PHYSICAL CHEMISTRY IN BRIEF

CHAP. 13: PHYSICAL CHEMISTRY OF SURFACES [CONTENTS] 441

Example

Ascertain the spreadability of n-octanol (oct) on water (w) and that of water on bromoform

(brm) at 20 ◦C if you have the following data (20◦C):

γw=γw,(g)= 72. 5 mN m−^1 , γoct=γoct,(g)= 27. 5 mN m−^1 , γbrm=γbrm,(g)= 41. 5 mN m−^1 ,

γw,oct= 8. 5 mN m−^1 , γbrm,w= 40. 8 mN m−^1.

Solution

For the air+octanol+water system we substitute into (13.13) to obtain (the lower layer is water)

Ss=γw,(g)−γw,oct−γoct,(g)= 72. 5 − 8. 5 − 27 .5 = 36. 5 > 0

and see that n-octanol spreads on water and does not form separate drops.

In the air+water+bromoform system (bromoform is the lower phase),

Ss=γbrm,(g)−γbrm,w−γw,(g)= 41. 5 − 40. 8 − 72 .5 =− 71. 8 < 0

and consequently water will not spread on bromoform and, when there is only a small amount of

water, drops will be formed.

13.1.7 Laplace-Young equation and Kelvin equation

The interfacial tension affects also other thermodynamic properties of a system when the in-
terface surface is curved.
If, e.g., the liquid is in the form of droplets of the radiusrwhich are surrounded by the gas
phase, theLaplace-Young equationapplies for the pressure in both phases

p(l)−p(g)= ∆p=

2 γ

r

, (13.15)

wherep(l)andp(g)stand for the pressures in the liquid and in the surrounding gas. The pressure
in the liquid is thus higher than in the gas.
Correspondingly, the pressure inside a bubble surrounded by a liquid is higher than that in
the liquid

p(g)−p(l)= ∆p=

2 γ

r

. (13.16)