### Activation Energy in Chemistry

Activation energy refers to the energy required for a molecule to change from a normal state to an active state in which a chemical reaction is likely to occur. (The activation energy in the Arrhenius formula is distinguished from the activation energy derived from the kinetics, also known as the activation energy of Arrhenius or the empirical activation energy). The difference between the average energy of the activated molecule and the average energy of the reactant molecules. It is the Activation Energy.

## Historical Origin

Activation energy is a chemical term, also known as Threshold Energy. This term was introduced by Arrhenius in 1889 to define the energy barriers that need to be overcome in the event of a chemical reaction. It can be used to represent the minimum energy required for a chemical reaction to occur. The activation energy of the reaction is usually expressed as Ea in kilojoules per mole (kJ/mol).

For a first-order reaction, the activation energy represents the height of the barrier (sometimes referred to as the energy barrier). The magnitude of the activation energy can reflect the ease with which chemical reactions occur.

Before Arrhenius proposed the concept of activation energy, one of the rules for solution reactions was that the reaction rate would increase exponentially for every 10 °C increase in solution temperature. And, in 1878, the British scientist Hood first summed up an empirical relationship through experiments:

Lgk=BC/T

Where B and C are empirical constants.
Subsequently, based on the influence of temperature on the equilibrium constant of chemical reaction in 1884, Van der Hoff first made a preliminary theoretical explanation for the above formula.

He rigorously derives an equation describing the relationship between temperature and chemical equilibrium constant K from thermodynamics. For solution reaction Kc can be written as:

dlnKc/dT= ⊿U/RT^2

And derive the relationship between temperature and reaction rate constant:

Dlnk/dT= (A/RT^2) + I

However, he did not give the physical meaning of A and the determined I method, so it did not attract people’s attention at that time.

### Put Forward

In 1889, Arrhenius revealed the Arrhenius empirical formula of the relationship between reaction rate and temperature through a large number of experiments and theoretical arguments. The form is as follows:
Exponential k=Ae^-Ea/RT
Logarithmic lnk=lnA-Ea/RT
Differential dlnKc/dT= ⊿U/RT^2

### Perfect

Arrhenius proposed the concept of activation energy, but the explanation of activation energy is not clear enough, especially considering activation energy as a temperature-independent constant, which is inconsistent with many experimental facts.

In the 1920s, scientist Tolman used statistical thermodynamics to discuss the relationship between chemical reaction rate and temperature, and in 1925 derived the following reaction formula:

Ea=<E*>-

Where: <E*> is the average molar energy of the activated molecule, the average molar energy of the unreacted molecule, and the activation energy is the difference between the average energy of the activated molecule and the average energy of the reactant molecules.
We can see that in the above formula, both <E*> are temperature dependent, so Ea should also be a function of temperature, but in some cases, the temperature effects of the two may cancel each other out. It is independent of temperature.

Here are some other Articles that you will Probably Enjoy-

The formula derived by Tolman better compensates for some of the shortcomings and shortcomings of Arrhenius’s theory, and no longer separates the activation energy from the temperature, but proposes a more general and more convincing an explanation.

### Basic Definition

Activation energy refers to the minimum energy required to reach an activating molecule from a reactant molecule in a chemical reaction.

Taking the enzyme and the substrate as an example, the difference between the potential energy of the Free State and the potential energy of the activated molecule formed by the combination of the two is the activation energy required for the reaction, so it is not said that the activation energy exists in the cell but in the cell.

Some of the energy provides the required activation energy for the reaction. The chemical reaction rate is closely related to the size of its activation energy. The lower the activation energy, the faster the reaction rate, so reducing the activation energy can effectively promote the reaction.

Enzymes promote the rapid development of some very slow biochemical reactions by slowing down the activation energy (actually by reducing the activation pathway) (or slowing down some of the faster biochemical reactions).

The factors affecting the reaction rate are extrapolation and internal factors: the internal factors are mainly the nature of the participating substances; in the same reaction, the influencing factors are external factors, that is, external conditions, mainly concentration, pressure, temperature, and catalyst.

### Chemical Reaction

#### The activation energy of the chemical reaction

Experiments have shown that an effective collision can occur only when the energy of the colliding molecule equals or exceeds a certain energy Ec (which can be called critical energy). A molecule having an energy greater than or equal to Ec is referred to as an activating molecule.

At a certain temperature, the percentage of molecules with certain energy is made to the molecular energy.

The energy of the reactant molecules can range from 0 to ∞, but the molecules with very low energy and high energy are few, and the number of molecules having the average energy Ea is quite large.

The corresponding relationship between the number of molecules with different energies and the magnitude of energy is called the molecular energy distribution curve at a certain temperature. In Figure 1, Ea represents the average energy of the molecule, Ec is the lowest energy the activated molecule has, and molecules with energy equal to or higher than Ec may produce an effective collision.

The difference between the lowest energy Ec of the activating molecule and the average energy Ea of the molecule is called the activation energy.

Different reactions have different activation energies. The lower the activation energy of the reaction, the more the number of activated molecules at a given temperature, the faster the reaction.

The molecular energy distribution is different at different temperatures. A schematic diagram of the energy distribution of molecules at different temperatures. When the temperature rises, the rate of movement of the gas molecules increases, not only increasing the number of collisions of gas molecules per unit time but more importantly, increasing the percentage of activated molecules due to the increase in energy of the gas molecules.

The curve t1 in Fig. 2 represents the molecular energy distribution at the temperature t1, and the curve t2 represents the molecular energy distribution at the temperature t2 (t2 > t1). The number of activated molecules at temperature t1 can be reflected by the area A1; when the temperature is t2, the number of activated molecules can be reflected by the area A1+A2. As can be seen from the figure, increasing the temperature increases the percentage of activated molecules and increases the reaction rate.

## Law formula

### Arrhenius formula

The energy required to convert the non-activated molecule into an activated molecule for the activation energy can be solved by the Arrhenius equation. The Arrhenius equation reflects the relationship between the chemical reaction rate constant K and temperature. In most cases, the quantitative law can be described by the Arrhenius formula.

K=Aexp(-Ea/RT) (1)

Where: κ is the rate of reaction (normal); Ea and A are called activation energy and pre-exponential factor, respectively, which are two important parameters in chemical kinetics, R is the molar gas constant, T is the thermodynamic temperature.

(1) Can also be written as:

Lnκ=lnA-Ea/RT (2)

Lnκ= is linear with -1/T, the slope of the line is -Ea/R, and the intercept is lnA. The κ value at different temperatures is measured experimentally, and lnκ is plotted against 1/T to find E. value.

Example: Calculating the reaction rate coefficient k by Ea

When k and Ea at a certain temperature are known, k at another temperature or a temperature T corresponding to another k can be calculated according to Arrhenius.

2N 2 O 5 (g) = 2N 2 O 4 (g) + O 2 (g)
Known: T 1 =298.15K, k 1 =0.469×10s
T 2 = 318.15K, k 2 = 6.29 × 10s Find: Ea and k 3 at 338.15K.
Ea = [RT 1 T 2 (lnk 2 /k 1)]/ (T 2 -T 1) =102kJ/mol
Lnk 3 /k 1 =Ea[(1/T 1 )-(1/T 3 )]/R
K 3 =6.12/1000S

For a more complex description of the relationship between κ and T, the activation energy E is defined as:

E=RT 2 (dlnκ/dT) (3)

In the meta-reaction, not every collision of the reactant molecules can react. SA Arrhenius believes that only the collision between the” activated molecules” can react, and the difference between the average energy of the activated molecules and the average energy of the reactant molecules is the activation energy. The modern reaction rate theory further points out that when two molecules react, they must pass through a transition state, an activated complex.

The transition state has higher potential energy than the reactant molecules and product molecules, and the colliding reactant molecules must have a higher potential.

The high energy is enough to overcome the potential energy barrier of the reaction, in order to form a transition state and react, which is the essence of activation energy.

For the composite reaction, the E value obtained by the above experimental method is only an apparent value and has no practical physical meaning.

### Physical Meaning

S.A. Arrhenius found a relationship between the velocity constant k of the chemical reaction and the absolute temperature T between d (lnk)/dt=E/RT2. Here E is the activation energy.

If the above formula is obtained by lnk=lnA-(E/RT), it can be seen from this formula that the k value is obtained at various temperatures, and lnk is plotted against 1/T (this figure is called Arrhenius diagram). A straight line is obtained, and since the slope of the straight line is -E/R, the E value can be obtained.

The physical meaning of activation energy is generally considered to be the same: there is a transitional state from the original reaction system to the intermediate stage of the product.

Here are some other Articles that you will Probably Enjoy-

The energy difference between this transition state and the original system is the activation energy E, and if the thermal energy RT is not greater than E, the reaction cannot be performed.

That is, there is an energy barrier between the original system and the product system, and its height is equivalent to the activation energy.

Thereafter Erin (H.Eyring) from the transition state (also called active complex) there is an approximate balance between the departure and the original system, the rate constant k derived from the following relationship: k = k (KT / h ) Exp(-ΔG*/RT)=k(KT/h)exp( ΔS */R)exp(−ΔH*/RT)k is the permeability coefficient,

K is the Boltzmann constant, and h is the Planck constant, ΔG*, ΔS*, ΔH* are activation free energy, activation entropy, and activation enthalpy, respectively. Moreover, the activation of free energy is approximately equal to the activation enthalpy.

The enzymatic reaction is mainly due to a decrease in the activation of free energy.