User:WilfriedC/Playground/Szyszkowski equation

The Szyskowski Equation has been used by Meissner and Michaels to describe the decrease of the surface tension in aqueos solutions of carboxylic acids, alcohols, esters, and few other components from pure water to increasing concentrations of the solved components. It describes the exponential decrease of the surface tension at smaller concentrations quite well but should be used only at concentrations below 1 mole%.

Equation
$$\sigma_m = \sigma_w * \left( 1. - 0.411 * log \left( 1 + \frac{x}{a} \right) \right)$$

with
 * $$\sigma_m$$: Surface tension of the mixture
 * $$\sigma_w$$: Surface tension of pure Water (approx. 72 mN/m, see also example below)
 * $$a$$: Component specific constant (see table below)
 * $$x$$: Mole fraction of the solved component

The equation can be rearranged to be explicit in a:

$$a=\frac{x}{10^{\left( \frac{\sigma_m / \sigma_w - 1}{-0.411} -1\right)}}$$

This allows the direct calculation of that component specific parameter a from experimental data.

Parameters
Meissner and Michaels published the following a constants:

Example
The following table and diagram show experimentally determined surface tensions in the mixture of water and propionic acid.

This example shows a good agreement between the published value a=26E-4 and the calculated value a=25.9E-4 at the smallest given concentration of xAcid=0.00861 mol/mol but at higher concentrations of propionic acid the value of a increases considerably and shows that the equation with a constant a should be used only for small solute concentrations.