For a given mass of a solid, large lumps have smaller surface area to volume ratios than smaller lumps or powders
If a large lump is divided or ground into a powder:
Its total volume stays the same
The area of exposed surface increases
The surface area to volume ratio increases
The greater the frequency of successful collisions, the greater the rate of reaction
If the surface area to volume ratio of a reacting solid is increased:
More reactant particles are exposed at the surface
The frequency of collisions between reactant particles increases
Therefore, the rate of reaction increases
Note that the mean energy of the particles does not change. However, since the frequency of collisions increases (they happen more often) the frequency of successful collisions also increases