Cycloalcanediacetic acids are the nonaromatic, cyclanic polycarboxylic acids; they are used as the pharmaceutical intermediates. In this communication the previously suggested by authors original method for the determination the parameters of dissociation of weak multibasic organic acids was used for an analysis of the processes of electrolytic dissociation of 1,1-cyclopentanediacetic and 1,1-cyclohexanediacetic acids which are not sufficiently investigated.

For weak dibasic organic acids the law of dilution for both dissociation steps may be expressed as follows:

[1]

[2]

where K₁ and K₂ are the thermodynamic dissociation constants of first and second steps, α₁ and α₂ are the usual degrees of dissociation of  these steps, α^′₂ is the “partial” degree of dissociation of second step, c is the total (analytical) concentration of acid, F₁ and F₂are the quotients of the activity coefficients for the corresponding steps:

[3]

[4]

The values of the activity coefficients were approximated by the Debye-Huckel equation:

[5]

where a_i is the cation-anion distance of closest approach, A and B are constants depending on the properties of water at given temperature, z_i is the charge of ion. Ionic strength I=c(α₁+2α₂)=cα₁(1+2α'₂).

According to equations [1] and [2] the degrees of dissociation α₁, α₂ and α^′₂can be evaluated successively by iterative solution of following two quadratic equations:

[6]

[7]

[8]

The equilibrium concentrations of the dissociation products: hydrogen ions, mono- and dianions and undissociated acid molecules can be calculated with the aid of the following equations:

[H⁺]=c(α₁+α₂)                    [9]

[HA^-]=c(α₁−α₂)                  [10]

[A^2-]=cα₂                          [11]

[H₂A]=c(1−α₁)                   [12]

The dissociation constants of 1,1-cyclopentanediacetic acid have the following values: K₁=1.585×10ˉ⁴; K₂=1.700×10ˉ⁷. The corresponding values for 1,1-cyclohexanediacetic acid are: K₁=3.236×10ˉ⁴; K₂=1.1×10ˉ⁷ (all values – for 25ºC).

In Tables I and II the values of α₁, α₂, α^′₂and pH for the dilute solutions of both acids at 25ºC are presented. 

Table I. The values of the dissociation parameters

               of 1,1-cyclopentanediacetic acid at 25ºC

Concentration, M	α1	α2	α′2	pH
0.0001 0.0002 0.0004 0.0006 0.0008 0.001 0.002 0.004 0.006 0.008 0.01	0.6983 0.5824 0.4668 0.4039 0.3623 0.3321 0.2499 0.1851 0.1545 0.1356 0.1224	1.758·10–3 8.904·10–4 4.512·10–4 3.035·10–4 2.291·10–4 1.842·10–4 9.375·10–5 4.783·10–5 3.235·10–5 2.447·10–5 1.973·10–5	2.518·10–3 1.529·10–3 9.666·10–4 7.514·10–4 6.323·10–4 5.547·10–4 3.752·10–4 2.584·10–4 2.094·10–4 1.805·10–4 1.612·10–4	4.159 3.938 3.735 3.623 3.546 3.487 3.312 3.143 3.047 2.980 2.928

Table II. The values of the dissociation parameters

               of 1,1-cyclohexanediacetic acid at 25ºC

 

Concentration, M	α1	α2	α′2	pH
0.0001 0.0002 0.0004 0.0006 0.0008 0.001 0.002 0.004 0.006 0.008 0.01	0.8042 0.7028 0.5877 0.5193 0.4722 0.4369 0.3370 0.2542 0.2139 0.1887 0.1711	0.001143 0.0005796 0.0002944 0.0001983 0.0001498 0.0001206 0.00006159 0.00003153 0.00002134 0.00001619 0.00001308	0.001421 0.0008247 0.0005009 0.0003819 0.0003172 0.0002760 0.0001828 0.0001239 0.00009958 0.00008585 0.00007656	4.094 3.858 3.636 3.515 3.432 3.369 3.171 3.007 2.908 2.839 2.785

We suggest also the simple empirical equations for fast approximate calculation of the dissociation parameters for both acids:

1,1-Cyclopentanediacetic acid

α₁=0.036475c^-0.0323    (up to 0.002M)        [11]

α₂=2.11349x10^-7c^-0.98 (up to 0.01M)         [12]

α^′₂=5.78096x10^-6c^-0.658 (up to 0.002M)    [13]

pH=1.469−0.667lgc      (up to 0.01M)        [14]

1,1-Cyclohexanediacetic acid

α₁=0.07187c^-0.264       (up to 0.0004M)      [15]

α₂=1.404x10^-7c^-0.977    (up to 0.01M)        [16]

α^′₂=2.04796x10^-6c^-0.706  (up to 0.002M)   [17]

pH=1.173−0.728lgc      (up to 0.01M)        [18]