The present invention relates to a process for the manufacture of microporous carbon materials to perform selective separations of nitrogen in gas mixtures such as hydrogen sulfide, carbon dioxide, methane and C2, C3 and C4+ hydrocarbons, with high efficiency, shaped of microspheres or cylinders from copolymers of poly (vinylidene chloride-co-methyl acrylate) with density of 1.3 to 1.85 g/cm3 or poly (vinylidene chloride-co-vinyl chloride) with density of 1.3 to 1.85 g/cm3, using two stages. The first stage consists of a surface passivation of the material by chemical attack in a highly alkaline alcohol solution, with the aim of effecting a precarbonization on the surface of the copolymer that during the pyrolysis process is not deformed and gradually develops microporosity. The material of the first stage presents, in the layer, percentages between 55% to 85% carbon, between 5% to 20% oxygen, and between 10% to 40% chlorine. The interior of the material presents lower percentages of carbon, between 30% to 65%, oxygen in the amount of between 2% to 6%, and chlorine in the amount of between 30% to 60%. The second stage consists of the gradual pyrolysis of the passivated copolymer, with the aim of developing microporosity and high surface area values; as well as during the melting and gas dehydrohalogenation stages thereof, the deformation of the material is avoided. The morphology of the copolymers are microspheres of 125 to 225 micrometers, or cylinders of 4 mm in height and 3 mm in diameter, which after pyrolysis reduce its size by 35% with respect to the initial one. The material of the second stage, which is already microporous carbon material, presents in the layer percentages between 90% to 100% carbon and between 10% to 0% oxygen.