Temporal convolution is used as a mathematical tool for modelling mass transfer processes based on linear differential equations such as the Nernst-Planck law or Fick’s law. The equivalence between the mass transfer rate operator and a convolution is demonstrated. This enables the mass transfer to be predicted and analysed independently of the perturbation which has been at its origin. The theory is based on the definition of characteristic functions depending on the nature of the mass transfer. They express the mass transfer properties along the distance and as an interesting consequence allow the determination of concentrations or fluxes at any distance for any time dependence of the perturbation. Restriction to the case of linear semi-infinite diffusion is detailed for providing a verifiable theory by mass flux measurement techniques such as optical beam deflection..This verification is described in Part 2.