Aims. We model the chemistry of the inner wind of the carbon star IRC+10216 and consider the effect of periodic shocks induced by the stellar pulsation on the gas to follow the non-equilibrium chemistry in the shocked gas layers. We consider a very complete set of chemical families, including hydrocarbons and aromatics, hydrides, halogens and phosphorous-bearing species. Derived abundances are compared to the latest observational data from large surveys and Herschel. Results. The shocks induce a non-equilibrium chemistry in the dust formation zone of IRC+10216 where the collision destruction of CO in the post-shock gas triggers the formation of O-bearing species (H2O, SiO). Most of the modelled abundances agree very well with the latest values derived from Herschel data on IRC+10216. Hydrides form a family of abundant species that are expelled into the intermediate envelope. In particular, HF traps all the atomic fluorine in the dust formation zone. Halogens are also abundant and their chemistry is independent of the C/O ratio of the star. Therefore, HCl and other Cl-bearing species should also be present in the inner wind of O-rich AGB or supergiant stars. We identify a specific region ranging from 2.5 R* to 4 R*, where polycyclic aromatic hydrocarbons form and grow. The estimated carbon dust-to-gas mass ratio derived from the mass of aromatics ranges from 1.2 x 10^(-3) to 5.8 x 10^{-3} and agrees well with existing observational values. The aromatic formation region is located outside hot layers where SiC2 is produced as a bi-product of silicon carbide dust synthesis. Finally, we predict that some molecular lines will show flux variation with pulsation phase and time (e.g., H2O) while other species will not (e.g., CO). These variations merely reflect the non-equilibrium chemistry that destroys and reforms molecules over a pulsation period in the shocked gas of the dust formation zone.
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