Many molecules exhibit multiple conformers that often easily interconvert under thermal conditions. Therefore, single conformations are difficult to isolate which renders the study of their distinct chemical reactivities challenging. We have recently reported a new experimental method for the characterization of conformer-specific effects in chemical reactions [Y.-P. Chang, K. Długołęcki, J. Küpper, D. Rösch, D. Wild, and S. Willitsch, "Specific chemical reactivities of spatially separated 3-aminophenol conformers with cold Ca(+) ions," Science 342, 98-101 (2013)]. Different conformers are spatially separated using inhomogeneous electric fields and reacted with a Coulomb crystal of cold, spatially localized ions in a trap. As a first application, we studied reactions between the two conformers of 3-aminophenol and Ca(+). We observed a twofold larger rate constant for the cis compared to the trans conformer which was rationalized in terms of the differences in the long-range ion-molecule interactions. The present article provides a detailed description of the new method and a full account of the experimental results as well as the accompanying theoretical calculations.