 Hz) and - 25.57 ppm (‘Jptp = 3401 Hz) which are attributable to cis-[(PMe,)z Pt(OHZ),]’ + and ci.s-[(PMe,)2Pt(/l-OH)]27respectively [lo], with an intensity ratio of about 5: 1. Accordingly, the addition of HNO, results in the decreaseand eventually the disappearance of the resonance at higher field, whereas that at
996
C. Muccci
rr al.
Tuluntu
lower field maintains its chemical shift and coupling constant values virtually unchanged (Table 1). Similarly, the addition of NaOH causes a progressive increase in the intensity of the singlet at -25.57 ppm, with the concomitant decrease of that at - 25.3 1, which becomes undetectable when the molar ratio PtjNaOH is 1: 1. Since the acid-base reactions are fast on the NMR time scale, only one set of resonances should be observable for the species involved in the straight dissociation equilibrium cis-[(PMe,),Pt(H,O)#
+
G cis-[(PMe,),Pt(OH)(H,0)]
+ + HT
H,O)J
+ cis-[( PMe,),Pt(p
i
-OH)],’
+ + 2H,O
991~-1000
K, = W,A,IW +I’ d(L) [H,A]’
(221
(where H,A = cis-[(PMe,),Pt(HzO)J2’) has the form of Eq. (7). The measurement of the equilibrium concentration ratio of cisand cis-[(PMe,),Pt [(PMe,)2Pt(H,0),]’ + (p - OH)lZ2 + in the solution of cis(PMe&Pt(NO,), through the integrals of the corresponding “P NMR resonances yields an approximate pK,,(,, value of 3.46. The formation of the dihydroxo complex cis(PMe,)?Pt(OH), according to Eq. (5) with the acidity constant expressed by
(20)
with chemical shift and coupling constants that should be the concentration-weighted averages for cis-[(PMe,),Pt(H,O),]‘+ and cis-[(PMe,)zPt(OH) (H,O)]+. Indeed, although the chemical shift difference (0.25 ppm) between the species ciscis-[(PMe,)zPt(Ll~H~Q$W-W~21‘ + and is rather small, the difference in their ’JRP’values (265 Hz) is remarkable. Thus, mixtures of cis-[(PMe,),Pt(HzO)$ + and cisNPMe3LPWWW20)l + are expected to exhibit a resonance whose coupling constant should change significantly with the molar ratio. In contrast. the data collected in Table 1, obtained within about 10 min after the mixing of the solutions, show that both the resonances maintain their chemical shift and ‘Jptp values unchanged (6, = + 0.01 ppm, ‘Jptr = + 1 Hz) during the titration of cis(PMe&Pt(NO,), with strong base. This result suggests that the equilibrium concentration of the mononuclear species cis-[( PMe&Pt(OH)( H,O)] + is not detectable as the consequence of the relatively fast and practically complete dimerization to cis-[(PMe,),Pt(p-OH)],‘+ : cis-[( PMe,),Pt(OH)(
43 (1996)
(21)
It can be concluded that the resonance at - 25.31 ppm is exclusively due to the diaquo complex and therefore the only equilibrium that can be studied under the prevailing experimental conditions is the one represented by Eq. (4). for which the acidity constant
(23) has also been monitored by 3’P NMR. The addition of NaOH to the solution of cis-[(PMe&Pt(pOH)12(N0,), causes the appearance of a new singlet at - 31.24 ppm, flanked by the 19’Pt satellites (‘J PtP= 3324 Hz), which is the only resonance detectable when the molar ratio NaOH/Pt is raised to one (as also occurs [l l] with an aqueous solution of an isolated sample of cisPMe,),WOH)). 4.2. PotentionletriL.
measurtwienls
The results obtained by treating, separately or together, the multiple addition and titration data of three experiments with different numerical procedures based on the model of complete dimerization (negligible concentration of HA) are summarized in Table 2. The plots of Eq. (11) for the determination of K,,(,, with known C are presented in Fig. 1. The linearity appears to be very good (the correlation coefficient is always larger than 0.9997); by inspection of the residuals of the linear least-squares fitting, only a very small downward convexity is detected in the very first part of the plot (closest to the origin, corresponding to the first additions). It is deduced that the data are only very slightly affected by some source of systematic error, possibly a limited validity of the model (see Section 5) and, in addition, the presence of a basic contaminant at very low concentrations in the supporting solution [ 181.
C. Macc~d
Table 2 Results of potentiometric
er ul.
Talanrtr
4.3 (1996)
991~
1000
997
measurements
Method
Parameter
Experiment I
Linearized
analyte
addition,
known
Linearized
analyte
addition.
unknown
Generalized
least-squares,
only
Generalized
least-squares,
analyte
concentration,
analyte
Eq. (1 I)
concentration,
Eq. (I 5)
additions
addition
+ titration
0
-I
“0 r -2
0
1
2
3
4
5
x .106
Fig. I. Potentiometric multiple additions of 7.50 x IO- ’ M cis-bis(trimethylphosphine)platinum(If) dinitrate (25”C, 0.2 M ionic strength) linearized with Eq. (I I) for the determination of K,,,,, at known concentration. Auxiliary variables. X, Eq. (12) Y. Eq. (13). r-1, experiment I: C. experiment 2. “. experiment 3 of Table 2.
3
PK.%,,4 s.d.
3.794 0.004
3.796 0.003
3.832 0.004
Ph;,,,, s.d. IO’ x C (mol s.d.
3.774 0.012 7.37 0.05
3.548 0.008 6.59 0.03
3.778 0.017 7.24 0.08
PK,?,,,, s.d.
3.814 0.004
3.866 0.022
3.863 0.010
P&W, s.d.
3.867 0.004 ‘3 171 k_.& 0.019
3.895 0.017 22.139 0.013
3.918 0.023 22.120 0.016
Pk:,,,,, s.d.
The final value of the first acidity constant. x 10PJ (pK,,,,, = 3.893 -t K~I,,, = (1.28~0.08) 0.025) as well as the value of the second one, (pK,,,,, = 22.17 + Ltc) = (6.7* 1.2) x 1O-‘3 0.07) were determined by generalized leastsquares fitting of the whole set of experimental
2
dm
‘)
points. Simultaneous optimization of the analyte concentration yielded a value of 7.50 mmol 1~ ‘, comparable with the nominal value of 7.63 ( - 1.7X1, possibly due to water impurity); for this purpose only two sets of experiments were used because in the third one drifting potentials near to the equivalence point of the titration resulted in a value affected by high uncertainty. For homogeneity, all the other results reported in Table 2 have been (re)calculated using the final concentration value; however, the difference between the mean values of Kalcc, calculated with Eq. (11) using the nominal concentration value, Kalcc, = (1.46kO.11) x IO- ‘, and using the final value, K,,,,,=(1.59*0.11) x 10 ’ (pK,,,,, =3.80+ 0.03). is small. These values of K,,(,, compare very well with those calculated from the same points by generalized least-squares fitting (Table 2). Eq. (15) was also tested. The plots of the linear function for the simultaneous determination of K a,icj and C from multiple addition of the analyte acid, Eq. (15) are shown in Fig. 2. The linearity is good (correlation coefficient IT/ > 0.998) in two experiments, while in the third (with 1~1= 0.995) an appreciable curvature is shown by the residuals. The calculated concentration of the analyte solution, although of the correct magnitude, is appreciably variable and systematically smaller
998
C. Mu&
et ul.
Talanta
33 (1996)
991-1000
constants (mere dissociation); Kc is the equilibrium constant of the dimerization (condensation) reaction (2 1):
8
K, = WA1 ’
/
0
I
/
I
2
4 x,
I
I
6
IO5
Fig. 2. Potentlometric multiple additions linearized with Eq. (15) for the determination of K,,,,, at unknown concentration of added sample. Auxiliary variables X. Eq. (16). I’. Eq. (17). Symbols as in Fig. 1.
than the nominal value. The value of K,,,,, is also larger than that resulting from the other methods of data treatment (Table 2). However, the results are not far from the final values determined by generalized least-squares, showing that Eq. (15) can be used as first approximation values in the situation where there is little information on the real composition of the tested analyte solution. Advantage was also taken of the diagnostic value of deviations from linearity of this linear transformation [ 181: a pair of preliminary experiments was discarded after inspection of the respective plots of Eq. (15) because systematically large deviations from linearity at low acid concentration revealed the presence of too large a concentration ( > 10 ’ M) of basic contaminant in the supporting electrolyte solution. Deviations were strongly reduced in the final experiments after changing the supporting electrolyte solution for one of controlled purity.
5. Discussion The equilibria occurring in the investigated system are summarized in Scheme 1, in which the ionic charges have been omitted for simplicity. K,, [reaction (20)] and K,,z are the straight acidity
(24)
[H?A]’
The equilibrium constants K,,,,, and Kazcc, for the dissociation through the dimer, reactions (4) and (5) have been defined above (Eqs. (22) and (23)). The ratio of the concentrations of monomeric and dimeric forms of ampholyte, [HA]/[H,A,], depends on the total concentration of the amphoteric species. In solutions of cis-bis(trimethylphosphine)platinum(II) dinitrate, i.e. during analyte addition. it decreases with increasing concentration. During titration, it reaches a minimum at the first neutralization point. The NMR experiments, performed at relatively high concentration, give evidence of the absence of the monomeric form of the ampholyte within the sensitivity of the method. With the conservative assumption that this finding indicates a monomer fraction not greater than 5% of the total Pt in the ampholyte, a value of log Kc 2 4.0 is calculated. The potentiometric experiments have been performed at much lower concentration (1.5 x 10 ~ 555.6 x 10 ’ M); in consequence, the important presence of the amphoteric monomer HA could not be excluded on the basis of the NMR data. However. the validity of the complete dimerization model has been confirmed by the satisfactory linearity of the analyte addition data transformed according to Eq. (1 I) (Fig. l), with some systematic deviation only in the very first points. In contrast, transformation via the linear equation for monoprotic acid (20). ( V” + l’)[H +I’ =
Ka,(CL'- [H ‘1)
(25)
3 HA--A H2A \ tKc/ * K al@)
HZ& Scheme
Ka2(c) I
taken, because the few useful points were possibly affected by systematic and random deviations of different origins. i 6. Conclusions
0
I
2
3
x ,103 Fig. 3. Transformation of potentiometric multiple additions of 7.50 x IO ’ M c,i.s-bis(trimethylphosphine)platinum(II) dinitrate with the linear Eq. (25) for the determination of K,,. the first acidity constant. according to the straight dissociation model. reaction (20). Auxiliary variables X= (Cl.[H + 1). Y = ( C”’ + I ‘)[H +12. Symbols as in Fig. I.
on the assumption of complete formation of the monomeric ampholyte, yields a strongly curved plot (Fig. 3). This result confirms the predominance of the dimeric form at least at a concentration greater than 10PJ M. At higher dilution, with increasing monomeric ampholyte fraction. the slope of the plot of Eq. (25) should approach K,,; accordingly, the value pK<,, 3 4.0 was calculated from the initial slope of the plots of Fig. 3. A better guess can be made by considering that. according to the linearization results, at least 90% of the ampholyte must still be present in the dimeric form at 10 -’ M total concentration of solute; in this way, a value of log Kc in the range 6-6.5 is calculated, from which the value 5.0-5.2 is obtained as the lower limit for pK,, = (p&,,, + log Kc):2 and 8.1 -7.9 as the higher limit for pKdz = (pK,,,,,, - log K,);2. The difference between the literature values of pK,, and pK,, for other platinum diaquo complexes is in the range of 2-4 units. Assuming pK,, - pK,, = i.3 an’upper limit of 5.5 is obtained for pK,, and a lower limit of 7.5 for pK,, and thereafter an upper limit of 7.1 for pK,. A more accurate calculation of Kc from the experimental data was not under-
Cis-bis( trimethylphosphine)platinum( II) is a stronger acid (pK,, = 5.0-5.5) than complexes with N-donor atoms (pK,, > 5.9 [2]). Its strength, as well as the difference in strength between the two acidities, is strongly enhanced by the dimerization equilibrium in comparison with other platinum diaquo complexes. As assumed, the difference between the two acidity constants is large enough such that the first dissociation can be treated as that of a monoprotic acid. Dimerization of the ampholyte is also practically quantitative over a large concentration range. The results of potentiometric measurements confirm that linearized standard acid additions can be profitably used for the limited purposes for which they have been proposed. References [I] K..4. Jensen, Z. Anorg, Allg. Chem., 242 (1939) 87. [2] T.G. .4ppleton. J.R. Hall. S.R. Ralph and C.S.M. Thompson, Inorg. Chem., 28 (1989) 1989. [3] M.C. Lim and R.B. Martin, J. Inorg. Nucl. Chem.. 38 (1976) 1911. [4] D.S. Gill and B. Rosenberg. J. Am. Chem. Sot.. 104 (198’) 4598. [5] R. Faggiani. B. Lippert. C.J.L. Lock and B. Rosenberg, J. Am. Chem. Sot.. 99 (1977) 777. [6] R. Faggiani. B. Lippert, C.J.L. Lock and B. Rosenberg. Inorg. Chem.. 16 (1977) 1192. [7] B. Lippert. C.J.L. Lock, B. Rosenberg and M. Zvagulis, Inorg. Chem.. 17 (1978) 2971. [8] S. Wimmer. P. Castan. L.L. Wimmer and N.P. Johnson, J. Chem. Sot.. Dalton Trans.. (1989) 403. [9] F.D. Rochon. A. Morneau and R. Melanson, Inorg. Chem., 27 (1988) IO. [II)] G. Trovb. G. Bandoli. I;. Casellato. B. Corain. M. Nicolim and B. Longato. Inorg. Chem., 29 (1990) 4616. [I I] T.K. Miyamoto. Y. Suzuki and H. Ichida. Chem. Lett.. (1992) 839. [I?] L.G. Sill&x. Acta Chem. Stand., 16 (1962) 159; 18 (1964) 1803. [I.31 D.J. Legger (Ed.). Computational Methods for the Determination of Formation Constants. Plenum. New York, 1985.
[I41 A.E. Martell and R.J. Motekaitis, Determination and Use of Stability Constants. VCH, New York. 1988. [I51 A. Albert and E.P. Serjeant, The Determination of lonization Constants. 3rd edn., Chapman and Hall. New York, 1984. [I61 P. Cans. A. Sabatini and A. Vacca. J. Chem. Sot.. Dalton Trans., (1985) 1195.
[17] C. De Stefano, P. Princi, C. Rigano and S. Sanmartano. Ann. Chim. (Rome), 77 (1987) 643. [IX] C. Mac&. A. Merkoci and G.G. Bombi. Talanta. 42 (1995) 1433. [Is)] C. Mac&. Fresenius‘ J. Anal. Chem.. 336 (1990) 29. [10] C. Macca and A. Merkoci. Talanta, 41 (1994) 2033.