Temperature Dependence and Solvent Effects

Our examination of collision events led to the conclusion that the rate of two-body collisions has a second order dependence on the concentration(s) of the species (Equation 6.7). We realize that a two-body collision event corresponds to an elementary second order (bimolecular) process, and hence, the rate law for a bimolecular process has the same second order dependence on concentration. A complete gas kinetic analysis of collisions requires that we recognize that molecules in a gas have a distribution of velocities. Since this distribution is prescribed by the temperature, we can ask what happens when the temperature is changed. 

The factor of is introduced so that the rate is in terms of moles rather than molecules. Notice 

an important feature is that the rate constant, k , varies with temperature. 

Laboratory determination of an exponential dependence of reaction rate constants on temperature was accomplished over 100 years ago by Svante Arrhenius (Sweden, 1859-1927). His work provided an expression that can be applied in studying most chemical reactions. 

E i stands for the activation energy which is the molar equivalent of the barrier height designated Vab in this discussion. The value A in Equation 6.40 is sometimes called a frequency or pre-exponential factor. It is somewhat dependent on temperature, var3dng as /T in the hard-sphere picture because of the collision rate s dependence on temperature. This factor can often be approximated as a constant over limited ranges of temperature. 

---