In this paper, the dehydration (heat charge) and hydration (discharge) reaction kinetics of thermochemical sorbents synthesised in previous work by the author is established by using the isothermal method, with the aim of understanding their thermochemical conversion behaviour and developing reaction models for numerical simulations. The effects of temperature, reaction advancement, and vapour pressure are fully considered and employed in a thermochemical energy storage model. The derived dehydration reaction activation energies of the LiOH/LiCl@ expanded graphite (LiO2C1@EG and LiO3C1@EG) sorbents are 54.7 and 52.2 kJ/mol, respectively, which are lower than that of pure LiOH·H2O. To achieve the dual-function of space heating and air purification in an efficient manner, a novel solar building envelope combining thermochemical energy storage and photocatalysis is proposed and studied numerically based on the established reaction kinetics. Fresh air can be produced during solar harvesting. The porous wall, which is made of a composite sorbent, absorbs thermal energy to heat air near the wall and thus creates a chimney effect in the channel for continuous space heating. During discharge, the desorbed heat storage wall adsorbs the moist air and the hydration reaction enthalpy can be used again for air heating. The total efficiency including the equivalent formaldehyde degradation efficiency and the thermal efficiency is around 81% when the solar radiation is 600 W/m2. Results indicate that this passive building envelope can achieve a higher heat harvesting and utilisation efficiency in a more compact space compared to previous studies. Moreover, the influence of radiation intensity on air purification and thermal performance is investigated. The present work provides new insights and promotes the integration of passive solar building envelopes and thermochemical energy storage.