Non-electrostatic ion-specific effects are strong for anions when water is involved. We study here the thermodynamic equilibrium of a water-in-oil microemulsion stabilized by a surfaceactive extractant in a Winsor-II regime. Acid extraction isotherms for different anions located differently in the Hofmeister series have been investigated. A Langmuir like model was written for the specific case of acids treated as electrolytes, describing acid extraction as the adsorption of extracted electrolytes on the polar/apolar interface of the aggregates. Except for sulfate, isotherms can be described at first approximation as simple Langmuir-type isotherms when plotted as a function of the acid activity in the aqueous phase. The validity of the model being hence demonstrated, acid extraction free energies could be derived and compared, taking into account the effect of the anion position in the Hofmeister series. The case of phosphate, chloride, and sulfate as kosmotropes can be distinguished. They are significantly extracted, only above a threshold since the sphere-to-rod transition of the reverse aggregates has to be triggered by high chemical potential of the acid required to compensate anion dehydration.