I am looking for a global dataset the describe the chemical composition of the desert dust in terms of soil mass or volume fraction or as an absolute mass
Perhaps this (recent!) reference is of help for you: Philip et al. (2014) Global Chemical Composition of Ambient Fine Particulate Matter for Exposure Assessment. Environmental Science & Technology 48:13060-13068
This one could be useful: Scheuvens et al. (2013) Bulk composition of northern African dust and its source sediments — A compilation. Earth-Science Reviews 01/2013; 116:170–194. DOI: 10.1016/j.earscirev.2012.08.005