High temperature heat storage is one of the key points for the development of solar power plants. Using reversible solid-gas chemical reactions is a promising solution to achieve high energy density and to reduce the storage volume. In order to achieve the high energy density, heat and mass transfer networks have to be optimized. In fact, such a reactive material presents antagonist behaviors for heat conductivity and gas permeability: increasing the reactive material density (i.e. the energy density) increases heat conductivity, but dramatically decreases permeability. An optimum has to be found. A method, combining constructal approach and exergy analysis is presented in this paper and applied to a solid/gas reactor, exchanging heat and matter (gas) with its surrounding. The gas is produced by the conversion of a solid S1 in a solid S2, implying a reaction heat. The method consists in evaluating the global entropy production of an elemental volume and minimizing it under two constraints: a given power density (kW/m(3)) and a given volume (i.e. given storage capacity), using Lagrange multipliers method. Then, a construction is done. The optimal shape and the number of elemental volumes constituting the reactor are searched. Taking into account heat and mass transfers, two networks emerge from the optimal construction: a heat conductive material network and a gas diffusers networks. The size of the conductive 'fins' and gas diffusers only depends on the properties of the reactive material (heat conductivity, permeability), the reactive gas (viscosity, pressure) and the heat of reaction. One important result is that global exergy destruction ex(d) could be put in a very attractive form: e(x) over dot(d) = Z(q) over dot(2) where (q) over dot is the thermal power consumed by the reaction (W) and Z is named exergy impedance, regarding analogy with electric Joule effect (e(x) over dot(d) = Zi(2)). (C) 2013 Elsevier Ltd. All rights reserved.