^{1}

^{*}

^{2}

^{*}

The solubilities (s, mol/L) of different oxyquinolinates (oxinates, MeL_{2}) are calculated using the formulae obtained according to elementary algebra, with the use of Excel spreadsheets. The calculations are involved with solution of algebraic equation of the third degree, obtained on the basis of concentration balances. The root of this equation, , is then inserted into the charge balance, and resolved according to zeroing procedure. In principle, the calculations are related to aqueous media. Nonetheless, the extension on liquid-liquid extraction systems is also proposed.

8-hydroxyquinoline (HL, _{2} with some divalent metal ions_{3} with some trivalent metal ions

The oxine and its complexes, functioning as a transcription inhibitor [

Oxidative damage is frequently found in many diseases such as aging, atherosclerosis, cancer, diabetes [

dismutases (SOD), results in the generation of reactive oxygen species (ROS) [

In conclusion, metal ions play a very important role in biological processes, and metal homeostasis is required for the maintenance of metal balance [

It is also worth noting that aluminum oxinate, AlL_{3}, is a common component of organic light-emitting diodes (OLED’s) [

In this context, we are interested in the manner of calculation of (1) the solubility s [mol/L] and (2) pH of the solution obtained after introducing pure oxinate MeL2 into pure water. The calculations will be made with use of Excel spreadsheets applied to an algorithm based on some balances and full physicochemical knowledge on the systems in question, involved in the related equilibrium constants.

The precipitates of oxinates are characterized by the solubility product _{2} type we have:

The soluble complex species

The stability constants

The

and ionic product of water:

Me^{+2 } | Solubility products_{ } | Stability constants of | Stability constants of | ||||
---|---|---|---|---|---|---|---|

_{ } | ^{ } | _{ } | |||||

Cd^{+2} | 22.0 | 7.2 | 13.4 | 4.3 | 7.7 | 10.3 | 12.0 |

Co^{+2} | 24.2 | 9.1 | 17.2 | 4.3 | 8.5 | 9.7 | 10.2 |

Cu^{+2} | 29.1 | 12.2 | 23.4 | 7.0 | 13.66 | 17.0 | 18.5 |

Ni^{+2} | 25.5 | 9.9 | 18.7 | 4.97 | 8.55 | 11.33 | - |

On the basis of (4) and (5) we get:

If pure MeL_{2} is introduced into pure water, then the following relationships (concentration and charge balances) are valid:

where _{2},

is the solubility of MeL_{2}. Assuming

where

where

The Equation (15) is named as depressed cubic equation [

In general, Equation (15) can have real and complex roots for

where

If

If Δ = 0, all roots are real and at least two are equal. If

where

and from Equation (1) we have

The sign of Δ (Equation (18)) can vary with change of the pH value; it also depends on the values of physicochemical constants involved in it. Three possible cases are exemplified by physicochemical systems considered in this paper, namely:

1) _{0} value;

2) _{0} value;

3) _{0} value.

The pH_{0} value results from the following calculation procedure. The

Zeroing the function (23), gives _{0}. For this pH_{0} value, considered as pH of the solution obtained after introducing the precipitate MeL_{2} into pure water, one can calculate concentrations of different species, e.g., the species involved in expression for solubility

In the calculations, the pH interval 6.0 - 8.5 was taken as the basis for calculation of pH_{0} value for the systems presented in _{0} values were calculated with accuracy < 0.01 pH units, see _{0} values, concentrations of individual species and then solubilities

Note that in all instances, where MeL_{2} is the equilibrium solid phase, we have:

i.e., it is a constant component in Equation (12), independent on pH values. For comparison, when applying the formula [

Me^{+2} | pH_{0 } | _{0}) = 0 in Equation (21) | s | ||||||
---|---|---|---|---|---|---|---|---|---|

^{ } | ^{ } | ^{ } | _{ } | ||||||

Cd^{+2} | 8.03 | 4.71E−07 | 1.01E−08 | 2.71E−11 | 1.16E−14 | 6.21E−19 | 1.09E−07 | 2.51E−09 | 5.93E−07 |

Co^{+2} | 7.68 | 8.56E−08 | 7.80E−10 | 5.65E−12 | 4.09E−17 | 5.92E−23 | 2.93E−07 | 1E−07 | 4.79E−07 |

Cu^{+2} | 7.17 | 3.26E−10 | 4.82E−10 | 3.26E−10 | 1.05E−13 | 4.93E−19 | 8.06E−08 | 2.00E−6 | 2.08E−06 |

Ni^{+2} | 7.41 | 1.72E−08 | 4.13E−10 | 4.04E−13 | 5.84E−18 | - | 1.85E−07 | 1.58E−07 | 3.61E−07 |

obtained on the basis of simplified assumptions:_{2} is demonstrated. All known species involved with this system and the related equilibrium constants (1) - (6) are included in the balances (9) - (11). It is an example of the two-phase system where minimal solubility of a precipitate is limited by the concentration of soluble species of the same formula (here: MeL_{2} and MeL_{2}).

Let us consider a two-phase liquid-liquid extraction system, composed of two practically immiscible solvents, e.g. H_{2}O + CHCl_{3}. The CHCl_{3} is not soluble in water (mutual solubility is less than 0.01%) [

where subscript

Let

MeL_{2} | CdL_{2} | CoL_{2} | CuL_{2} | NiL_{2} |
---|---|---|---|---|

5.93E−07 | 4.79E−07 | 2.08E−06 | 3.61E−07 | |

s^{* } | 2.92E−08 | 5.40E−09 | 1.26E−10 | 1.99E−09 |

At

Then we get the equation

For resolution of cubic equations, the Excel spreadsheets were used; the coefficients of these equations were the functions of pH; resolution of the related equation was the primary step for zeroing the transformed charge balance,_{4}PO_{4} [_{3})_{2} [

Derivation of Equation (15) at

Setting

in Equation (15), after further rearrangements we get

At

from (A2) and (A3) we have

Setting

in (A3) we have

where

As we see (Equation (A7)), the formulae for

Then, on the basis of Equations (A7) and (A9),

i.e.,