Tiny particles (diameter < 100 mu m) of porous CaO have been reacted with SO3 in inert N-2 at atmospheric pressure and temperatures between 600 and 900 degrees C. These particles of CaO were well characterized by BET analysis and mercury porosimetry. Conditions were such that the kinetics of the reaction: CaO + SO3 --> CaSO4, whereby one solid gives another, controlled the rate of production of CaSO4. Thus it was established that, for the initial stages of reaction, the diffusion of SO3 to a particle of CaO in the thermogravimetric balance used was relatively rapid, as was the diffusion of SO3 both inside the pores of a particle of CaO and through the layer of product, CaSO4. The reaction is first order in SO3, the rate constant (defined per unit area of solid CaO) being 3.2 +/- 0.3 x 10(-6) exp(-746 +/- 108/T) m s(-1). Thus the apparent activation energy is only 6.2 +/- 0.9 kJ mol(-1). The rate constant is almost identical to that for SO2 reacting with CaO to give CaSO3; in each case the steric factor is extremely low,being ca. 2 x 10(-8). The diffusivity for SO3 through the product, CaSO4, is ca. 2 x 10(-13) m(2) s(-1) .