The Rate-equation for Biogenic Silica Dissolution in Seawater – New Hypotheses

Abstract

This paper investigates the kinetics of biogenic silica dissolution in seawater, through batch dissolution, where the reaction is observed as the increase in dissolved silicic acid concentration with time. It utilises new data from dissolution of the marine diatom Cyclotella cryptica, and the freshwater diatom C. meneghiniana, as well as literature results. The sum of exponentials form: \(C_{\rm t}=A_{\infty}(1-e^{-k_at})+B_{\infty}(1-e^{-k_bt})\), is hypothesised as the most general rate equation, with the single exponential form occurring in a minority of cases. The consistency of this behaviour with a near-exponential decay of surface area with time, an appropriate mathematical integration, and surface heterogeneity, is discussed. (Serious errors in some existing integrations are identified.) The rate of dissolution at constant surface area is shown to decrease non-linearly as the ambient concentration of silicic acid increases. A fractional order with respect to silicic acid in the back reaction, close to 0.5, leads to a mechanism in which an intermediate is formed from the surface and an, as yet, unidentified molecule, probably water. Good preliminary fits are found between the model and literature results found using entirely different methods. A parallel treatment of hydrogen ion dependency is suggested. The likely distortion of full reaction curves from exponential behaviour imposed by the back reaction, is considered in detail.