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Hydrolysis of light metals and hydrides can potentially be used for the generation of hydrogen on-board fuel cell vehicles, or, alternatively, for refilling their fuel tanks with H2 generated and pressurised without compressor on site, at near-ambient conditions. Implementation of this approach requires solution of several problems, including the possibility of controlling H2 release and avoiding thermal runaway. We have solved this problem by developing the apparatus for the controlled generation of pressurised H2 using hydrolysis of Mg or MgH2 in organic acid solutions. The development is based on the results of experimental studies of MgH2 hydrolysis in dilute aqueous solutions of acetic, citric, and oxalic acids. It was shown that the hydrogen yield approaches 100% with a fast hydrolysis rate when the molar ratio acid/MgH2 exceeds 0.9, 2.0, and 2.7 for the citric, oxalic, and acetic acids, respectively. In doing so, the pH of the reaction solutions after hydrolysis corresponds to 4.53, 2.11, and 4.28, accordingly, testifying to the buffer nature of the solutions “citric acid/magnesium citrate” and “acetic acid/magnesium acetate”. We also overview testing results of the developed apparatus where the process rate is effectively controlled by the control of the acid concentration in the hydrolysis reactor.