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Talanta 52 (2000) 555–562

Short communication

The catenation and isomerisation effects on stabilityconstants of complexes formed by some diprotic acids

Dariusz Janecki a, Katarzyna Styszko-Grochowiak b, Tadeusz Michal*owski b,*a Faculty of Chemistry, Jagiellonian Uni 6ersity, 30 -060 Krakow, Poland

b Faculty of Engineering and Chemical Technology, Department of Analytical Chemistry, Technical Uni 6ersity of Cracow,

ul . Warszawska 24 , 31-155 Krakow, Poland

Received 19 July 1999; received in revised form 25 February 2000; accepted 3 March 2000

Abstract

Stability constants (K ijk ) of complexes Nai K j Hk L+i + j +k −2 (0B i + j +k 52) formed by dicarboxylic (oxalic,

malonic, succinic, glutaric, adipic and methylmalonic, dimethylmalonic, ethylmalonic) acids in solutions of mixed

salts (NaNO3, KNO3) of ionic strength I =1.64 mol l−1 are presented. The unbiased values for K ijk , (K ijk )% e=0, were

obtained from the linear relationships log K ijk =a+b(% e) stated on the basis of the results of repeated titrations

made in titrand+titrant systems of high ionic strength, % e is the relative error of determination of the weak acid(H2L) concentration. These data were then applied to indicate the catenation or the isomerisation effects on the K ijk values. © 2000 Elsevier Science B.V. All rights reserved.

Keywords: Potentiometric titration; Stability constants of complexes; Catenation; Isomerisation; Curve fitting

www.elsevier.com /locate/talanta

1. Introduction

In order to evaluate the stability constants K ijk of complexes Nai K j Hk L [1] formed by weak di-

carboxylic acids (H2L) with Na

+

and K

+

ions,the pH-metric titration procedure was applied [2]

for concentrated (ionic strength I ca. 1.64 mol

dm−3) electrolytic systems. The conditions of

constancy of ionic strength and dielectric perme-

ability (m ), together with the additivity of titrand

and titrant volumes during titration, are fulfilled

there. The stability constants (K ijk ), activity coeffi-

cient ( f ) of hydrogen ions and concentration (C 0)

of the acid H2L (11 parameters altogether) areinvolved in the regression equation [2,3]

pH=− log!

2x1/2 cos y

3

−z"

(1)

where, pH=− log(h), h — activity of hydrogen

ions (h= f [H]), f and [H] — activity coefficient

and concentration of H+; x=x(W ), y= y(W ),

* Corresponding author. Tel.: +48-12-330300; fax: +48-

12-333374.

E -mail address: [email protected] (T.

Michal*owski)

0039-9140/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.

PII: S 0 0 3 9 - 9 1 4 0 ( 0 0 ) 0 0 3 6 1 - 1

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D. Janecki et al . / Talanta 52 (2000) 555–562 556

z=z(W ) are the (specified meticulously in [2])

functions of total volume W =V 0+V of the sys-

tem at the defined point of titration, V 0 is the

volume of titrand, V volume of titrant added at

this point. Eq. (1) ensures the set of 11 parameters

of the equation to be obtained on the basis of

results (V j , pH j ) of single titration made in the

system. The results obtained from this titration

are usually loaded, with the very nature of things,with a systematic error. However, the linear corre-

lations between log K ijk and relative error (% e) of

C 0 determination was stated on the basis of sev-

eral titrations, made at identical a priori condi-

tions of analysis. It enables the unloaded values,

(K ijk )% e=0, for K ijk to be determined, preferably

according to interpolation procedure. The weak

acid is considered to be an internal standard in

the system in question; it is another advantage of

the method. The linear correlation coefficients

found there are close to 1 or −1; similar regular-ities were also stated in earlier papers [4–6].

In this paper, the alkyl chain length and iso-

merisation effects were tested on a set of juxta-

posed homologous series of dicarboxylic acids

expressed by the general formula (CH2)n(COOH)2(n=0, 1, 2, 3, 4), i.e. oxalic, malonic, succinic,

glutaric (butyric) and adipic acids and methyl-

malonic (CH3CH(COOH)2), ethylmalonic

(C2H5CH(COOH)2) and dimethylmalonic

((CH3)2C(COOH)2) acids.

2. Experimental

2 .1. Materials and equipment

Solutions of NaNO3 and KNO3 were prepared

by dissolving the corresponding salts (PPH, POCh

Gliwice, anal. grade) in water. Aqueous solutions

of diprotic acids (H2L) were obtained by dissolv-

ing the corresponding preparations, oxalic acid (ZOCH Lublin); malonic, succinic, glutaric and adipic (Merck-

Schuchardt); methylmalonic, dimethylmalonic and ethyl-

malonic (Aldrich);

in water and standardising them against NaOHsolution, standardised previously against potas-

sium hydrogen phthalate (POCh Gliwice, anal.

grade). Doubly distilled water, boiled to remove

CO2, was applied for preparation of stock solu-

tions, titrand (D) and titrant (T).

pH-metric titrations were performed with an

automatic titrator (Mettler-Toledo DL 25)

equipped with electrode DG 11-SC (Mettler-

Toledo) and interfaced with a Pentium 90 com-

puter where the results were stored and then

handled according to the iterative computer pro-gram. The titrations were made at 20°C. The

electrode was calibrated against standard buffer

solutions with pH equal to 4.00 and 7.00 (POCh

Gliwice).

2 .2 . Procedure

The series of mixtures (D and T) were prepared

in V f =200 ml flasks, in accordance with Table 1

[2,3].

The composition (concentrations (mol dm−3)

and volumes (cm3) of stock solutions) of D and T

is shown in Table 2. In all series, six titrations

were made; V 0=50 ml of titrand (D) was titrated

up to pH ca. 6. The number (N ) of titration

points (V j , pH j ) taken for evaluation was equal to

64. The overdetermined set of experimental points

covers the pH-interval where a relatively high

level of concentrations of particular form is

available.

3. Results and discussion

The set of 11 optimised parameters consisting

of C 0, f and nine stability constants of complexes

(K ijk ) was obtained according to optimisation pro-

cedure specified in [2]. The sum of unweighted

squares

Table 1

Composition of titrand (D) and titrant (T) [2,3]

D (V 0)Substance T (V )

V tV tHnL (C 0)

V MMOH (C ) –

MB (C 1) V %MBV MB

V KB

V %KBKB (C 2)

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Table 2

Composition of D and T in series 1}4

Series 2Solution Series 3Series 1 Series 4

T D T DD T D T

5H2L (C 0 mol dm−3) 55 5 5 5 5 5

25 – 25 – – 25NaOH (C mol dm−3) – 25

30 30 100 70NaNO3 (C 1=2.5 mol dm−3) 60100 60 70

100 101.17a 30 61.17a31.17a 70KNO3 (C 2=2.5 mol dm−3) 71.17a 60

a The volume of KNO3 in D depends on NaOH concentration, so the isomolar condition [2,3] is fulfilled.

SS= %N

j =1

(pH j −pH(V j ))2

was chosen as the criterion of optimisation, where

pH(V j ) is the pH-value calculated for j th experi-

mental point (V j , pH j ), j =1,…, N , at defined

stage of optimisation procedure, W j =V 0+V j is

the total volume of the system at this point. The

optimised values obtained from six separate titra-tions performed at identical a priori conditions of

analysis were used to plot the linear relationships

[2] between log K ijk and % e, where

% e=100C 0−C 00

C 00

[%]

and C 00 is the value of C 0 found from indepen-

dent, preliminary titrations of the acids made with

the standardised NaOH solution. Then the values

K ijk =(K ijk )% e=0 and f =( f )% e=0 found at %

e=0 were considered as unloaded values of thecorresponding parameters. For a given acid, H2L,

four series of measurements (Table 2) were made.

The procedure was repeated for different acids

specified in Table 3.

3 .1. Homologous series ( CH 2 ) n( COOH ) 2 ( n=0 ,

1, 2 , 3 , 4)

The values for dissociation constants are similar

to ones quoted in literature [7–10] (see e.g. Table

4) but the comparison can only be approximatedue to different conditions in which the experi-

ments were conducted. Comparing the dissocia-

tion constants,

k 1=[H][HL]

[H2L]; k 2=

[H][L]

[HL]

for the acids that belong to homologous series we

can observe general tendency, the longer the chain

the smaller dissociation constant. Only in the case

of adipic acid, the first dissociation constant is

higher, coming close to the value k 1 for malonic

acid (Table 5).

Table 3

Concentrations (C , C 0) of the solution in Table 2

NaOH C (molAcid H2L C 0 (mol dm−3)

dm−3)

Oxalic 0.1139 0.09953

Malonic 0.10034a0.1583a

Succinic 0.1386 0.10087

Glutaric 0.1386 0.10017

Adipic 0.1139 0.09989

0.1004Methylmalonic 0.10423

0.1111 0.10240Dimethyl-malonic

Ethylmalonic 0.1111 0.10139

a From ref. [2].

Table 4

Comparison of dissociation constants for some dicarboxylic

acids

Acid n pk 1 pk

2 Literature This worka

pk 1

pk 2

4.19Oxalic 1.230 4.201.06[7,8]

1 2.83 5.69Malonic [7–10] 3.41 5.80

5.652 4.15Succinic [7–10]5.484.12

5.984.50[7]5.42Glutaric 4.343

4 4.42Adipic 5.41 5.54[7] 4.58

a Series 1.

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Table 5

Dissociation constants (k i ) for the homologous series calculated in this study; (I =1.64 mol dm−3; pk i =− log (k i ), i =1,2)

Oxalic MalonicSeries Succinic Glutaric Adipic

4.20 5.74pk 1 5.651 5.98 5.54

4.122 5.72 5.77 6.22 5.42

4.44 5.72 5.413 6.05 5.39

3.91 – a 6.01 5.944 5.39

1.06 3.34 4.151 4.50pk 2 4.57

1.03 3.062 4.35 4.39 4.631.02 3.18 4.063 4.43 4.61

1.51 – a 3.93 4.62 4.634

a Dissociation constants for malonic acid were calculated from the data in [2].

Fig. 1.

Along the homologous series, stability con-

stants for hydrocomplexes increase up to glutaric

acid. For the next acid in the series, log K 101 and

log K 011 decreases. This may suggest the forma-

tion of hydrogen bonds in the case of glutaric

acid. The same feature can be observed for other

complexes (NaL, KL, Na2L and K2L). It does not

matter what the amount of K+ or Na+ in the

system (Fig. 1).

3 .2 . The influence of alkyl substituents

Dicarboxylic acids are stronger than monocar-

boxylic acids with the same number of carbon

atoms in aliphatic group, see Table 6. One car-

boxylic group affects the other one with the

strength depending on their distance in the chain.

The closer they are the stronger the influence is.

Other groups attached to the chain also influence

acidity. In general, any substituent that delocalises

the charge of the group COO−, lowers its energy

and increases the dissociation constant. The study

of this effect was done on a group of four acids,

glutaric; methylmalonic; dimethylmalonic and

ethylmalonic [11,12], see Table 7.

In the case of dimethylmalonic and ethyl-malonic acids, which are isomers of glutaric acid,

we can notice that their stability constants are

similar regardless of the series (Table 7). The

protonation constants for metylmalonic acid are

also similar to other substituted acids but higher

then those for glutaric acid.

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First dissociation constants (k 1=K 001/K 002),

with pk 1=2.96, 3.04, 3.00 for methylmalonic,

dimethylmalonic and ethylmalonic acids, respec-

tively (series 1), are higher than those for glutaric

acid (pk 1=4.50). The second dissociation con-

stants (k 2=1/K 001; pk 2=6.39, 6.37, 6.37) are

lower than pk 2=5.98 (series 1) for glutaric acid

(the same applies to other series). There are two

effects involved, 1° interaction between carboxylic

groups; 2° influence of alkyl group from the chain

on acidity. Alkyl groups destabilise the anion of

the acid and thus lower its strength.

The values of stability constants for hydrocom-

plexes (K 101 and K 011) of isomers of glutaric acid

Table 6

Stability constants and f for (CH2)n (COOH)2 homologous acids (1–4 series); (I =1.64 mol dm−3; 20°C)

Series Oxalic acid Malonic acid Succinic acid Glutaric acid Adipic acidParameters

log K 002 (H2L) 5.2690.041 9.0890.03 9.8090.04 10.48190.008 10.1190.03

5.290.2 8.7890.03 10.1290.03 10.6190.04 10.0590.022

10.0090.0110.48790.0059.4790.028.9090.065.590.43

10.5690.019.9490.08 – a 10.0290.025.4290.044

Log K 001 (HL) 4.2090.011 5.7490.03 5.690.1 6.090.1 5.5490.07

2 4.190.2 5.72090.004 5.7790.03 6.2290.08 5.4290.01

5.3990.016.0590.055.4190.045.7290.044.4490.033

5.399

0.015.99

0.26.019

0.08 –

a

3.919

0.034 5.6790.04 5.6590.06 6.2290.014.17090.008 5.4790.061log K 101 (NaHL)

4.59690.002 4.590.2 6.0290.04 6.0990.08 5.090.062

5.3090.016.22290.0095.5490.025.8490.044.6390.023

5.2090.034 4.62590.005 6.2090.03 – a 5.2490.08

log K 011 (KHL) 5.9490.09 4.4790.03 5.890.1 5.090.54.5590.011

4.48790.002 5.7090.01 5.690.2 5.7890.072 5.3690.03

4.5590.03 5.590.1 4.5490.083 5.6990.06 5.2490.02

4.52490.005 – a 5.490.14 5.990.1 5.3490.01

0.2990.051.190.10.3190.040.5590.02log K 100 (NaL) 0.81190.0061

2 0.8890.09 0.6290.03 0.4690.09 0.9590.02 0.2290.02

0.1690.020.8790.01−0.1690.040.4490.080.9290.033

0.7790.030.590.2 – a 0.1690.020.8790.014

1log K 010 (KL) 0.4390.06 0.4590.04 0.38690.005 1.50490.007 0.5890.07

2 0.83290.008 0.3490.03 0.390.1 1.43190.007 0.49390.003

3 0.9090.02 0.590.1 0.1690.02 1.49490.003 0.5090.02

0.4690.021.4490.020.4290.02 – a0.88490.0094

0.1190.03 0.3890.06 0.890.20.57290.004 0.290.11log K 200 (Na2L)

0.5990.01 0.5990.09 0.890.22 1.0390.08 −0.1390.09

1.090.2 0.490.3 −0.4190.063 0.8790.01 −0.390.1

−0.2890.050.8590.090.5490.02 – a0.5690.034

-4.90.2 0.1890.07log K 020 (K2L) 0.7290.051 1.290.3 −0.890.2

2 0.5190.02 −0.1390.06 0.590.1 0.4190.03 0.2390.01

−0.3290.070.6390.030.7490.010.890.20.390.13

0.290.10.4090.070.6490.02 – a0.590.24

1 −0.0190.3 −0.0290.02 0.3490.03 0.390.1 0.1990.04log K 110 (NaKL)

2 0.4190.02 −0.190.1 0.490.2 −0.3790.04 −0.1690.02

−0.0690.53 −0.1790.04 0.6390.03 −0.3890.090.290.13−0.3190.05−0.690.20.4290.03 – a0.3590.054

2.4290.08 1.1190.07 1.0390.021.23690.008 1.29890.0021 f

1.0290.02 1.3290.01 1.190.12 1.0090.04 0.9790.02

3 1.24190.009 1.4590.09 1.0690.01 1.01890.004 1.1490.01

1.2090.011.0390.021.0190.03 – a4 1.0990.01

a Stability constant and f for malonic acid were calculated from the data in [2].

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Table 7

Stability constants (K ijk ) and f for glutaric, methylmalonic, dimethylmalonic and ethylmalonic acids (1}4 series); (I =

log K 101 log K 011log K 002 log K 100log K 001 log K 010SeriesAcid log K 200(NaHL) (Na2L)(H2L) (NAL)number (KL)(HL) (KHL)

Glutaric 1.190.11 1.5090.01 0.890.2 6.090.1 10.4890.01 6.2290.01 5.890.10.9590.02 1.43190.007 1.0390.08 2 6.290.1 10.6190.04 6.0990.08 5.7890.070.8790.01 1.49490.003 0.8790.01 5.6990.06 10.4890.01 6.2290.013 6.0590.05

5.990.14 0.7790.03 1.4490.02 0.8590.09 5.990.2 10.5690.01 6.2090.036.5490.011 5.9290.02 1.5590.04 1.44390.007 0.590.2 6.3990.02 9.35190.004Methyl-

malonic

1.6590.07 1.44490.001 1.090.1 6.4790.04 6.4190.049.4490.036.38290.00321.7890.05 1.47390.001 0.790.4 3 6.4190.01 9.39690.008 6.57790.005 6.3990.021.7790.02 1.46990.001 0.6490.02 6.4290.01 6.40490.0044 6.56390.0029.39490.005

6.4490.081 6.590.1 0.8890.01 1.4990.01 0.9590.02 6.3790.03 9.4190.03Dimethyl-malonic

3 6.4790.01 1.07290.002 1.47390.003 1.37890.0066.5290.01 9.6490.01 6.7090.030.6990.02 1.49890.004 0.6990.03 6.50090.002 6.50090.0029.5190.026.30090.0023

0.88190.001 1.49490.001 0.87890.0014 6.32790.003 9.48490.003 6.52090.002 6.51890.0026.5590.02 0.9990.04 1.5190.01 0.990.1 6.3190.01 6.3790.01 9.3790.01Ethyl- 1

malonic2 6.4690.01 1.78790.002 1.1390.05 0.9690.04 6.34690.004 9.46490.003 6.890.1

6.55290.0023 0.7890.03 1.48490.001 1.36690.0036.37690.004 9.41190.002 6.3490.010.85290.001 1.47890.001 1.37590.0016.54490.0014 6.36090.001 6.3090.029.46190.004

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Fig. 2.

are very similar for all series. They are higher than

those for glutaric acid itself.

A very interesting feature concerns K 010 (KL)

constant. It stays on the same level regardless of

the acid or the composition of the solution. A

higher concentration of KNO3 (series 1 and 3) has

no influence on this stability constant. As for K 100(NaL) constant, we can observe that one alkyl

substituent stabilises NaL complexes. Adding an-

other methyl group in the chain decreases thestability almost to that of glutaric acid. This also

depends on the concentration of NaNO3 in the

solution (for series 2 and 4 with a higher NaNO3

concentration, the constant is higher than that of

glutaric acid; for series 1 and 3, it is lower).

The parameters K 200 (Na2L), K 020 (K2L) and

K 110 (NaKL) have little influence on the fitting

function, probably because of their low stabilities.

For this reason, it is not possible to determine

them with higher accuracy, only rough evaluation

is possible (Fig. 2).

3 .3 . Acti 6ity coefficient of protons

The proton activity coefficient ( f ) was one of

the parameters of the system, i.e. the calculations

were not aided by the doubtful formulae for f

value. The problem of calculating f values was

already described above as the ‘uncertainty princi-

ple’ [3]. From Table 7, it results that f values are

generally higher for the series with a higher con-

centration of NaNO3 (series 1 and 3). The activity

coefficient ( f ) for glutaric acid homologues is on

the same level, regardless of acid or system com-

position (Fig. 3).

The correlation between the activity coefficient

( f ) and %e is less established. This state of matter is probably affected by the covalent char-

acter of bonds between H+ and basic forms HL−

and L2− of the acid that is felt particularly at a

lower pH interval. On the other hand, the electro-

static interactions predominate within the pH in-

terval where the inequality

[H2L]+ [HL−] [L2−]

is valid. The problem emerges from the fact that

the reliable data for the stability constants are

obtained from results of pH-metric titrations onlyif the points (V j , pH j ) cover the pH-interval where

any particular form of the acid affects the results

significantly, if not predominantly, at defined

stage of the titration. The (mutually excluding)

requirements are a kind of ‘uncertainty principle’

affecting the f value despite of the isothermal

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Fig. 3.

(T =constant) conditions of the titration made at

constant I and m values. The problems indicated

cannot be resolved within the Debye –Huckel the-ory. Unlike in some commonly used procedures,

we shall not expatiate here upon the dubious

assumptions of this theory (and its extensions, as

well), but rather questionable assumptions of, (1)

electrostatic interactions in isotropic systems and

(2) assumption that the activity coefficient, f =

f (I , m , T ), does not take into account the changes in

strength of interactions between H+ and basic

forms HL− and L2− during titration, should be

stressed. It incurs some inevitable errors in our

calculations. Apart from coulombic forces, thereare other types of interactions, which are not

capable of interpretation within the Debye –Huckel

theory.

The emerging problem is very difficult and

largely unsolved although some empirical exten-

sions of the correct model Eq. (1) can be

considered.

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[7] I.O. Southerland (Ed.), Comprehensive Organic Chem-

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