Concentration evolution for second-order reversible reactions

2 Concentration evolution for second-order reversible reactions 

For second-order elementary reactions, we similarly have K=kf/k. The evolution of concentrations is, however, much more complicated. One specific case, the ionization of water (Reaction 1-9), 

To solve the above equation, it is necessary to express [H+] and [OH ] in terms 

Before presenting the general method to solve the above ordinary differential equation, let s first consider a simple case with special initial condition. 

The method for solving Equation 2-14 for the general initial condition is instructive because it is the method to solve all second-order reversible reactions. The first step is to note that the terms inside the braces in the right-hand side of Equation 2-14 is a quadratic form +([H+]o+[OH ]o) +([H+]o[OH ]o fCw), which can be rewritten as i)( 2), with and 2 being the two zeros of the 

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