Smalley and co-workers discovered that chemisorption reactivities of silicon clusters vary over three orders of magnitude as a function of cluster size. In particular, they found that Si-33, Si-39, and Si,, clusters are least reactive towards various reagents compared to their immediate neighbors in size. We explain these observations based on our stuffed fullerene model. This structural model consists of bulk-like core of five atoms surrounded by fullerene-like surface. Reconstruction of the ideal fullerene geometry gives rise to fourfold coordinated crown atoms and rr-bonded dimer pairs. This model yields unique structures for Si-33, Si-39, and Si-45 clusters without any dangling bonds and thus explains their lowest reactivity towards chemisorption of closed shell reagents. This model is also consistent with the experimental finding of Jarrold and Constant that silicon clusters undergo a transition from prolate to spherical shapes at Si-27. We justify our model based on an in depth analysis of the differences between carbon and silicon chemistry and bonding characteristics. Using our model, we further explain why dissociative chemisorption occurs on bulk surfaces while molecular chemisorption occurs on cluster surfaces. We also explain reagent specific chemisorption reactivities observed experimentally based on the electronic structures of the reagents. Finally, experiments on Si(x)X(y) (X = B, Al, Ga, P, As, AlP, GaAs) are suggested as a means of verifying the proposed model. We predict that Si-x(AlP)(y) and Si-x(GaAs)(y) (x=25,31,37;y=4) clusters will be highly inert and it may be possible to prepare macroscopic samples of these alloy clusters through high temperature reactions.