Federations of RDF data sources offer great potential for queries that cannot be answered by a single data source. However, querying such federations poses several challenges, one of which is that different but semantically-overlapping vocabularies may be used for the respective RDF data. Since the federation members usually retain their autonomy, this heterogeneity cannot simply be homogenized by modifying the data in the data sources. Therefore, handling this heterogeneity becomes a critical aspect of query planning and execution. We introduce an approach to address this challenge by leveraging vocabulary mappings for the processing of queries over federations with heterogeneous vocabularies. This approach not only translates SPARQL queries but also preserves the correctness of results during query execution. We demonstrate the effectiveness of the approach and measure how the application of vocabulary mappings affects on the performance of federated query processing.