The process for synthesizing heterogeneous sulfur-free catalysts based on molybdenum oxide, as well as their use in biomass transformation processes, constitutes the central part of this invention. These materials were shown to be active and selective in three biomass transformation processes of industrial importance, namely: (i) hydrodeoxygenation of fatty acids, (ii) hydrogenation and (iii) dehydrogenation of terpenes. The synthesis conditions of these catalysts allow to obtain 100% conversion of fatty acids and the production of linear hydrocarbons without oxygen in their structure above 95%. The products generated using the heterogeneous catalysts of this invention have great relevance in various industries such as energy, chemicals, oil, among others. The operating conditions of these catalysts were also optimized to achieve their application in the most favorable conditions, reducing reaction time, temperature and pressure. The versatility of these materials, their simple handling, the use of inexpensive metals and in small quantities facilitate their use in large-scale industrial processes.