How does an increase in surface area affect the rate of a chemical reaction?
In the absence of any other change, increasing surface area to volume ratio increases the rate of reaction.
Rates of reaction increase according to the frequency of collisions between the reacting species. If you have, for example, a solid reactant which is in contact with an aqueous solution of another, increasing the surface area to volume ratio, by grinding the solid into a finer powder, for example, means that the same number of moles of reactant now exist in a greater surface area form.
This means that the surface of the reactant, where collissions take place and reactions occur, is greater, so there is scope for more collisions per mole to take place. Therefore the rate of reaction increases.
However - be careful. I did say above "In the absence of other changes". Surface area is only one factor that affects rate. If you increase the surface area, and also drop the temperature, for example, you may find that there is no overall change in rate, because the effect of one change is nullified by the other.