where is activity of surfactant.

For an ideal solution activity of solute is equal to its concentration . So,

Thus with the increase in surfactant concentration, the interfacial tension decreases. is not independent of and it also increases with the bulk concentration of the solute. This dependence is captured by the adsorption isotherm.

Here, is the interfacial tension for the pure surface, i.e. when no solute was present. A linear adsorption isotherm implies that varies linearly with the bulk solute concentration.