Complex chemical reactions are commonly described by systems of nonlinear ordinary differential equations. Rate and equilibrium constants of these models are usually not directly accessible and have to be indirectly inferred from experimental observations of the system. As a consequence, parameter identification problems have to be formulated and computationally solved. Because of a limited amount of information and uncertainties in the data, the Solutions to Such parameter identification problems typically lack uniqueness and stability properties and hence cannot be found in a reliable way by a pure minimization of the data mismatch (i.e., the discrepancy between experimental observations and simulated model output). To overcome these difficulties, so-called regularization methods have to be used. In this article, we suggest a sparsity promoting regularization approach that eliminates unidentifiable model parameters (i.e., parameters of low or no sensitivity to the given data). That way, the model is reduced to a core reaction mechanism with manageable interpretation while still remaining in accordance with the experimental observations. For the Computational realization, we utilize the adjoint state technique for an efficient calculation of the gradient of the objective with respect to model parameters as well as uncertain initial and experimental conditions. Illustrations of our approach are given by means of the chlorite-iodide reaction for which reference parameter values are available.