Abstract
In this section we consider a first-order irreversible chemical reaction and how it is modeled by compartmental equations [161], [169], [241]. A common industrial process is treated: the reduction of limestone into its main products, calcium oxide and magnesium oxide, through the chemical reactions $$ \begin{array}{*{20}c} {CaCO_3 {\text{ }}\xrightarrow{{k_1 }}CaO + CO_2 } {MgCO_3 \xrightarrow{{k_2 }}MgO + CO_2 } \end{array} $$ (3.1) with the respective positive rate constants kj. We assume that the limestone consists of a fraction β of CaC03 and a remaining fraction 1 — β of MgC03 (0 < s < 1). Each mole of reactant which decomposes yields one mole of product plus one mole of carbon dioxide; C02 does not affect the rates at which the reactions occur and its production is not of interest.
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