An electrochemical method is used to measure mass transfer coefficients between an electrolytic solution and the inner core of a system formed by stationary coaxial cones of the same apex angle. A swirling decaying flow is induced by means of a tangential inlet at the system base. The average mass transfer coefficients are measured at three axial positions from the tangential inlet for both laminar and turbulent flow regimes. Pressure drops between the inlet and the outlet of the experimental device are also investigated. Flow visualization revealed the existence of axially fixed toroidal vortices. The overall mass transfer coefficients along the conical gap are found to be greater than those measured in annular swirling decaying flow for the same values of the annular gap thickness, of the tangential inlet diameter and of the Reynolds number based on the mean axial velocity at the bottom of the conical gap. The enhancement in mass transfer, up to 50% compared with that measured in a cylindrical arrangement, is not counter-balanced by an increase in pressure drop, which remains of the same order of magnitude as that measured in a classical annular configuration.