This work presents a comprehensive sensitivity analysis of a paradigm dissolver model that has been selected because of its applicability to material separations and its potential role in diversion activities associated with proliferation and international safeguards. This dissolver model consists of eight active compartments in which the time-dependent nonlinear differential equations modeling the physical and chemical processes comprise 16 time-dependent spatially dependent state functions and 635 model parameters related to the model’s equation of state and inflow conditions. The most important response for the dissolver model is the computed nitric acid in the compartment farthest away from the inlet, where measurements are available for comparisons. The sensitivities to all model parameters of the acid concentrations at each of these instances in time are computed exactly and efficiently using the adjoint sensitivity analysis method for nonlinear systems. The relative importance of the sensitivities in contributing to the uncertainties in the computed model responses is quantified numerically and analyzed in the dissolver’s physics context. The sensitivities computed in this work will be used in a companion paper for uncertainty analysis and predictive modeling, which aims at validating the paradigm dissolver model using the available experimental data and subsequently obtaining best-estimate predicted nominal values for the acid concentrations, with reduced predicted uncertainties, for the longer-term purpose of coupling this dissolver model to other nuclear facilities of interest to nonproliferation objectives.