A new theoretical approach of the insertion/deinsertion of lithium cations in host materials is proposed to take into account two main phenomena which are not included in the classical analysis i.e. the concentration dependence of the diffusion coefficient and the influence of the gradient of chemical potential arising from the departures from ideality (thermodynamic enhancement factor). The error function is used to obtain a suitable representation of the thermodynamic and kinetic properties of the system. The electrochemical process is analysed by numerical integration of the diffusion equation. This procedure proves to be useful to analyse the behaviour of systems involving phase-transition processes and large changes in the chemical potential when the concentration varies. The theoretical analysis is illustrated on the model case of lithium insertion in V2O5 thin film prepared by atomic layer chemical vapour deposition (ALCVD).