The electrokinetic effects in membranes and porous materials can be used for direct conversion of pressure into electricity or conversion of electricity into pumping power, and they have potential applications within actuators, small scale pumping and energy harvesting devices. Still, in the literature only electrokinetic effects with liquid reservoirs on each side of the membrane are considered. In the present paper, isothermal electrokinetic effects are investigated using non-equilibrium thermodynamics in the case with gas phase reservoirs on each side of the membrane. For comparison the case with liquid reservoirs is included. We describe how the figure-of-merit, energy conversion efficiency, power density, compressor and generator curves depend on observable transport properties. The derived equations are used to analyse two examples with gas phase reservoirs. The first being related to electrochemical hydrogen compression/liquefaction, and the second being the electrochemical gas compression for cooling cycles. In the latter case, experimental transport data predict high efficiency and a power density which is promising with respect to membrane-based electrochemical cooling applications. (C) 2015 Elsevier B.V. All rights reserved.