The rate and cross-section of chemical reactions

This section is a review of the macroscopic notions we are familiar with from chemical kinetics. Our final purpose is to build rate constants from the bottom up and therefore to describe the rate of chemical reactions in systems that are not in thermal equilibrium. Thermally equihbrated reactants are more typical of the laboratory than of the real world and, even in the laboratory, it takes care and attention to insure that the reactants are indeed thermally equilibrated. Outside of the laboratory, whether in the internal combustion engine (which fires many thousands of times per minute), in the atmosphere, or in outer regions of space, this is not the case. 

For our purpose it is essential to emphasize that the thermal reaction rate is defined only when the experiment does maintain a diermal equilibrium for the reactants. 

If necessary, the reaction needs to be slowed down, say Ity the addition of a buffer gas, so that non-reactive collisions rapidly restore the reactants to thermal equilibrium. If this is not possible, Appendix 3.A introduces the reaction rate constant under more general conditions. Under non-equilibrium conditions the rate constant defined through Eq. (3.1) may however depend on other variables such as the pressure and even on time. 

The experimental temperature dependence of the thermal reaction rate constant is often represented in an Arrhenius form 

We write the Boltzmann constant k with a subscript B to avoid confusion with the reaction rate constant. If the activation energy is specified per mole, the exponent needs to be written as E /RT where R = Aa/cb is the gas constant and Na is Avogadro s number. 

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