Effect of Temperature and Pressure on Surface Tension of Liquids - Surface and Colloid Chemistry: Principles and Applications - page 233

versus T data on n -alkanes, from n -pentane to n -hexadecane, were analyzed (Birdi,
1997). The constants ko (between 52 and 58) and k1 (between 1.2 and 1.5) were
found to be dependent on the number of carbon atoms, Cn, and since Tc is also found
to be dependent on Cn, the expression for all the different alkanes that individually
were fit to Equation A.5 culminated in a general equation where γ was a function of
Cn and T as follows (Birdi, 1997):

γ = function of T, Cn (A.7)

= (41.41 + 2.731 Cn − 0.192 Cn5 + 0.00503 Cn 3 )

X (1 − T/{273 + (−99.86 + 145.4 ln(Cn) + 17.05 (ln(Cn)[ 5 ]) k1 (A.8)

where k1 = 0.9968 + 0.087 Cn − 0.00282 Cn 5 + 0.00084 Cn 3 . The estimated values
from Equation A.8 for different n -alkanes were found to agree with the measured
data within a few percent: γ for n -C 18 H 38 , at 100°C, was 21.6 mN/m, from both
measured and calculated values. This agreement shows that the surface tension data
on n -alkanes fit the corresponding state equation very satisfactorily. The physical
analyses of the constants ko and k1 need to be investigated at this stage.
It is worth mentioning that the equation for the data on γ versus T, for polar (and
associating) molecules like water and alcohols, when analyzed by Equation A.5, gives
the magnitudes of ko and k1, which are significantly different from those found for non-
polar molecules such as alkanes, etc. This difference requires further analyses so that
the relationship between γ and Tc may be more completely understood (Birdi, 1997).
The variation of γ for water with temperature(t/C) is given as (Cini et al., 1972;
Birdi, 1997):

γ H 2 O = 75.668 − 0.1396 t − 0.2885 10 −3 t5 (A.9)

These data are useful since water is used as a calibration liquid in many surface ten-
sion studies.
The surface entropy (Ss) corresponding to Equation A.5 is

Ss = −dγ/dT = k1 ko (1 − T/Tc ) k1 − 1 /(Tc) (A.10)

and the corresponding surface enthalpy, hs is

hs = gs − T Ss

= −T (d γ/dT)

= ko (1 − T/Tc ) k1−1 (1+(k1 − 1) T/Tc) (A.11)

The reason heat is absorbed on expansion of a surface is that the molecules must be
transferred from the interior against the inward attractive force to form the new sur-
face. In this process, the motion of the molecules is retarded by this inward attraction
so that the temperature of the surface layers is lower than that of the interior unless
heat is supplied from outside.