Abstract: In view of the fact that there is no precise analytic solution for a penetration mass transfer model accompanied with instantaneous non-reversible reactions in the liquid phase, a numerical solution method for the enhancement factor is developed. This method can be used to calculated the enhancement factor under the condition of the ratio of diffusivities r>005 and the ratio of stoichiometric concentrations S>1. The two constant exponents in the approximate equation of enhancement factor are expressed respectively as a six-parameter function f(S) and (g(S).) The numerical solution is fitted as the 12-parameter function by Maquart method. The maximum relative error between the fitting value and the numerical solution is less than 0\^5%.