Szyszkowski equation

The Szyszkowski Equation, as applied by Meissner and Michaels, describes the decrease in surface tension of aqueous solutions containing carboxylic acids, alcohols, and esters at varying mole fractions. It effectively models the exponential decline in surface tension at low concentrations but is recommended for use only when concentrations are below 1 mole%. The equation expresses the surface tension of the mixture (\( \sigma_m \)) as a function of pure water's surface tension (\( \sigma_w \)), a component-specific constant (\( a \)), and the solute's mole fraction (\( x \)). Rearranging the equation allows direct calculation of \( a \) from experimental data.

Another form of the equation relates surface tension (\( \gamma \)) to pure water's surface tension (\( \gamma_0 \)), with terms involving the ideal gas constant (\( R \)), temperature (\( T \)), and molecular cross-sectional area (\( \omega \)). Pure water's surface tension depends on temperature, measuring 71.97 mN/m at 298 K.

Meissner and Michaels published specific \( a \) constants for various substances. An example with propionic acid shows close agreement between the calculated and published \( a \) values at low concentrations (e.g., mole fraction 0.00861), but deviations occur at higher concentrations, indicating limitations in the equation's predictive accuracy beyond low solute levels.