Chemical Activation Energy What does it consist of, Calculation

The chemical activation energy (from the point of view of kinetic studies) refers to the least possible amount of energy required to start a chemical reaction. According to the theory of collisions in chemical kinetics, all molecules that are in motion are said to have a certain amount of kinetic energy.

This means that the greater the speed of its movement, the greater the magnitude of its kinetic energy. In this sense, a molecule that carries a fast movement cannot be divided into fragments by itself, so a collision must occur between it and another molecule for a chemical reaction to take place..

When this happens - when there is a collision between the molecules - a fraction of their kinetic energy is transformed into vibrational energy. Likewise, if at the beginning of the process the kinetic energy is high, the molecules that participate in the collision will present such a great vibration that some of the chemical bonds present will be broken..

This breaking of bonds constitutes the first step in the transformation of reactants into products; that is, in the formation of these. On the contrary, if at the beginning of this process the kinetic energy is of small magnitude, there will be a phenomenon of "rebound" of the molecules, through which they will be separated practically intact..

Article index

• 1 What does?
  • 1.1 Activated complex
• 2 How is it calculated?
  • 2.1 Calculation of the activation energy of a chemical reaction
• 3 How does activation energy affect the rate of a reaction?
• 4 Activation energy calculation examples
• 5 References

What does it consist of?

Starting from the concept of collisions between molecules to initiate chemical reactions previously described, it can be said that there is a minimum amount of energy required for a collision to occur..

So, if the energy value is less than this necessary minimum, there will simply be no alteration between the molecules after the collision occurs, which means that when this energy is absent, the species involved remain practically intact and it will not happen. any change due to this crash.

In this order of ideas, the minimum energy that is needed for a change to occur after a collision between molecules is called the activation energy..

In other words, the molecules involved in a collision must possess a quantity of total kinetic energy equal to or greater than the activation energy for a chemical reaction to occur..

Likewise, in many cases the molecules collide and originate a new species called the activated complex, a structure which is also called the "transition state" because it only exists temporarily..

It is caused by the reactant species due to the collision and prior to the formation of the reaction products.

Activated complex

The activated complex mentioned above forms a species that has very low stability but, in turn, has a large magnitude of potential energy..

The following diagram shows the transformation of reactants to products, expressed in terms of energy and noting that the magnitude of the energy of the activated complex that is formed is considerably greater than that of the reactants and products..

If at the end of the reaction the products have a greater stability than the reactant substances, the release of energy occurs in the form of heat, giving an exothermic reaction..

On the contrary, if the reactants result in a greater stability than the products, it means that the reaction mixture manifests an absorption of energy in the form of heat from its surroundings, resulting in an endothermic reaction..

Likewise, if one case or the other happens, a diagram like the one shown previously must be constructed, where the potential energy of the system that reacts against the advance or progress of the reaction is plotted..

This is how the potential energy changes that occur as the reaction proceeds and the reactants are transformed into products are obtained..

How is it calculated?

The activation energy of a chemical reaction is closely related to the rate constant of said reaction, and the dependence of this constant with respect to temperature is represented by the Arrhenius equation:

k = Ae^{-Ea / RT}

In this expression k represents the rate constant of the reaction (which depends on temperature) and the parameter TO is called the frequency factor, and is a measure of the frequency of collisions between molecules.

For his part, and expresses the base of the series of natural logarithms. It is raised to a power equal to the negative quotient of the activation energy (Ea) between the product resulting from the gas constant (R) and absolute temperature (T) of the system to consider.

It should be noted that the frequency factor can be considered as a constant in certain reaction systems over a wide temperature range..

This mathematical expression was originally supposed by the Dutch chemist Jacobus Henricus van't Hoff in 1884, but the one who gave it scientific validity and interpreted its premise was the Swedish chemist Svante Arrhenius, in 1889.

Calculation of the activation energy of a chemical reaction

The Arrhenius equation specifies the direct proportionality that exists between the rate constant of a reaction and the frequency of collisions between molecules.

Likewise, this equation can be represented in a more convenient way by applying the property of natural logarithms to each side of the equation, obtaining:

ln k = ln A - Ea / RT

When the terms are rearranged in terms of obtaining the equation of a line (y = mx + b), the following expression is achieved:

ln k = (- Ea / R) (1 / T) + ln A

So, when constructing a graph of ln k against 1 / T, a straight line is obtained, where ln k represents the coordinate and, (-Ea / R) represents the slope of the line (m), (1 / T) represents the x coordinate, and ln A represents the intercept with the ordinate axis (b).

As can be seen, the slope resulting from this calculation is equal to the value of -Ea / R. This implies that, if you want to obtain the value of the activation energy by means of this expression, you must carry out a simple clearing of this, resulting in:

Ea = -mR

Here the value of m is known and R is a constant equal to 8.314 J / K mol.

How does activation energy affect the rate of a reaction??

When trying to get an image of the activation energy, it can be considered as a barrier that does not allow a reaction to occur between the lower energy molecules..

As in a common reaction it happens that the number of molecules that can react is quite large, the speed - and equivalently, the kinetic energy of these molecules - can be very variable.

It generally happens that only a small amount of the totality of the molecules that experience a collision - those that have a greater speed of movement - have enough kinetic energy to be able to exceed the magnitude of the activation energy. So these molecules are fit and capable of being part of the reaction.

According to the Arrhenius equation, the negative sign -which precedes the quotient between the activation energy and the product of the gas constant and the absolute temperature- implies that the rate constant decreases as there is an increase in the activation energy, as well as a growth when the temperature increases.

Activation energy calculation examples

To calculate the activation energy by constructing a graph, according to the Arrhenius equation, the rate constants for the decomposition reaction of acetaldehyde have been measured at five different temperatures and it is desired to determine the activation energy for the reaction, which is expressed as:

CH₃CHO (g) → CH₄(g) + CO (g)

The data for the five measurements are as follows:

k (1 / M^1/2S): 0.011 - 0.035 - 0.105 - 0.343 - 0.789

T (K): 700 - 730 - 760 - 790 - 810

In the first place, to solve this unknown and determine the activation energy, a graph of ln k vs 1 / T (y vs x) must be constructed, to obtain a straight line and from here take the slope and find the value of Ea, as explained.

Transforming the measurement data, according to the Arrhenius equation [ln k = (- Ea / R) (1 / T) + ln A], the following values ​​are found for y and x, respectively:

ln k: (-4.51) - (-3.35) - (-2.254) - (-1.070) - (-0.237)

1 / T (K^-1): 1.43 * 10^-3 - 1.37 * 10^-3 - 1.32 * 10^-3 - 1.27 * 10^-3 - 1.23 * 10^-3

From these values ​​and by means of the mathematical calculation of the slope -either in a computer or in a calculator, by means of the expression m = (Y_two-Y₁) / (X_two-X₁) or using the linear regression method- it is obtained that m = -Ea / R = -2.09 * 10⁴ K. Thus:

Ea = (8.314 J / K mol) (2.09 * 10⁴ K)

= 1.74 * 10⁵ = 1.74 * 10^two kJ / mol

To determine other activation energies through the graphical way, a similar procedure is carried out.

References

1. Wikipedia. (s.f.). Activation Energy. Recovered from en.wikipedia.org
2. Chang, R. (2007). Chemistry, Ninth edition. Mexico: McGraw-Hill.
3. Britannica, E. (s.f.). Activation energy. Retrieved from britannica.com
4. Moore, J. W. and Pearson, R. G. (1961). Kinetics and Mechanism. Recovered from books.google.co.ve
5. Kaesche, H. (2003). Corrosion of Metals: Physicochemical Principles and Current Problems. Obtained from books.google.co.ve