The Szyszkowski EquationB. von Szyszkowski, Z. physik. Chemie, 64, 385 (1908) has been used by Meissner and MichaelsH.P. Meissner, A.S. Michaels, Surface Tension s of Pure Liquids and Liquid Mixtures", Ind. Eng. Chem., 41(12), 2782, (1949) to describe the decrease in surface tension of aqueous solutions of carboxylic acids, alcohols and esters at varying mole fractions. It describes the exponential decrease of the surface tension at low concentrations reasonably but should be used only at concentrations below 1 mole%.Bruce E. Poling, John M. Prausnitz, John P. O’Connell, The Properties of Gases and Liquids, 5th Edition

Equation

with: σm is surface tension of the mixture σw is surface tension of pure water a is component specific constant (see table below) x is mole fraction of the solvated component

The equation can be rearranged to be explicit in a:

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

The equation can also be written as:

with: γ is surface tension of the mixture γ0 is surface tension of pure water R is ideal gas constant 8.31 J/(mol*K) T is temperature in K ω is cross-sectional area of the surfactant molecules at the surface

The surface tension of pure water is dependent on temperature. At room temperature (298 K), it is equal to 71.97 mN/m NIST Chemistry WebBook http://webbook.nist.gov/chemistry/

Parameters Meissner and Michaels published the following a constants: + Szyszkowski Equation Constants Compound a.104 Compound a.104 Propionic acid 26 n-Propyl alcohol 26 Isopropyl alcohol 26 Methyl acetate 26 n-Propyl amine 19 Methyl ethyl ketone 19 n-Butyric acid 7 Isobutyric acid 7 n-Butyl alcohol 7 Isobutyl alcohol 7 Propyl formate 8.5 Ethyl acetate 8.5 Methyl propionate 8.5 Diethyl ketone 8.5 Ethyl propionate 3.1 Propyl acetate 3.1 n-Valeric acid 1.7 Isovaleric acid 1.7 n-Amyl alcohol 1.7 Isoamyl alcohol 1.7 Propyl propionate 1.0 n-Caproic acid 0.75 n-Heptanoic acid 0.17 n-Octanoic acid 0.034 n-Decanoic acid 0.0025

Example The following table and diagram show experimentally determined surface tensions in the mixture of water and propionic acid. + Surface Tension of Propionic Acid solved in WaterSuarez F., Romero C.M., J.Chem.Eng.Data, 56(5), 1778-1786, 2011 xAcid [mol/mol] xWater [mol/mol] σ [mN/m] T [K] a.1041(Pure Acid)026.68293.15298.0.182290.8177133.08293.1590.70.171020.8289833.15293.1585.60.14940.850633.54293.1577.20.128030.8719734.18293.1569.70.109470.8905334.56293.1561.40.08690.913135.3293.1551.80.07470.925335.77293.1546.30.066020.9339836.43293.1543.20.054360.9456438.51293.1542.20.04550.954540.07293.1540.30.032680.9673242.34293.1535.10.020750.9792546.78293.1532.80.014570.9854350.17293.1531.40.008610.9913953.61293.1525.901(Pure Water)72.58293.15  

This example shows a good agreement between the published value a=2.6*10−3 and the calculated value a=2.59*10−3 at the smallest given mole fraction of 0.00861 but at higher concentrations of propionic acid the value of an increases considerably, showing deviations from the predicted value.

See also Bohdan Szyszkowski

References