Supersonic turbulence is a large reservoir of suprathermal energy in the interstellar medium. Its dissipation, because it is intermittent in space and time, can deeply modify the chemistry of the gas. We further explore a hybrid method to compute the chemical and thermal evolution of a magnetized dissipative structure, under the energetic constraints provided by the observed properties of turbulence in the cold neutral medium. For the first time, we model a random line of sight by taking into account the relative duration of the bursts with respect to the thermal and chemical relaxation timescales of the gas. The key parameter is the turbulent rate of strain a due to the ambient turbulence. With the gas density, it controls the size of the dissipative structures, therefore the strength of the burst. For a large range of rates of strain and densities, the models of turbulent dissipation regions (TDR) reproduce the CH+ column densities observed in the diffuse medium and their correlation with highly excited H2. They do so without producing an excess of CH. As a natural consequence, they reproduce the abundance ratios of HCO+/OH and HCO+/H2O, and their dynamic range of about one order of magnitude observed in diffuse gas. Large C2H and CO abundances, also related to those of HCO+, are another outcome of the TDR models that compare well with observed values. The abundances and column densities computed for CN, HCN and HNC are one order of magnitude above PDR model predictions, although still significantly smaller than observed values.
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