TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: The method additionally involves combining the second aqueous sodium hydroxide stream with the first aqueous sodium hydroxide stream; forming water (102) and oxygen (106) in anolyte chamber (136) of the electrolytic cell; pressurizing the sodium and the water before combining the sodium with the water to produce a high pressure hydrogen; separating at least a portion of water and impurities from the hydrogen; heating the sodium and the water using heat produced from an exothermal reaction in the reactor. The separating step involves: i) feeding the first aqueous sodium hydroxide stream into an anolyte chamber of an electrolytic cell; ii) feeding mineral oil (116) into a catholyte chamber (134) of the electrolytic cell; iii) applying an electric potential to the electrolytic cell, the anolyte chamber and the catholyte chamber separated by a ceramic membrane (142) for selectively transporting sodium cations from the anolyte chamber to the catholyte chamber; and iv) forming sodium in the catholyte chamber of the electrolytic cell. Step (iv) involves combining a sodium cation with an electron in the catholyte chamber for producing sodium; and submerging the sodium in mineral oil. The combining step involves feeding the sodium into a reactor at greater than 98 degrees C; feeding the water into the reactor; reacting the sodium and the water in the reactor; generating the hydrogen and the second aqueous sodium hydroxide stream; and forming additional sodium using the second aqueous sodium hydroxide. The feeding water into the reactor involves feeding superheated water or steam into the reactor; or feeding high pressure water into the reactor for reacting sodium and water to produce a second aqueous sodium hydroxide stream and high pressure hydrogen. Applying an electric potential to the electrochemical cell involves supplying an electric potential to the electrochemical cell from at least one of solar power, geothermal power, hydroelectric power, wind power, and nuclear power. Forming the additional sodium involves combining the second aqueous sodium hydroxide stream with the first aqueous sodium hydroxide stream. Preferred System: In the system (S1), the separator comprises an electrolytic cell comprising: an anolyte chamber configured with an anode for containing aqueous sodium hydroxide; a catholyte chamber configured with a cathode for containing mineral oil; a membrane disposed between the anolyte chamber and the catholyte chamber configured for transporting sodium cations from the anolyte chamber to the catholyte chamber; and a source of electric potential electrically connected to the cathode and to the anode for causing sodium cations to pass through the membrane from the anolyte chamber to the catholyte chamber. The membrane comprises a ceramic membrane comprising Na-superionic conductor (NaSICON) material. The system (S1) additionally comprising a gas separator configured for separating the hydrogen from impurities and moisture; and at least one pump configured for pressurizing the water. The system (S2) additionally comprises at least one gas separator coupled to the at least one reactor configured to remove moisture and impurities from the hydrogen produced by the at least one reactor; and at least one conduit configured for returning the aqueous sodium hydroxide produced in the reactor to the at least one electrolytic cell. The electrolytic cell comprises a NaSICON membrane configured for transporting sodium cations from an anolyte chamber to a catholyte chamber of the at least one electrolytic cell. Preferred Components: The sodium comprises a liquid. EXAMPLE - No suitable example given.