The multi-environment conditional probability density function (MECPDF) model is a mathematical description of the turbulent mixing of two streams of chemical reactants along with the complex sequence of chemical reactions that follow. The processes of mixing and chemical reactions can be intricately connected and complex, particularly when the rates of both processes are nearly equal. Furthermore mixing has the potential to completely determine the outcome of the chemical reactions. Mixing will have the strongest effect on chemical reactions when there are multiple reactions with competing pathways that proceed at different rates. As multiple reactions with competing pathways progress, with interaction of mixing, the resulting dynamics are very non-linear and as a result have eluded accurate mathematical description, except in the extreme case of using the world's largest computers to simulate all of the length scales of a turbulent flow. It is proposed that the MECPDF model provides a sufficiently accurate description of these dynamics with a model that is computationally practical for engineering work. The primary objectives of this thesis will be to describe the MECPDF model and to demonstrate its use and effectiveness.