This work deals with the experimental analysis and the mathematical modelling of the CO2 absorption in an initially quiescent aqueous solution of NaHCO3 and Na2CO3 inside a Hele-Shaw cell. This absorption, initially driven by the coupling between diffusion and chemical reactions, eventually leads to the apparition of a peculiar gravitational instability with non-monotonic dynamics, and liquid plumes generated at some distance from the gas-liquid interface (Wylock et al., 2014). Considering that this instability is triggered by a Rayleigh Taylor like mechanism, a two-dimensional model, coupling diffusion, chemical reaction and convection, is proposed to simulate the onset and the dynamics of such an instability. It is observed that the simulated instability dynamics agree qualitatively with the experimental observations and that the order of magnitude of the onset time is well estimated. Thanks to the simulation, the interaction between the various phenomena after the instability onset is further investigated and a mechanism is proposed to explain the unusual dynamics of the studied system. It is notably shown that this dynamics is due to the particular non-monotonic liquid density variations with the depth, induced by the absorption. A criterion to obtain such type of density profile is presented. In addition, the simulation enables to assess the influence of the instability on the CO2 absorption rate and it is observed that the generated flow pattern does not lead to a significant enhancement of the gas liquid absorption rate. This result is of significant importance for optimizing chemisorption (e.g. for CO2 capture or sequestration) processes. 2016 Elsevier Ltd. All rights reserved.