Question

What does the exponential factor represent in the Arrhenius equation?
(a) The amount of energy needed to start a chemical reaction
(b) The fraction of reaction energy given off per unit of time
(c) The fraction of products that have approached the activation energy hill and made it over per number of attempts
(d) The fraction of reactants that have approached the activation energy hill and made it over per number of attempts
(e) The total number of reactants in a reaction

Answer 1

Hint: The pre-exponential factor (A) is a key component of the Arrhenius equation, which was developed by Svante Arrhenius, a Swedish scientist, in 1889. The frequency factor, also known as the pre-exponential factor, describes the frequency of reactant-molecule collisions at a standard concentration. Although it is frequently stated as temperature independent, it is really temperature dependent since it is linked to molecular collision, which is a temperature dependent process.

Complete answer:
The Arrhenius equation is a formula describing the temperature dependence of reaction rates in physical chemistry. Svante Arrhenius published the equation in 1889, based on the work of Dutch scientist Jacobus Henricus van 't Hoff, who noticed in 1884 that the van 't Hoff equation for the temperature dependence of equilibrium constants implies such a formula for forward and reverse reaction rates. The Arrhenius equation expresses the rate constant of a chemical process as a function of absolute temperature.
\[k = A{e^{\frac{{ - {E_{\text{a}}}}}{{RT}}}}\]
R is the universal gas constant, k is the rate constant (frequency of collisions resulting in a reaction), T is the absolute temperature (in kelvins), A is the pre-exponential factor, a constant for each chemical reaction, ${E_a}$ is the activation energy for the reaction (in the same units as RT), and A is the pre-exponential factor, a constant for each chemical reaction.
The exponential factor reflects the percentage of reactants who have approached and crossed the activation energy hill in the number of tries.
This is a different version of the exponential decay rule. The magnitude of the rate constant as a function of the exponent\[-\frac{{{E_a}}}{{RT}}\] is what is “decaying” here, not the concentration of a reactant as a function of time. The exponent is simply the ratio of the activation energy to the average kinetic energy where RT is the average kinetic energy. The smaller the rate, the higher this ratio, which is why it has a negative sign. High temperatures and low activation energies prefer higher rate constants, thus a process will speed faster under these conditions. Because these components appear in an exponent, their impact on the rate is significant.

So, the correct answer is “Option A”.

Note:
This equation has a wide range of applications, including estimating the rate of chemical processes and calculating activation energy. The formula was given a physical rationale and interpretation by Arrhenius. It's best to think of it as an empirical relationship for now. It may be used to simulate temperature-dependent diffusion coefficients, crystal vacancy populations, creep rates, and a variety of other thermally induced processes and reactions. The connection between rate and energy is also expressed via the Eyring equation, which was discovered in 1935.