In container there are two kinds of molecules A and B which are distributed uniformly. Initially the quantities of A and B are $N_A$ and $N_B$ respectively A and B are distributed uniform, i.e., in any small space (of cause the space should be large enought that there are thousands of molecules in the space), the ratio of number A and B is equal to the ratio of total number of A and B.
Assume the molecules are fixed all the time (i.e., we don't consider diffusion) and in every peroid, there is at most one molecule $B_j$ around molecule $A_i (i=1,2,...,N_A)$ be transformed to molecule A: if the molecule $B_j$ is on the boundary/neighbor of molecule $A_i$, the molecule $B_j$ would be transformed to A, otherwise (i.e., all molecules neighboring $A_i$ are molecule A) no molecule around $A_i$ be transformed. In addition, if there are several $A_k$ and $B_j$ on the neighbor of molecule $A_i$, the closest $B_j$ would be transformed to A.
Now the problem is: Is there any analytical expression to show how many molecules (approximately) would be transformed to A in every peroid until all molecule B are transformed to molecule A?
Thanks, Tang Laoya