In short, the<unk>  gives "the dependence of the rate constant k of chemical reactions on the temperature T (in Kelvin) and activation energy  Ea", as shown below:
where A is the pre-exponential factor or simply the prefactor and R is the gas constant. The units of the pre-exponential factor are identical to those of the rate constant and will vary depending on the order of the reaction. If the reaction is first order it has the units s-1, and for that reason it is often called the frequency factor or attempt frequency of the reaction. When the activation energy is given in molecular units, instead of molar units, e.g. joules per molecule instead of joules per mole, the Boltzmann constant is used instead of the gas constant. It can be seen that either increasing the temperature or decreasing the activation energy (for example through the use of catalysts) will result in an increase in rate of reaction.
Given the small temperature range in which kinetic studies are carried, it is reasonable to approximate the activation energy as being independent of the temperature.  Similarly, under a wide range of practical conditions, the weak temperature dependence of the pre-exponential factor is negligible compared to the temperature dependence of the 
exp
⁡
(
−
E
a
/
R
T
)
{\displaystyle \scriptstyle \exp(-E_{a}/RT)}
 factor; except in the case of "barrierless" diffusion-limited reactions, in which case the pre-exponential factor is dominant and is directly observable.
Some authors define a modified<unk> , that makes explicit the temperature dependence of the pre-exponential factor.  If one allows arbitrary temperature dependence of the prefactor, the<unk>  description becomes overcomplete, and the inverse problem (i.e. determining the prefactor and activation energy from experimental data) becomes singular.  The modified equation is usually of the form
where T0 is a reference temperature and allows n to be a unitless power.  Clearly the original<unk>  expression above corresponds to n = 0.  Fitted rate constants typically lie in the range -1<n<1.  Theoretical analyses yield various predictions for n.  It has been pointed out that "it is not feasible to establish, on the basis of temperature studies of the rate constant, whether the predicted T½ dependence of the pre-exponential factor is observed experimentally." However, if additional evidence is available, from theory and/or from experiment (such as density dependence), there is no obstacle to incisive tests of the<unk>  law.
Another common modification is the stretched exponential form
where β is a unitless number of order 1.  This is typically regarded as an experimental fit, but can have theoretical meaning, for example showing the presence of a range of activation energies or in special cases like the Mott variable range hopping.
Taking the natural logarithm of the<unk>  yields:
So, when a reaction has a rate constant which obeys the<unk> , a plot of ln(k) versus T -1 gives a straight line, whose slope and intercept can be used to determine Ea and A. This procedure has become so common in experimental chemical kinetics that practitioners have taken to using it to define the activation energy for a reaction. That is the activation energy is defined to be (-R) times the slope of a plot of ln(k) vs. (1/T):
Arrhenius equation
Quantum yield
Equation of state
Gibbs free energy
Langmuir equation
Greenhouse effect
Extraction ratio
Potential energy