I was told that anions can not exist in air and always decompose. Is this correct?
Well this is more than an over-simplification!. Atmospheric carbonates usually correspond to some of the mineral components of airborne particulate matter, actually fragments of rocks resuspended from soil and/or desert dust in the form of calcium and to a lesser extent, magnesium carbonates to which omologues from human activities must be added locally (cement, building excavating...) which are remobilized and mixed in the air like all the particles. This class of particles are mostly coarse (> 1 µm) with a high probability of being fast dry removed to the ground by gravitational settling . However we have to remind the concept of environmental fate for anything recirculated across the planet which includes not only transport but also physical chemistry and chemistry ( even biochemistry) during motion. For carbonate you can expect dissolution by collision with droplets during wet removal processes (therefore a strong influence of meteorological processes) and acid-base reactions which may actually bring to carbonate dispacement and adaptation to carbonate equilibrium conditions (Droplets of rain contains also dissolved CO2 which undergo hydration and dissociation and unpolluted rain has a pH of around 5.7, less in the case of acid rain). One further possible reaction of acid displacement of carbonates may be traced to HCl which is fairly volatile, after release from emissions (eg volcanoes) or atmospheric chemistry. However, airborne particulates are historically known to possess predominantly acid properties due to traces of H2SO4, HNO3 and mono and di-carboxylic acids (all substances with high vapour pressure) from atmospheric oxidation of gaseous precursors. In case of collision between carbonates and other aerosol particles more or less loaded with moisture, acidity can be expressed and release CO2. It is clear that any generalization is not allowed. Proof is therfore given in decades of aerosol science and not just research, but also in basic textbooks of atmospheric chemistry such as Fynlayson-Pitts & Pitts, and Seinfeld Pandis From the first through the third edition
Aerosol composition includes not only mineral components, but also ammonium sulfate and nitrate, Seasalt, elemental and organic carbon and virtually all the elemets in trace amount, not to mention bioparticles. To your knowledge One of the basic characterization aerosol requires is ion chromatography: anions and the corresponding cations not only do exist but are a priority.
The atmospheric residence time is most likely dominated by that of airborne particulate matter and is mainly a function of particle size and fate (dry wet removal)
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