In this paper, the kinetics of shell-progressive reaction in a solution of finite volume is investigated. A more general finite solution volume condition is obtained from material balance. The theoretical treatment supplements what is lacking in the mathematical model proposed by previous authors, who assume that there is no invasion of electrolyte over that of the fixed ionic groups in the resin, and the concentration of counter-ion in solution is independent of reaction time. The description of shell-progressive reaction in ion exchange resin is now more nearly perfect and definite than was before. Some numerical calculations have been done with a computer. On the basis of the great number of calculations, it may finally be concluded that (1) shell-progressive reaction is different from that occurs simultaneously throughout resin beads in the dependence of reaction rate on various factors; (2) as long as the solution volume is finite, there is a necessary condition for the application of the theoretical expressions deduced by former authors; (3) under the ordinary conditions of finite solution volume, the fractional conversion of the resin can be determined experimentally from the concentrations of counter-ion in solution.

Key words: CALCULATION, REACTION KINETICS, ION EXCHANGING, EXCHANGE REACTION, GRAIN SIZE, SHELL-PROGRESSIVE MECHANISM, RUNGE-KUTTA METHOD