Recent experimental evidence underlines the importance of reduced diffusivity in amorphous semi-solid or glassy atmospheric aerosols. This paper investigates the impact of diffusivity on the ageing of multi-component reactive organic particles approximating atmospheric cooking aerosols. We apply and extend the recently developed KM-SUB model in a study of a 12-component mixture containing oleic and palmitoleic acids. We demonstrate that changes in the diffusivity may explain the evolution of chemical loss rates in ageing semi-solid particles, and we resolve surface and bulk processes under transient reaction conditions considering diffusivities altered by oligomerisation. This new model treatment allows prediction of the ageing of mixed organic multi-component aerosols over atmospherically relevant timescales and conditions. We illustrate the impact of changing diffusivity on the chemical half-life of reactive components in semi-solid particles, and we demonstrate how solidification and crust formation at the particle surface can affect the chemical transformation of organic aerosols.