Given X + Y --> XY, it is as hard to know k and A as it is to know E(a). In fact, the intuitive path would be that a knowledge of A and E(a) can tell you what k is.
E(a) is simply the energy of the highest point along the reaction co-ordinate. The exact value of E(a) can be determined though complex Qunatum Mechanical calculations...though there may be some pattern that is exhibited that depends on the type of reaction.
Here are some of the factors that E(a) depends on :
- geometry of the molecules
- bonds strengths of all bonds
- the number of bonds of each type that are broken/formed