A process can produce alcohols having at least two carbon atoms by catalytic conversion of synthesis gas into a mixture containing alkanes, alkenes, and alcohols. Alkenes are converted into corresponding alcohols in a subsequent step by hydration of the alkanes. Before the hydration and after the catalytic conversion, gas and liquid phases may be separated. Specific catalysts can be employed that have a markedly higher selectivity for alkenes than for alkanes. These catalysts comprise grains of non-graphitic carbon having cobalt nanoparticles dispersed therein. The cobalt nanoparticles have an average diameter dp from 1 to 20 nm, and an average distance D between nanoparticles is from 2 to 150 nm. The combined total mass fraction of metal ω in the grains ranges from 30% to 70% by weight of the total mass of the grains of non-graphitic carbon, wherein 4.5 dp/ω>D≥0.25 dp/ω.