The frequency factor, symbolized as A, is the coefficient in front of the exponential term in the Arrhenius equation. It represents how often reactant molecules collide with the correct orientation to potentially form products. The full equation is k = Ae−Ea/RT, where k is the rate constant, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. While the exponential part accounts for whether collisions have enough energy to react, A captures everything else: how frequently collisions happen and whether the molecules are lined up the right way when they hit.
What the Frequency Factor Actually Represents
At the molecular level, A is the product of two components from collision theory: the collision frequency (Z) and the steric factor (ρ). The collision frequency is simply how many times molecules bump into each other per unit of time. The steric factor is the probability that those colliding molecules happen to be oriented correctly for a reaction to occur. Not every collision leads to a product, even if there’s enough energy. Two molecules might slam together with plenty of force but at the wrong angle, so nothing happens.
Putting these together, A = Zρ. This means the frequency factor filters the total number of collisions down to only those with a realistic shot at reacting based on geometry alone. A reaction where molecules need very precise alignment to react will have a small steric factor and therefore a smaller A. A reaction that’s less picky about orientation will have a larger one.
Units Depend on Reaction Order
Because A and the rate constant k always share the same units, the units of A change depending on the overall order of the reaction:
- Zero-order reactions: M/s (moles per liter per second)
- First-order reactions: s−1 (per second)
- Second-order reactions: M−1·s−1 (per molar per second)
This is worth keeping in mind when comparing frequency factor values across different reactions. A large A for a first-order reaction and a large A for a second-order reaction aren’t directly comparable because they’re measured in different units.
Typical Values
For a first-order gas-phase reaction, a typical order-of-magnitude value for A is around 1013 s−1. That enormous number reflects the sheer frequency of molecular collisions in a gas. Bimolecular (second-order) gas-phase reactions tend to have frequency factors in a similar ballpark when expressed in their own units, though the exact value depends heavily on the size of the molecules and how restrictive the orientation requirement is. A reaction with a very small steric factor, meaning the molecules need to collide in one very specific arrangement, can have an A value several orders of magnitude lower than one where almost any collision angle works.
How to Find A from Experimental Data
The standard method uses a linearized version of the Arrhenius equation. Taking the natural log of both sides gives:
ln(k) = ln(A) − Ea/RT
If you plot ln(k) on the y-axis against 1/T on the x-axis, you get a straight line. The slope equals −Ea/R, which gives you the activation energy, and the y-intercept equals ln(A). To recover A itself, you take the exponential of the y-intercept (ey-intercept). For example, one analysis of reaction rate data using this approach yielded a frequency factor of 9.98 × 1017 M−1·s−1 for a second-order reaction.
Is A Really a Constant?
In introductory chemistry, A is treated as a temperature-independent constant. That’s a useful simplification, but it’s not perfectly accurate. Collision frequency itself depends on temperature because molecules move faster when they’re hotter, so they collide more often. Research published in the Journal of Thermal Analysis and Calorimetry has shown that ignoring this temperature dependence can introduce significant errors in calculated activation energies, sometimes larger than errors from other common approximations in kinetic analysis.
For most practical purposes, especially over modest temperature ranges, treating A as a constant works well. But in precise kinetic modeling or when analyzing data over a wide temperature range, the temperature dependence of A becomes something that can’t be ignored without consequences.
Connection to Transition State Theory
Collision theory gives one way to interpret A, but transition state theory (also called Eyring theory) offers a deeper perspective. In this framework, A is related to the entropy of activation, which describes how “ordered” the transition state is compared to the starting reactants. A large frequency factor corresponds to a transition state that’s relatively loose and disordered. A small frequency factor means the transition state is highly organized, with the atoms locked into a very specific arrangement.
This connection is useful because it ties A to something physically intuitive. A reaction that requires two floppy molecules to line up in one precise configuration before they can react will have low activation entropy and a small A. A reaction where a single molecule simply falls apart, with the transition state being looser than the starting material, will have high activation entropy and a large A.
Other Names for the Same Thing
You’ll see the frequency factor called by several names depending on the textbook or source. The IUPAC Gold Book, which sets the official terminology for chemistry, lists the preferred term as “pre-exponential factor” with the symbol A. Common synonyms include “Arrhenius A factor,” “A-factor,” and “frequency factor.” All refer to the same quantity. “Pre-exponential factor” is the most precise name since it simply describes where A sits in the equation, without implying any particular physical interpretation.