AN APPROXIMATION LEADING TO THE BINOMIAL DISTRIBUTION IN THE STOCHASTIC TREATMENT OF A REVERSIBLE CHEMICAL REACTION

~UJ.I ~ ~~~ 'ij ~j~ J! ':?J~ ~fo cL..u~l ~~~ u~LUJ.J ~~~~ ~'·t·"~ fo.L:a. t· t ABSTRACT The exact equilibrium distribution of the number of molecules of C in the reversible chemical reaction A+ B ~ C is shown to converge to the binomial distribution when N is finite, "· M->x, K->0 in such a way that KM is finite, where M, Nand K are respectively, the total number of molecules of A, the total number of molecules Band the ratio of the forward to the backward reaction rates, K 1/K2 • The practical implication of this limiting condition have been investigated by numerically computing the two distributions for a wide range of values of the parameters. Under the same conditions, the transient distribution of C(t), the number of C molecules at timet, is shown to be approximately a convolution of two binomial distributions.