Computing reachable sets for continuous-stirred tank reactors (CSTRs) under uncertainty is crucial for designing efficient model-based control strategies or developing robust process monitoring protocols. This paper, the first in the three-part series, develops a linear transformation to project the dynamics of a CSTR reaction system onto a transformed state space. The proposed transformation is invertible, and leads to a “sparse” system representation in the transformed state space – a property crucial for the methods developed to compute reachable sets of CSTR reaction systems. The second and third papers in this series discuss how the transformation developed here can be used to compute effectively outer interval approximations to the reachable sets of CSTR reaction systems. To this effect, two new bounding methods – direct and indirect-bounding methods – are proposed in the second and third paper, respectively, to compute tight interval enclosures for the reachable sets of CSTR reaction systems. Several numerical examples are also provided to demonstrate efficacy of the proposed direct and indirect-bounding methods.