For second-order supersaturation dependency, the rate expression takes the following form. We calculated the area under the rate constant-time curve and Table 2 contains the results. 14.1 10.49 8.93 7.89 7.06 Table 2 also shows half-life values for other maximum temperatures after neutralization. The computed numbers clearly show a faster aluminosilicate formation with higher temperatures. If one can control the rate of caustic addition in such a way as to maintain isothermal conditions in the evaporator, then the following expression gives the half-life of formation for the aluminosilicate.
C o is the initial aluminate or silicate ion concentration.
Table 3 provides the half-life times for different isothermal temperatures. Aluminosilicate formation under approximate isothermal conditions. Achieving approximate isothermal conditions requires the net rate of heat generated during neutralization must exactly match the heat withdrawal rate of the tube bundle. The arithmetical translation of this condition follows. We again neglect the small heat loss due to aluminosilicate formation.