We present a kinetic study on the reduction of 4-nitrophenol (NO2) with borohydride, catalyzed by silver nanoparticles. The latter are immobilized inside the hydrogel shell of core-shell nanoreactors, comprising a polystyrene core and surrounded by a thermoresponsive poly-N-isopropylacrylamide (PNIPAM) hydrogel shell. Cryogenic transmission electron microscopy shows that silver nanoparticles with an average diameter of 5.6 +/- 2.4 nm are located deep inside the PNIPAM shell. The Levenberg-Marquardt algorithm is applied for the decomposition of the UV-vis spectra recorded during the reduction of NO2, and its potential use in the assessment and evaluation of model reactions is demonstrated. The decomposition of the UV-vis spectra, obtained in a wavelength range of 240-500 nm, shows that the reactant NO2 is directly transferred to the product 4-aminophenol (NH2) without accumulation of intermediates. Hence, a stationary state for the intermediate 4-hydroxylaminophenol is present from the beginning of the reaction onwards. Based on this, a kinetic model is presented, which is related to a model previously derived for the kinetic analysis of the reaction catalyzed by gold. The kinetic data, obtained at room temperature at nine different combinations of NO2 and borohydride concentrations, are globally fitted by a genetic approach. The results are in good accordance with previous results obtained on gold and, furthermore, show that the adsorption of NH2 to the catalyst surface has a substantial influence on the kinetics of silver. The measurements between T = 10 and 50 degrees C reveal a non-Arrhenius dependency of the reaction rate, caused by the thermoresponsive PNIPAM hydrogel. We show how a systematic decomposition of kinetic, adsorption, and partitioning effects provides useful qualitative insights into the partitioning coefficients of reactants and products, i.e., the ratio of the concentration inside/outside the hydrogel network, which play a significant role in the kinetics of PNIPAM-based catalysts. Furthermore, it is found that small ions like chloride and borohydride show a similar partitioning behavior in PNIPAM.