Calculating the solubility of a solid solute in a viscous solvent can be complex, as it depends on several factors, including temperature, interactions between solute and solvent molecules, the nature of the solute and solvent, and the solvent’s viscosity. However, a few approaches and models can provide estimates of solubility.

Key Factors Affecting Solubility:

Common Methods to Estimate Solubility:

1. Empirical Measurements

• Solubility Test: The most straightforward way to determine solubility is through experimental measurement. By adding a known amount of solute to the solvent, heating (if necessary), and allowing the system to reach equilibrium, the concentration of dissolved solute can be determined. However, for viscous solvents, stirring and heat management may be required to ensure uniform solute distribution.
• Method: Add the solute incrementally to the solvent, stir until no more dissolves, and then measure the concentration of the dissolved solute at equilibrium (using techniques like gravimetric analysis, spectrometry, or titration).

2. Thermodynamic Models

Thermodynamic models can be used to predict the solubility of a solute in a solvent, particularly in cases where empirical data is unavailable. These models typically require knowledge of parameters such as molecular properties, temperature, and interactions between solute and solvent.

a. Ideal Solubility

The ideal solubility of a solute can be estimated using the solubility equation based on Gibbs free energy of mixing, particularly if you assume ideal behavior. For a solid solute in a solvent, the formula for ideal solubility is:

ln⁡x2=−ΔHfusR(1T−1Tfus)\ln x_2 = \frac{-\Delta H_{fus}}{R} \left( \frac{1}{T} - \frac{1}{T_{fus}} \right)lnx2​=R−ΔHfus​​(T1​−Tfus​1​)

Where:

• x2x_2x2​ = mole fraction of solute (solubility),
• ΔHfus\Delta H_{fus}ΔHfus​ = heat of fusion of the solute,
• TTT = temperature (in K),
• TfusT_{fus}Tfus​ = melting temperature of the solute (in K),
• RRR = universal gas constant.

This gives an estimate of solubility in an ideal system but does not consider solvent viscosity or non-ideal behavior.

b. Activity Coefficient Models (for non-ideal systems)

To account for non-idealities (as is common with viscous solvents), models such as

Thank you for sharing your idea.

But the problem is: My solvent, due to its adhesive properties, makes it difficult for me to determine how much has dissolved or how much has dispersed.