PHYSICAL CHEMISTRY IN BRIEF

CHAP. 13: PHYSICAL CHEMISTRY OF SURFACES [CONTENTS] 444

E ̈otv ̈os and later Ramsay-Shields found out that in a very broad temperature interval (up
to almost critical temperature) the following empirical relation applies
(
d
dT

)[

γ(Vm(l))^2 /^3

]

= const, (13.19)

which can be rewritten into the form of the Ransay-Shields equation

γ(Vm(l))^2 /^3 =k(Tc−T−δ), (13.20)

whereVm(l)is the molar volume of a saturated liquid at temperatureT,Tcis the critical tem-
perature of a substance, andk,δare empirical constants which for nonassociated liquids have
the values
k= 2.12 (mN m−^1 )(cm^3 mol−^1 )^2 /^3 , δ= 6 K. (13.21)

Relation (13.20) does not apply for substances such as water, alcohols, organic acids, etc.
Another empirical relation between temperature and surface tension was found by Mac Leod

[P] =

M γ^1 /^4

ρ(l)−ρ(g)

, (13.22)

whereMis the molar mass,ρ(l)andρ(g)are the densities of a saturated liquid and a saturated
vapour.^1 The quantity [P] is called theparachor. It is practically independent of temperature,
and it may be estimated on the basis of atomic and structural contributions. This means that
if we know the temperature dependence of the density, we may also estimate the temperature
dependence of the surface tension.

13.1.9 Dependence of surface tension on solution composition

The surface tension of mixtures largely depends on their composition, and there is not yet any
exact method for its calculation. For a mixture of substances of a similar character we may at
least approximately use the empirical equation for the parachor, from which it follows that

γ^1 /^4 =ρ(l)

∑k

i=1

xiγi^1 /^4

ρ(l)i

, (13.23)

(^1) At low temperatures we may naturally neglect the density of the gas phase as compared with that of the
liquid phase.