# Is it possible to convert carbon soot/ black carbon in mg to CO2-equivalent? If so, how?

Since global warming is expressed in terms of carbon emissions or CO2 equivalent, can the short lived carbon soot/ black carbon that is produced from incomplete combustion be expressed in terms of CO2 equivalent? I learnt Carbon soot is a major health risk. The purpose of doing this is to calculate how much of heating effect can be reduced by controlling the emissions of these carbon particles.

Though both $$\ce{CO2}$$ and particulate carbon (soot) cause warming, a direct mathematical relationship of the effects would be specious for a few reasons:
• The life-times of atmospheric $$\ce{CO2}$$ and soot differ, and vary with amount of sunlight (enabling plants to absorb $$\ce{CO2}$$, but not affecting soot appreciably), with amount of precipitation (affecting both), etc.
• The heating effects differ: $$\ce{CO2}$$ remains in the atmosphere, absorbing and re-emitting infrared radiation and thereby raising atmospheric temperatures more than surface temperatures. Soot eventually settles out, warming the surface more than the atmosphere when radiation is absorbed.
BTW, particulate carbon and products of incomplete combustion also have direct impact on health, such as in burning fuels indoors or urban smog while the physoiological impact of $$\ce{CO2}$$ (at current levels) is less severe.