Why does adding salt increase solubility and why do you think that heating stirring and increasing surface area increases the rate of solubility?
In general, my experience is adding salt (for example NaCl) decreases solubility. That is why a saturated water solution is used to dry other liquids. (since it is saturated, it wants water, but does not dissolve much of anything else) If the solute you are talking about has a Na or Cl there is also the common ion effect.
The rate of dissolution (I think that is what you are referring to) is increased by heating is faster molecular motion, stirring allows more material to be contacted in less time so the interaction speeds up. Increasing surface area also allows more material to be contacted in less time so the interaction speeds up. That interaction can be dissolution, or a chemical reaction.
When salt is dissolved in water then the ions so formed get hydrated by the water molecules and decrease the movement of water molecules and solubility also decreases, hence, on agitation and stirring the solubility increases. Proteins are surrounded by the salt counterions and these screening results in decreasing electrostatic free energy of the protein and increasing activity of the solvent, which in turn leads to increasing solubility. As the temperature increases, the particles of the solid move faster which increases the chances that they will interact with more of the solvent particles. This results in increasing the rate at which a solution occurs. With greater surface area, there can be more contact between particles of solute and solvent. For many solids dissolved in liquid water, the solubility increases with temperature. The increase in kinetic energy that comes with higher temperatures allows the solvent molecules to more effectively break apart the solute molecules that are held together by intermolecular attractions this is the reason. When sugar dissolves in water, it dissolves faster if the water is agitated. The stirring ensures that new solvent molecules are constantly in touch with the solute.
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