CHEMICAL KINETICS: FACTORS, ORDER OF REACTION AND APPLICATIONS - CHEMISTRY - 2024

The chemical kinetics is the study of reaction rates. Deduce experimental or theoretical data on the molecular mechanism, through laws expressed by mathematical equations. Mechanisms consist of a series of steps, some of which are fast and some are slow.

The slowest of these is called the speed determining step. Therefore, knowing the intermediate species and the operating mechanism of this step is very important in kinetic terms. One visualization of the above is to assume that the reagents are enclosed in a bottle and that, when reacting, the products escape to the outside.

Finally, the products emerge freely from the mouth of the bottle without further kinetic impediments. From this perspective, there are bottles of many sizes and designs. However, they all have one element in common: a narrow neck, an indicator of the decisive step of the reaction.

What does chemical kinetics study?

Experimentally, this branch of chemistry studies the concentration variations involved in a chemical reaction, based on the measurement of a specific property.

Chemical kinetics is the branch of chemistry in charge of studying all the information that can be derived from the speed of a reaction. Its name invites you to imagine a pocket watch marking the time of a process, no matter where it occurs: in a reactor, in a cloud, in a river, in the human body, etc.

All chemical reactions, and therefore all transformation, have thermodynamic, equilibrium and kinetic aspects. Thermodynamics indicate whether a reaction is spontaneous or not; the balance its degree of quantification; and kinetics the conditions that favor its speed and as well as the data about its mechanism.

Many of the essential aspects of chemical kinetics can be observed in everyday life: in the refrigerator, which freezes food to reduce its spoilage by freezing the water that is part of it. Also, in the maturation of the wines, whose aging gives it its pleasant flavors.

However, "the time of molecules" is very different in its tiny scales, and varies enormously according to many factors (number and types of bonds, sizes, states of matter, etc.).

Because time is life, and it is also money, knowing which variables allow a chemical reaction to proceed as quickly as possible is of the utmost importance. However, sometimes the opposite is desired: that the reaction occurs very slowly, especially if it is exothermic and there are risks of explosion.

What are these variables? Some are physical, such as at what pressure or temperature a reactor or system should have; and others are chemical, such as the type of solvent, pH, salinity, molecular structure, etc.

However, before finding these variables, we must first study the kinetics of the present reaction.

How? Through the variation of concentration, which can be followed if a particular property that is proportional to the first is quantified. Throughout history, methods have become more sophisticated, allowing more accurate and precise measurements, and with increasingly shorter intervals.

Reaction speed

To determine the speed of a chemical reaction, it is necessary to know how the concentration varies over time of any of the species involved. This speed depends to a great extent on many factors, but the most important thing is that it is measurable for those reactions that occur "slowly".

Here the word "slowly" is relative and is defined for everything that can be measured with the instrumental techniques available. If, for example, the reaction is much faster than the measurement capacity of the equipment, then it will not be quantitative and its kinetics cannot be studied.

Then, the reaction rate is determined at the threshold of any process before it reaches equilibrium. Why? Because in equilibrium the speed of the forward reaction (product formation) and the reverse reaction (reactant formation) are equal.

By controlling the variables that act on the system, and consequently, its kinetics or the speed of the reaction, the ideal conditions can be chosen to generate a certain amount of product in the most desired and safe time.

On the other hand, this knowledge reveals the molecular mechanism, which is valuable when increasing the yield of a reaction.

Definition

Velocity is the change of a magnitude as a function of time. For these studies, the interest lies in determining the variation of the concentration as the hours and minutes pass; nano, pico, or even femtoseconds (10 ^-15 s).

It can have many units, but the simplest and easiest of all is M · s ^-1, or what is equal to mol / L · s. Regardless of its units, it should always have a positive value, since it is a physical quantity (such as dimensions or mass).

However, by convention the rates of disappearance for a reactant have a negative sign, and those of appearance for a product have a positive sign.

But if the reactants and products have their own velocities, then how to determine the overall reaction rate? The answer is in the stoichiometric coefficients.

General equation

The following chemical equation expresses the reaction of A and B to form C and D:

a A + b B => c C + d D

Molar concentrations are usually expressed in square brackets, so, for example, the concentration of species A is written as. Thus, the reaction rate for each of the chemical species involved is:

According to the mathematical equation, there are four routes to reach the reaction speed: the variation in concentration of any of the reactants (A or B) or of the products (C or D) is measured.

Then, with one of these values, and its correct stoichiometric coefficient, divide by the latter and thus obtain the reaction rate rxn.

Since the reaction rate is a positive quantity, the negative sign multiplies the negative rate values ​​of the reactants; for this reason the coefficients a and b are multiplied by (-1).

For example, if the rate of disappearance of A is - (5M / s), and its stoichiometric coefficient a is 2, then the rate rxn is equal to 2.5M / s ((-1/2) x 5).

Dessert example

If the product were a dessert, the ingredients by analogy would be the reagents; and the chemical equation, the recipe:

7 Cookies + 3 Brownies + 1 Ice Cream => 1 Dessert

And the speeds for each of the sweet ingredients, and the dessert itself are:

Thus, the speed with which the dessert is made can be determined with the variation of either the cookies, the brownies, the ice cream, or the set itself; then dividing it by its stoichiometric coefficients (7, 3, 1 and 1). However, one of the routes may be easier than the other.

For example, if you measure how it increases at different time intervals, these measurements can be complicated.

On the other hand, it may be more convenient and practical to measure, due to their number or some of their properties that make their concentration easier to determine than that of brownies or ice cream.

How to determine it

Given the simple reaction A => B, if A, for example, in aqueous solution, exhibits a green coloration, then this depends on its concentration. Thus, as A becomes B, the green color disappears, and if this disappearance is quantified, then a vs t curve can be obtained.

On the other hand, if B is an acidic species, the pH of the solution will drop to values ​​below 7. Thus, from the decrease in pH, the graph vs t is obtained consecutively. Then superimposing both graphs we can see something like the following:

The graph shows how it decreases over time, because it is consumed, and how the curve increases with a positive slope because it is the product.

It can also be seen that it tends to zero (if there is no equilibrium) and that it reaches a maximum value governed by stoichiometry and if the reaction is complete (all A is consumed).

The reaction rate of both A and B is the tangent line on either of these curves; in other words, the derivative.

Factors Affecting Reaction Rate

Nature of chemical species

If all chemical reactions were instantaneous, their kinetic studies would not exist. Many have speeds so high that they cannot be measured; that is, they are not measurable.

Thus, the reactions between the ions are usually very fast and complete (with a yield around 100%). On the other hand, those involving organic compounds require some time. A reaction of the first type is:

H ₂ SO ₄ + 2NaOH => Na ₂ SO ₄ + 2H ₂ O

The strong electrostatic interactions between the ions favor the rapid formation of water and sodium sulfate. Instead, a reaction of the second type is, for example, the esterification of acetic acid:

CH ₃ COOH + CH ₃ CH ₂ OH => CH ₃ COOCH ₂ CH ₃ + H ₂ O

Although water is also formed, the reaction is not instantaneous; even under favorable conditions, it takes several hours to complete.

However, other variables have more influence on the speed of the reaction: concentration of the reactants, temperature, pressure and presence of catalysts.

Reagent concentration

In chemical kinetics the space under study, separated from infinity, is called a system. For example, a reactor, a beaker, a flask, a cloud, a star, etc., can be considered as the system under study.

Thus, within the system the molecules are not static but rather "travel" to all its corners. In some of these displacements it collides with another molecule to bounce back or produce products.

Then the number of collisions is proportional to the concentration of the reactants. The image above illustrates how the system changes from low to high concentrations.

Also, the more collisions there are, the higher the reaction rate, as the chances of two molecules reacting increase.

If the reactants are gaseous, then the pressure variable is handled and is related to the gas concentration assuming any of the many existing equations (such as the ideal gas); Or, the volume of the system is reduced to increase the chances that the gaseous molecules collide.

Temperature

Although the number of collisions increases, not all molecules have the energy required to exceed the activation energy of the process.

This is where temperature plays an important role: it performs the function of thermally accelerating the molecules so that they collide with more energy.

Thus, the reaction rate generally doubles for every 10 ° C increase in system temperature. However, for all reactions this is not always the case. How to predict this increase? The Arrhenius equation answers the question:

d (lnK) / dT = E / (RT ²)

K is the rate constant at temperature T, R is the gas constant and E is the activation energy. This energy is indicative of the energy barrier that the reactants must scale to react.

In order to carry out a kinetic study, it is necessary to keep the temperature constant and without catalysts. What are catalysts? They are external species that take part in the reaction but are not consumed, and that decrease the activation energy.

The image above illustrates the concept of catalysis for the reaction of glucose with oxygen. The red line represents the activation energy without the enzyme (biological catalyst), while with it, the blue line shows a decrease in the activation energy.

Reaction order in chemical kinetics

In a chemical equation, the stoichiometric indices, related to the reaction mechanism, are not equal to the indices of the order of the same. Chemical reactions usually have first or second order, rarely third order or higher.

For what is this? Because the collisions of three energetically excited molecules are unlikely, and even more so are quadruple or quintuple collisions, where the probability is infinitesimal. Fractional reaction orders are also possible. For example:

NH ₄ Cl <=> NH ₃ + HCl

The reaction is first order in one direction (from left to right) and second order in the other (from right to left) if it is considered to be an equilibrium. While the following equilibrium is second order in both directions:

2HI <=> H ₂ + I ₂

Molecularity and reaction order the same? No. Molecularity is the number of molecules that react to give rise to products, and the overall reaction order is the same order as the reactants involved in the rate-determining step.

2KMnO ₄ + 10KI + 8H ₂ SO ₄ => 2MnSO ₄ + 5I ₂ + 6K ₂ SO ₄ + 8H ₂ O

This reaction, despite having high stoichiometric indices (molecularity), is actually a second order reaction. In other words, the speed determining step is second order.

Zero order reactions

They occur in the case of heterogeneous reactions. For example: between a liquid and a solid. Thus, the speed is independent of the concentrations of the reactants.

Likewise, if a reactant has a reaction order of zero, it means that it does not participate in the speed determining step, but in the rapid ones.

First order reaction

A => B

A first-order reaction is governed by the following rate law:

V = k

If the concentration of A doubles, the reaction rate V doubles. Therefore, the rate is proportional to the concentration of the reagent in the determining step of the reaction.

Second order reaction

2A => B

A + B => C

Two species are involved in this type of reaction, just as in the two chemical equations just written. The speed laws for the reactions are:

V = k ²

V = k

In the first, the reaction rate is proportional to the square of the concentration of A, while in the second, the same occurs as in first-order reactions: the rate is directly proportional to the concentrations of both A and B.

Reaction order vs molecularity

According to the previous example, the stoichiometric coefficients may or may not coincide with the orders of the reaction.

However, this does occur for elemental reactions, which determine the molecular mechanism of any step in a reaction. In these reactions the coefficients are equal to the number of participating molecules.

For example, a molecule of A reacts with one of B to form a molecule of C. Here the molecularity is 1 for the reactants and therefore in the expression of the rate law they coincide with the reaction orders.

From this it follows that molecularity must always be an integer, and probabilistically, less than four.

Why? Because in the passage of a mechanism it is very unlikely that four molecules participate at the same time; two of them could react first, and then the remaining two would react with this product.

Mathematically this is one of the main differences between reaction orders and molecularity: a reaction order can take fractional values ​​(1/2, 5/2, etc.).

This is because the former only reflects how the concentration of the species affects the speed, but not how their molecules intervene in the process.

Applications

- It allows to determine the time that a drug remains in the body before its complete metabolization. Likewise, thanks to kinetic studies, enzymatic catalysis can be followed as green methods compared to other catalysts with negative environmental impacts; or also to be used in innumerable industrial processes.

- In the automotive industry, specifically within engines, where electrochemical reactions must be carried out quickly for the vehicle to start. Also in its exhaust pipes, which have catalytic converters to transform the harmful gases CO, NO and NO _x into CO ₂, H ₂ O, N ₂ and O ₂ during the optimal time.

2NaN ₃ (s) = 2Na (s) + 3N ₂ (g)

-It is the reaction behind why airbags inflate, the 'airbags', when vehicles collide. When the tires brake hard, a detector electrically detonates the sodium azide, NaN ₃. This reagent "explodes" releasing N ₂, which occupies the entire volume of the bag quickly.

The metallic sodium then reacts with other components to neutralize it, because in its pure state it is poisonous.

References

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6. Khan Academy. (2018). Reaction rates and rate laws. Retrieved on April 30, 2018, from: khanacademy.org
7. Germán Fernández. (July 26, 2010). Chemical kinetics. Retrieved on April 30, 2018, from: quimicafisica.com