# What is the speed coefficient

## Rate constant

The **Rate constant** has the symbol $ k $. It is used in chemistry to determine the proportionality of the reaction rate $ v $ to the concentrations of two substances A and B in the equation

- $ v = k \ cdot c_ \ mathrm {A} \ cdot c_ \ mathrm {B} $

to represent.

In the calculation of the rate constants *k* (according to the Arrhenius equation) go to the frequency factor *A.* (or also called pre-exponential factor), the activation energy $ E_ \ mathrm {A} $ (unit: J / mol), the universal gas constant*R.* (= 8.314 J / (K mol)) and the absolute temperature*T* (in Kelvin K) a:

- $ k = A \ cdot e ^ \ frac {-E_ \ mathrm {A}} {R \ cdot T} $

The empirical Arrhenius equation assumes that the frequency factor *A.* is not temperature-dependent, which is a sufficiently accurate approximation for most matters. On the other hand, an equation is derived from the impact theory that shows the temperature dependence of the frequency factor *A.* considered.

- $ k = \ sigma \ cdot \ left (\ frac {8 \ mathit {k} T} {\ pi \ mu} \ right) ^ \ frac {1} {2} N_A \ cdot e ^ {- \ frac {E_ \ mathrm {A}} {R \ cdot T}} = A \ cdot e ^ {- \ frac {E_ \ mathrm {A}} {R \ cdot T}} $

The frequency factor *A.* corresponds to the product of the number of collisions *Z* and the orientation factor *P*. The frequency factor *A.* thus indicates the maximum number of collisions in the gas phase, taking into account the orientation of the molecules necessary for the reaction.

The unit of the rate constant depends on the reaction order and follows the general formula $ \ mathrm {mol} ^ {- n + 1} \ cdot \ mathrm {l} ^ {n-1} \ cdot \ mathrm {s} ^ {- 1} $, where $ n $ corresponds to the reaction order.

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