PHYSICAL CHEMISTRY IN BRIEF

CHAP. 13: PHYSICAL CHEMISTRY OF SURFACES [CONTENTS] 442

Obr.13.2:Pressure inside a bubble

Example

Determine the difference between the pressure inside a soap bubble (Figure13.2) of the radiusr

and the surrounding atmospheric pressure. The surface tension of the soap solution forming the

cover of the bubble isγ.

Solution

According to the Laplace-Young equation (13.15) the following relation applies between the

atmospheric pressure and the pressure in the liquid making up the cover of the bubble

p(l)−p(g1)=

2 γ

r 1

whereas between the pressure in the liquid and inside the bubble we have

p(g2)−p(l)=

2 γ

r 2

.

By summing up the two equations, on condition thatr 1 ≈r 2 ≈r, we obtain

p(g2)−p(g1)=

4 γ

r

.

Given that the liquid inside a droplet has a higher pressure than the liquid over the non-
curved surface, it also has a higher chemical potential or fugacity.
S Symbols: The chemical potential or fugacity for a curved surface will be denoted using the