A reactor/purifier for generating pure hydrogen in a stack or array of pairs of alternatingly connected high and low pressure reactor chambers wherein a gas-porous turbulence-promoting screen structure washcoated with a steam-reforming catalyst is sandwiched between a planar hydrogen-selective palladium alloy membrane and a planar gas-impermeable heat-conducting metal plate within the high pressure reactor chamber of each high pressure reactor chamber; and wherein the catalyst-coated structure in each high pressure chamber is reacted with steam and hydrocarbon fuel, such as methane or syn/gas, and/or carbon monoxide at an appropriately controlled temperature of between about 200.degree. C. to 650.degree. C. to produce hydrogen and carbon oxides within an isothermal temperature range in each high pressure reactor chamber, while simultaneously permeating pure hydrogen therefrom through the membrane into the corresponding connected low pressure reactor chamber.