1364
The Electrolytic Dissociation of 1,4-Cyclohexanedicarboxylic Acid
For weak dibasic organic acids the law of dilution for both dissociation steps may be expressed as follows:
where K_{1} and K_{2} are the thermodynamic dissociation constants of first and second steps, α_{1} and α_{2} 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, F_{1} and F_{2}are the quotients of the activity coefficients for the corresponding steps:
The values of the activity coefficients were approximated by the Debye-Huckel equation:
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 .
According to equations [1] and [2] the degrees of dissociation α_{1}, α_{2} and α^{′}_{2}can be evaluated successively by iterative solution of following two quadratic equations:
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:
The dissociation constants of trans-1,4-cyclohexanedicarboxylic acid have the following values: K_{1}=6.607×10ˉ^{5}; K_{2}=3.802×10ˉ^{6}.
In Tables I the values of α_{1}, α_{2}, α^{′}_{2}and pH for the dilute solutions of acid are presented.
Table I. The values of the dissociation parameters
of trans-1,4-cyclohexanedicarboxylic acid
at 16ºC
Concentration, M |
α_{1} |
α_{2} |
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 |
0.5507 0.4365 0.3358 0.2849 0.2525 0.2295 0.1691 0.1233 0.1021 0.08926 0.08035 |
0.03472 0.01826 0.009473 0.006427^{} 0.004875^{} 0.003932^{} 0.002014 0.001030 0.0006954^{} 0.0005267^{} 0.0004246 |
0.06305 0.04183 0.02821 0.02256 0.01931 0.01713 0.01191 0.008354^{} 0.006811^{} 0.005901^{} 0.005284 |
4.236 4.046 3.866 3.764 3.693 3.639 3.474 3.314 3.221 3.156 3.106 |
We suggest also the simple empirical equations for fast approximate calculation of the dissociation parameters of trans-1,4-cyclohexanedicarboxylic acid: