The overall objective of the work described in this Dissertation was to develop and verify a general reaction and diffusion model for non-catalytic reactions between gases and porous solids, particularly those relevant to the clean use of fossil fuels. Here, the internal pore structure of the solid was characterised by observing the kinetics in a regime limited only by intrinsic chemical reaction. It was hypothesised that a simple arbitrary function, f(X), determined from experimental measurements of rate vs. conversion in a kinetically-controlled regime, could be used in place of formal, mathematical pore models, to describe the evolution of pore structure during a reaction influenced by intraparticle mass transfer. The approach was used to study (i) the gasification of chars by CO2, where the only product was gaseous, (ii) the calcination of CaCO3 cycled between calcined and carbonated states, where the products were a gas and a solid, and (iii) the sulphation of virgin and sintered CaO by SO2, the only product being solid. Studies of calcination showed that, at least for limestones subjected to a history of cycling between the calcined and carbonated states, a correctly-determined f(X) could be applied to different sizes of particles at temperatures different to that at which f(X) was determined. Somewhat surprisingly, it was found that the f(X) determined from one, cycled, limestone was successful in predicting the conversion of other cycled limestones of different geological origin. It was concluded that the process of cycling between the calcined and carbonated states at the same process condition had significantly reduced the differences apparent in the pore structures of the different limestones when first calcined from the virgin materials. The experimentally-observed effects of pressure, concentration of CO2 and temperature described in the literature were explained successfully by the mathematical model. Finally, the study of sulphation explained satisfactorily (i) the reason for there being a maximum in the ultimate conversion of CaO to CaSO4 at a specific temperature, and (ii) the processes controlling the overall uptake of SO2 by sintered CaO, such as might be produced from a calcium-looping cycle for capturing CO2 from flue gases. For both the virgin and the cycled calcines, the ultimate conversion to CaSO4 seemed to be limited by the pore volume below 300 nm diameter. Two mechanisms were identified to explain why CaO cannot be fully sulphated to CaSO4. In summary, this work has demonstrated the applicability of the general reaction and diffusion model to gasification, calcination and sulphation reactions, and verified the f(X) approach for describing pore evolution during reaction.