Here we show theoretically that the design of a thermochemical energy storage system for fast response and high thermal power can be predicted in accord with the constructal law of design. In this fundamental configuration, the walls of the elemental cylinder are impregnated with salt, while humid air is blown through the tube. Cases with constant salt volume or constant fluid volume or both are considered. It is shown that the best design in each case meets the equipartition of imperfections principle. The predictions are confirmed by full numerical experiments, allowing to consider various shape ratios and study their impact on the overall performance.