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     ...Introduction to Solubility

CSLogWS  Predictor Capabilities

CSLogWS Calculates Predictions for the Following:

Intrinsic Solubility (LogWSo)
Aqueous Solubility pH Profile of:
    pH 2.0 (LogWS2.0)
    pH 5.0 (LogWS5.0)
    pH 7.4 (LogWS7.4)
Available option to calculate a pH solubility profile from pH 0.0 to pH 14.0 in intervals of 0.2 pH units

The only input required from the user is a structure for each compound to be predicted.  The structure may be submitted as either a MOL file or SD file and it is not necessary for the structure to be in a three dimensional format or to be optimized to a minimum energy confirmation.  CSLogWS predictions are expressed as mol/L or mg/mL.

Definition of Log WS Property Data

Intrinsic solubility (WSo) is defined as the number of moles per liter of solute that disolves into solution. Equilibrium between solute and solution is maintained at a specific temperature, usually 25°C.   Units can be expressed as mol/l, mg/ml or ppM.  CSLogWS expresses units as mol/L or mg/mL.

For a neutral compound, the total solubility equals the intrinsic solubility because only the neutral compound is involved.  For a compound with ionizable groups, the solubility expression is more complex because multiple species with varying solubility are present.  It is necessary to use the term aqueous solubility to define the solubility of compounds with ionizable groups.

Aqueous solubility is the sum of the individual solubilities for the neutral compound and all ionized species present.  For compounds with ionizable groups, aqueous solubility is a function of pH.  

Given WSo (the solubility of the neutral compound) and the solubility of each ionized species Ci the equation for aqueous solubility becomes:

A pH-solubility profile is a set of solubility values at specified pH values.  The values given in a pH profile refer to solubility as a function of pH for all species of the compound (ionizable and neutral) in solution.  Solubility profiles are necessary to delineate solubility in complex situations where multiple ionnizable species are present.  CSLogWS reports a pH solubility profile giving the solubility at pH 2.0, pH 5.0 and pH 7.4 for all ionizable compounds.  For a neutral compound, aqueous solubility is equal to the intrinsic solubility, so only WSo is reported.

The principle relationship between solubility and pH can be derived under equilibrium conditions for a saturated solution of an ionizable compound such as monoprotic (A), monobasic (B) or ampholytic (AB).  CSLogWS covers 14 cases from monoprotic to tri-ampholytes (e.g., ABB, BBA, ABA).  Below are derived expressions for WS for a simple monoprotic acid and di-ampholyte (AB) to illustrate examples of the underlying expressions to predict LogWS.

Monoprotic Acid Compounds

Monoprotic Acid:

Two expressions may be written for dissociation of the acid and the equilibrium between solid and solution.

Where the equilibrium expressions are:

Combining equations (3), (4) and (5) gives an expression for total solubility:

Using H+ in terms of pH and k1 in terms of pK1 and then taking the log yields an expression in conventional form:

An example of expression (7), given for a typical organic acid, is plotted below as a function of pH along with the percentage of acid ionized.  The intrinsic solubility (WSo) for this example is 6.76E-3 (mol/l).  As seen from the plot, as the calculated percent ionized acid increases, WS also increases as more of the ionized species enters solution.  It should be noted that the increase in WS shown in this simplified example is not bounded.  This simplification is unrealistic because it assumes infinite solubility.  Solubility is limited by ion-pairing.

Ion-pairing ( e.g., RCO2- + Na+               RCO2- •• Na+ ) occurs at a given pH when the solubility product, Ksp, is reached and then salt precipitation starts when sufficient counterions are present. 

Examples of how a monoprotic acid and base behave with cut-offs for LogWS are shown below. With a base the bounded part of the curve occurs at a low pH value while the opposite is true for an acid.  When calculating LogWS, it is necesssary to implement solubility cutoffs due to lack of available data for Ksp's for diverse organic compounds.

Di-ampholyte (AB) Compounds

Di-ampholyte (AB):

Since it is virtually impossible to compute microconstants, except for simple systems, the equilibria expressions for di-ampholyte can be reduced to:

Combining equations (1) and (2) leads to a fourth expression for total solubility:

...where k1 and k2 are the macroscopic (apparent dissociation) constants and HX the neutral form (net charge =0) of  the compound.   The latter is the sum of concentrations for neutral species, [HXo], and the zwitterion, [HX±].


we have combined expressions (1) through (4) into (5), an expression in terms of [H+], and (6), an expression in terms of pH.  Both equations are general expressions for the AB-ampholyte:

Show below is a typical AB-ampholyte pH-solubility profile.  The given example makes use of the same WS "Rule of Thumb" solubility cutoff values described above.

The shape of the curve in a pH-solubility plot is variable, and dependant upon pKa and intrinsic solubility (WSo) values.

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