Arrhenius equation is an equation in chemistry that helps calculate **how chemical reactions change their speed based on temperature**.

Index

**The Equation**

The equation states that

Let us understand the terms involved:

**k**is the**rate constant**, which tells how fast the reaction proceeds.**A**is the**pre-exponential factor**or**probability factor**or**Arrhenius constant**. In simple terms, it is the frequency of correctly oriented collisions between the reactants which lead to products.**e**is Euler’s number, which is an important mathematical number related to natural growth. It is approximately equal to 2.718.**E**is the_{a}**activation energy**of the reaction. In other words, it is the energy needed to be provided to make the reactants become products.**R**is the**universal gas constant**. It is equal to 8.314 J mol^{-1}K^{-1 }in SI units.**T**is the**temperature**at which the reaction is taking place, in units*Kelvin*.

**Implications of the Equation**

In simplest terms, the equation means just this: *the higher the temperature, the faster the reaction proceeds.*

How do we understand this mathematically? In the equation, notice that an exponent is involved. All the terms (E_{a}, R, and T) involved in the exponent are positive, so the use of the negative sign outside makes the exponent negative.

The term involving temperature is in the denominator, which means that **more** temperature makes the exponent **less** negative. Because of a less negative exponent, the overall term involving the exponent becomes bigger, when the temperature rises.

Thus, the value of k also becomes more when the temperature increases. The equation proceeds faster.

**Physical Interpretation**

To understand the equation in a physically meaningful way, Arrhenius explained as follows. He assumed that the equation proceeds only when the reactants have an energy greater than the activation energy. The fraction of total particles that have this much energy can be obtained from the **Maxwell-Boltzmann distribution**, a distribution that has wide-ranging applications in statistical mechanics. This gives rise to the *exponential term *in the equation.

As for the *pre-exponential factor A*, Arrhenius explained it in terms of successful collisions between reactant molecules. It is a term that depends on the *relative sizes of the reactant molecules* and *their ability to fit with each other*.

**Applications**

The Arrhenius equation has applications in many fields involving rates of reactions. For example, it can be used to predict how the rate of a **reaction can be optimized by increasing temperature**. This could be used to **maximize the yield** of products in given conditions.

It could also be used to calculate the activation energy of a reaction based on studies of rates of the reaction.

**Conclusion**

The Arrhenius equation is a very useful tool in modeling rates of reactions. Even though it is more of an empirical relation than a fundamental law, now from the standpoint of modern physical chemistry, it still is valuable in quick calculations.