There are many factors that can influence the speed at which a reaction takes place, and these can change with time. In general, it is a function of the state of the system. It is reasonable to assume that, for a reaction to occur, the molecules of the reactants must collide. The number of collisions per unit time can be expected to grow with the number of molecules of the reactants available. At higher temperatures the number of collisions is also expected to increase (the molecules are more agitated). The rate law may also depend on the concentration of catalysts or inhibitors. These materials increase or decrease the reaction speed, respectively, although they don't appear in the stoichiometric equation. Finally, the concentrations of the products can affect the reaction rate as well. The reaction speed may increase in the presence of the products (the case of auto-catalytic reactions), or it may decrease (the case of self-inhibiting reactions). Below we present some theories for the forms of these dependencies -- the rate laws. For now, let's assume the reaction rate for (1.1) depends on some of the factors just mentioned:
where 
denotes the temperature. Then the mathematical
equations describing the time-evolution of the concentrations of
the different chemical species in (1.1) are
This system of first order, ordinary differential equations can be solved (either exactly or approximately), for given initial concentrations, provided we know the function, f([A],[B],[C],[D],T,t), that gives the reaction rate. The next sub-sections discuss particular types of reaction and how their rates are suggested from theory and determined experimentally.
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