Is Passynski's Approach to Hydration Numbers Consistent with Thermodynamics?

Area of Science:

• Physical Chemistry
• Thermodynamics
• Solution Chemistry

Background:

• Hydration number characterizes solute hydration in aqueous solutions.
• Passynski's method uses isentropic compressibility to determine hydration numbers.
• Isentropic compressibility is a fundamental thermodynamic property.

Purpose of the Study:

• To thermodynamically analyze Passynski's method for hydration number determination.
• To evaluate the consistency of Passynski's assumptions with fluid thermodynamics.
• To derive an alternative formula for hydration number based on thermodynamic principles.

Main Methods:

• Application of Passynski's assumptions to mixture volume.
• Strict thermodynamic derivation of hydration number formula.
• Analysis of isentropic compressibility dependence on solute mole fraction.

Main Results:

• Passynski's method is shown to be empirically derived, not thermodynamically rigorous.
• A new formula for hydration number, resembling Onori's, was derived.
• Passynski's numbers are an empirical measure of compressibility slope.

Conclusions:

• Passynski's method is inconsistent with fluid thermodynamics and mechanics.
• The derived hydration number formula offers a more thermodynamically sound alternative.
• Conclusions on molecular interactions from Passynski's numbers require significant caution.