A freely moving, machined sphere of graphite (or a rounded particle of a coal char) attached to a very thin, flexible thermocouple has been burnt in a bed of silica sand fluidized by air. Simultaneous measurements were made of [CO] and [CO2] in the off-gases, as well as of the temperature of the burning particle. Each sphere of carbon was large enough (>2 mm) for its burning to be controlled by external mass transfer. These measurements, together with the relative rates of formation of CO and CO2 obtained previously, enabled mass transfer coefficients and Sherwood numbers to be derived. Such measurements were made for different temperatures in the bed, sizes of sand, superficial velocities, and initial diameters of a graphite sphere. Only a slight decrease in Sh was found when the bed's temperature was raised; this was accounted for by changes in the following physical properties: the density of the fluidizing gas, the diffusivity of O-2, the viscosity, and minimum fluidizing velocity of the air. There was no clear trend of Sh with the actual superficial velocity of the fluidizing air. On the other hand, Sh was increased significantly by using larger sand particles, mainly as a consequence of increasing the gas velocity in the interstices between the sand particles. All the measurements were correlated best by: Sh = 2epsilon(mf) + 0.61((v)/U(p)d)(0.48)((D)/(v))(1)/(3). where U-p = U-mf(1 -e(b)) {1 - (pi)/(2) ln (1 - (pi)/(6epsilon)(b))}. The first correlation gives Sh mid-way between all those from previous expressions in the literature. It holds only when the reacting particle is much larger than the fluidized inert particles of sand. An almost equally good correlation, but only for reacting spheres above a certain size, is: Sh = 2epsilon(mf) + 0.69 (vepsilon(mf)/U(mf)d)(1/2)((D)/(v))(1/3).