The apparatus comprises a first air duct with a first opening and a second opening, in the first air duct are: a cooler, a first suction device and at least part of a sorption heat exchanger having an integrated heating and/or an upstream device for preheating the incoming air. An element for collecting condensed water is also included. The apparatus also comprises a recuperative heat exchanger, which is positioned in the first air duct between the cooler and the sorption exchanger and simultaneously also between the cooler and the second opening. The recuperative heat exchanger has at least two internal conduits connected in such manner, that the first of these internal conduits air-interconnects the sorption exchanger and the cooler and that the second of these internal conduits air-interconnects the cooler and the second opening. The first and second internal conduits of the recuperative heat exchanger are in mutual thermal contact. The sorption exchanger is also air-interconnected to the first opening.