Activation Energy (section 14.5)
Although the collision model is reasonable (atoms and molecules should have to come into contact in order to react), it is insufficient to explain reaction rates. According to kinetic molecular theory, one should expect the number of collisions per second between particles to be approximately the same at a given temperature. Since temperature is defined in terms of the average energy of molecules, collisions at a particular temperature should, on average, occur with the same energy. Some reactions proceed, even in very fluid aqueous or gas phases, at a sluggish pace. Other reactions conducted at the same temperature are quite rapid. Clearly, not all collisions between particles cause the breakage and formation of chemical bonds.
Reaction rate constants, and the associated reaction rates,generally increase with temperature. [A “rule of thumb” used by industrial chemists is that the reaction rate doubles with every 10°Cincrease in temperature.] For molecules in the gas state, temperature is proportional to the average kinetic energy of ideal gas particles (K = 3/2 kT, where K is kinetic energy, T is temperature in Kelvins, and k is the Boltzmann constant). Furthermore, kinetic energy K = 1/2 mv2, where m is the particle mass (a constant) and v is average particle speed. As temperature increases, the speeds of particles, and the resulting violence of the collisions, must increase.
The associated increase in reaction rates must be connected to the increase in average particle speeds. At lower temperatures, many of the collisions are not energetic enough to break existing chemical bonds. As temperature—and therefore average particle speed—increases, more of the collisions must be of sufficient energy to allow bonds to break and new bonds to form.
The minimum collision energy necessary for colliding particles to reactis termed the reaction’s activation energy(Ea). The activation energy can be viewed as an “energy barrier” that must be overcome in order for particles to react. When particles possessing the necessary kinetic energy collide, they form an unstable, evanescent activated complex, or transition state, that immediately forms the reaction products.
A transition state cannot be isolated—it is too reactive, and immediately leads to the formation of the reaction products.
Even for an exothermic process such as that represented in the figure, some initial energy must be supplied to trigger the reaction. In the case of an exothermic process, more energy is released as a result of product formation than is required for formation of the activated complex (denoted AB‡above).
The rate constant is related to the activation energy by the Arrhenius equation:
where Ea is the activation energy of the
reaction in J/mol, and R is the gas
constant (8.314 J / K ∙ mol). A, the collision frequency factor, is a constant.
As before, a rearrangement allows one to observe a linear relationship between inverse temperature and rate constant.
Of import is the slope of the line, which is equal to Ea /R; the activation energy can be determined from the graph of ln k vs. inverse temperature:
The collision factor A need not be known if the rate constants k1 and k2 are known at two different temperatures T1 and T2 or if the activation energy and one of the rate constants are known. The complex-appearing, but very useful, relation is: