The rate constant, or rate at which a chemical reaction occurs, depends on a number of variables, including the temperature during the reaction and internal properties of the substance. One such property is the frequency factor, which is the value of the rate constant as the temperature approaches infinity. The frequency factor is important for characterizing substances based on their dependence between rate reactions and temperature, which can offer insight into the chemical reactions at the molecular level. Finding the frequency factor at a given temperature can be found through a straightforward analysis of what's known as the Arrhenius equation.

Take the natural logarithm of the rate constant. For example, if the rate constant is 20 per second, taking the natural logarithm of this number gives 3 per second.

Multiply the given temperature by the gas constant, which has a value of 8.31 joules per mole per Kelvin. For example, if the given temperature is 293 Kelvin, the resulting number will be 2434.8 joules per mole.

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Divide the activation energy of the chemical by the number resulting from the previous step. If the activation energy is 40,000 joules per mole, you would divide 40,000 joules per mole by 2434.8 joules per mole, which gives the unitless number 16.43.

Divide the resultant number from the first step by the resultant number from the previous step. In the example given, you would divide 3 per second by 16.43, giving 0.18 per second. This is the frequency factor.

#### Tip

If you do not know the rate constant offhand, you may need to determine the value experimentally. In this case, the frequency factor can be found by graphing the relationship between the rate constant and the temperature.