Szyszkowski equation
   HOME

TheInfoList



OR:

The Szyszkowski Equation has been used by Meissner and Michaels to describe the decrease in surface tension of aqueous solutions of carboxylic acids, alcohols and
ester In chemistry, an ester is a compound derived from an oxoacid (organic or inorganic) in which at least one hydroxyl group () is replaced by an alkoxy group (), as in the substitution reaction of a carboxylic acid and an alcohol. Glycerides a ...
s 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%.


Equation

:\sigma_m =\sigma_w\left(1-0.411\log\left(1+\frac\right)\right) 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'': :\begin a&=\frac\\ &=x10^ \end This allows the direct calculation of that component specific parameter ''a'' from experimental data. The equation can also be written as: :\gamma=\gamma_0-\frac\ln(1+K_c) 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:


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=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 Bohdan Szyszkowski (born June 20, 1873, in Trybuchy, Podolia, Russia (now village in Ukraine) – August 13, 1931 in Myślenice, Poland) was a Polish chemist and member of PAU. Szyszkowski published important papers on electrochemistry and ...


References

{{DEFAULTSORT:Szyskowski Equation Fluid mechanics Surface science Thermodynamic equations