Why does the rate of reaction decrease with time?
This can be answered by the collision theory:
Let's take an example:
Say I added some Lithium to Hydrochloric Acid and I decided to measure the rate of the reaction. Over time I would see the reaction rate drop. The equation would be:
At the start of the reaction, the maximum amount of Lithium is exposed to the Hydrochloric Acid. As a result, there is more surface area for successful collisions between the reactant particles - the result of these collisions is the products (namely, Lithium Chloride and Hydrogen)
As the reaction progresses, less surface area becomes available and, thus, the reaction slows down until eventually there is nothing left to react.
Of course, there are ways to increase the reaction rate; namely by adding a catalyst (such as liver).