Activation Energy

An activation energy determines the rate of reaction by requiring energy to occur.


Key Takeaways

Power of activation The catalytic process In a state of transition

Chemical reactions, and almost all biochemical reactions, do not occur spontaneously and require an initial input of energy (called activation energy) to get started.An analysis of both endogenous and exerganic reactions must take into account activation energy.The exhaustion of energy occurs as a result of exergonic reactions. However, their energy-releasing steps need a small input of energy to occur.The small amount of energy required for all chemical reactions to occur is called the activation energy (or free energy of activation) and is abbreviated as EA.



.The horizontal axis of this diagram describes the sequence of events over time.


Activation Energy in Chemical Reactions

Is it possible that an energy-releasing, negative G reaction would actually need energy to proceed?.There are several steps that must take place during the reaction.The formation of new chemical bonds occurs during chemical reactions.As one example, when glucose molecules are broken down, bonding between atoms of carbon is broken.The broken bonds release energy.To force the bonds to break, the molecules must be contorted somewhat.A small amount of energy is needed to achieve this contorted state, called the transition state. It is an unstable state with a high energy level.

In some cases, cells can couple exergonic reactions with endergonic reactions (Delta ext[G]lt0), allowing them to continue.Energy coupling is the change from one reaction to another that occurs spontaneously.During the endergonic reaction, free energy released by the exergonic reaction is absorbed.The use of ATP for energy coupling includes a transmembrane ion pump, which is essential for the function of cells.

Free Energy Diagrams

Energy profiles for a given reaction are illustrated by free energy diagrams.Depending on whether the reaction is exergonic (*G0), the products will exist at a lower or higher energy level than the reactants.As a result, the activation energy is independent of the reaction's ΔG.In other words, at a given temperature, activation energy depends on the type of chemical transformation taking place, not on the relative energy state of the reactants and products.

Although the image above discusses activation energy in the context of an exergonic forward reaction, the same principles apply to the reverse reaction, which must be endergonic.The activation energy for the reverse reaction is much higher than the one for the forward reaction.



Heat Energy

A reaction is typically pushed forward by heat energy generated from the surrounding environment.The heat energy in a chemical reaction increases the frequency and force with which molecules collide by increasing the total bond energy between reactants and products.A slight shift in atoms and bonds within the molecule also helps to reach the transition state.Thus, heating up a system will result in chemical reactants in that system reacting more frequently.Pressure applied to the system will have the same effect.In order for a reaction to proceed, reactants must absorb enough heat energy from their surroundings to reach a transition state.

A reaction's activation energy determines how quickly it will proceed.If the activation energy is high, it means the chemical reactions will proceed more slowly.For example, rust on iron illustrates that inherently slow reaction.The high coefficient of friction causes it to work slowly over time.The burning of many fuels, which are strongly exergonic, occurs at a negligible rate unless the activation energy of the fuel is overridden by sufficient heat from a spark.As they burn, however, the chemical reactions release enough energy to keep the combustion process going, supplying the activation energy for surrounding fuel molecules.

The activation energy for most cellular reactions is too high for heat energy to overcome efficiently. .Cells appreciate this because it is good for them.There is considerable energy stored by macromolecules, such as proteins, DNA, and RNA, and their breakdown is exergonic.

The Arrhenius Equation

The Arrhenius equations link the rate of a chemical reaction to the activation energy of the reaction:

Ext[k] = ext[A]*/ext[E]/ext[RT]

When


The Collision Theory

By appealing to the principle of collision, collision theory accounts for the qualitative nature of chemical reactions and the rate at which they occur.


Learning Objectives

Collision theory considers activation energy, collisions, and molecular orientation


Key Takeaways

Energies of activation

This theory provides a qualitative explanation of chemical reactions and how they occur.The collision theory proposes that molecules must collide in order to react.Analyzing the ordinary reaction mechanism follows this fundamental rule.

In the elementary bimolecular reaction, ext{A} + ext{B}

Molecules A and B need to be in sufficiently close proximity for chemical bonds to burst in order for them to react.This is a collision.As long as A and B are both gases, the frequency of collisions between them will be proportional to the concentration of each gas.Doubling A concentration will double the frequency of A-B collisions, and doubling B concentration will have the same effect.Therefore, according to collision theory, the rate at which molecules collide will have a significant impact on the overall reaction rate.



Activation Energy and Temperature

Billiard balls simply collide and bounce off each other.The same happens when two molecules, A and B, come into contact: they bounce off each other, completely unchanged and unaffected.In order for a collision to result in a chemical reaction, A and B must collide with enough energy to cause chemical bonding to break.Chemical bonds between reactants and products are shattered during any chemical reaction.Thus, in order to effectively initiate a reaction, the reactants must move fast enough (with sufficient kinetic energy) so that they collide with enough force to cause bonds to dissolve.The activation energy is the minimum amount of movement required for a chemical reaction to occur when molecules collide.

Gas kinetic energy is directly proportional to temperature as we know from the kinetic theory of gases.The molecules in a gas pick up energy and move faster as the temperature increases.Due to this, when molecules collide, the higher the probability of them moving with enough activating energy for a reaction to occur.

Molecular Orientation and Effective Collisions

If two molecules collide with sufficient activation energy, the collision does not necessarily succeed.In reality, even if molecules are moving with enough energy, collisions are not always successful.In order to accomplish this, molecules need to collide in an orientation that allows the electrons to line up with each other, and bonds to break and re-form successfully.For example, in the gas-phase reaction of dinitrogen oxide with nitric oxide, the oxygen end of N2O must hit the nitrogen end of NO; if either molecule is not aligned correctly, no reaction occurs.Nevertheless, because molecules in the liquid and gas phases are forever moving randomly, it is always possible for two molecules to collide in just the right way for a reaction to unfold.

As a general rule, the more critical this orientational requirement, such as it is for larger or more complex molecules, the fewer collisions will be effective.A collision that occurs as a result of sufficient energy and proper orientation is called an effective collision.

Conclusion

For chemical reactions to occur, the collision theory states that the following conditions must be met:


Key Takeaways

Indies Energy that activates

Reactant Concentrations

Reactions go faster when reactant concentrations increase. .When concentration increases, the number of molecules with the minimum required energy will increase, which therefore increases the rate of the reaction.One in a million particles may have sufficient activation energy, causing only 100 particles out of 100 million to be activated.200 million of these particles will, however, react if they are all contained in the same volume.Doubling the concentration also doubles the rate of reaction.


Surface Area

.Due to the fact that only the liquid-solid interface, which is on the surface of the solid, is capable of bumping into each other.Molecular interactions between solid molecules within the solid body cannot occur.The increase in surface area of the solid will expose more solid molecules to the liquid, which enables a faster reaction.

Consider, for example, a brick with dimensions of 6 x 6 x 2 inches.The exposed surfaces of the brick have a surface area of 4 (6 x 2) + 2 (6 x 6)=120; ext{cm}^2.However, when the brick is divided into nine smaller cubes, each cube has a surface area of 6(2 imes 2) = 24 ext[cm]*2, meaning the total surface area is 9 imes 24 = 216 ext{cm}^2.

By dividing a large body into smaller pieces, the total exposed area increases.Thus, since a reaction happens on the surface of a substance, increasing the surface area would increase the amount of substance capable of reacting, and thus increase the rate of the reaction.



Pressure

For a reaction involving gases, increasing the pressure will increase the rate of reaction. .Thus, increasing pressure increases concentration (n/V), and promotes more frequent collisions between the molecules of gas.

Temperature

Experiments have shown that increasing the temperature by 10 °C triples or doubles the speed of bacterial reactions between molecules.In general, the activation energy required to initiate a reaction remains constant as temperature increases.The average increase in particle kinetic energy caused by the absorbed heat, however, gives a larger percentage of the reactant molecules the minimum energy needed to collide and react.Increased temperature causes molecules involved in the reaction to have higher energy levels, so the rate of reaction increases.The rate of reaction will also decrease as the temperature decreases.


Presence or Absence of a Catalyst

Catalysts work by lowering the activation energy necessary to initiate a reaction, which increases the reaction's rate.As a catalyst is not damaged during a reaction, you can reuse it.Normally, H2 and O2 do not combine.In the presence of platinum, which acts as a catalyst, they combine, causing the reaction to occur rapidly.

Nature of the Reactants

Chemical transformation rates vary dramatically between substances.Different reactions may have different reactivity depending on the structure of the materials involved; for example, how the substances are incorporated into the solid or liquid state.Additionally, the relative bond strength within the molecules of the reactants plays a role.Molecules that are atoms are strongly bonded by covalent bonds, so their reactions will proceed at a slower rate than molecules with weakly bonded atoms.Because the bonds between molecules with strong bonds are more difficult to break, it requires more energy.


The Arrhenius Equation

Temperature-dependent reactions are described by the Arrhenius equation.


Learning Objectives

What are the variables in the Arrhenius equation and what does it mean?


Key Takeaways

kTEaARThe Decline in Expansion

Arrhenius' equation gives a simple, but shockingly accurate, formula for the temperature dependence of the reaction rate constant, which determines a chemical reaction's rate.Svante Arrhenius first formulated the equation in 1884.After five years, in 1889, the Dutch chemist J.Hendrik.van ’t Hoff provided a physical explanation for the phenomenon.Among the most important relationships in chemistry, the activation energy equation is derived from the Boltzmann distribution law and the activation energy concept:

As shown, k is the rate constant, T is the absolute temperature, Ea is the activation energy, A is the pre-exponential factor, and R is the universal gas constant.

For now, ignore the A factor and focus on the meaning of this equation.This is an application of the exponential decay law."Decaying" here is not a function of the concentration, but rather of the magnitude of the rate constant.

What does this number mean?.You will notice that RT is the average kinetic energy, and that its exponent is simply the ratio of Ea to the average kinetic energy.A higher ratio indicates a lower rate, which is why the sign in the equation is negative.High temperatures and low activation energies favor large rate constants, increasing the speed of a reaction.

Plotting the Arrhenius Equation in Non-Exponential Form

.As a result, separating the exponential and pre-exponential terms in each side results in the following: ext[ln]( ext[k])=ext[ln]( ext[A])-rac[ ext[E]_[ ext[a]]][ ext[RT]

When plotting the slope of ln(k) against 1/T we get a straight line with the slope –Ea/R.


*

It is possible to determine activation energy from the values of k observed at different temperatures using this approach.By plotting ln(k) versus 1/T, we can determine the slope required for Ea.

The Pre-Exponential Factor

Arrhenius' equation contains a pre-exponential factor A. .This fraction is dependent on the magnitude of Ea and the temperature, and can range from zero, where no molecules can react, to unity, where all molecules have enough energy to react.

The Arrhenius law reduces to k = A if the fraction is unity.Therefore, A represents the maximum possible rate constant, which is what the rate constant would be if every collision between molecules resulted in a chemical reaction.Only if either the activation energy would be zero or if all molecules had kinetic energy greater than Ea would this happen, which is highly unlikely."Barrier-less" reactions have been observed, but these are rare, and even in these cases, molecules must collide with the right orientation to cause the reaction.When molecules collide in real-life, not every collision will be an effective collision, and the value of ext[e]*[ rac[- ext[E]_ ext[a]][ ext[RT]] will be less than one.


Transition State Theory


Key Takeaways

Transient State Theory Complex activation

A transition state theory describes a hypothetical "transition state" that occurs between the reactants and the products during a chemical reaction.The species that forms during the transition state is called the activated complex.This theory describes how chemical reactions occur based on collision theory.With the rate constant of a reaction, TST can calculate the standard enthalpy of activation, standard entropy of activation, and standard Gibbs energy of activation.The TST is also known as "activated-complex theory," "absolute-rate theory," or "theory of absolute reaction rates."


Postulates of Transition State Theory

In transition state theory, there is an intermediate state between the state in which a molecule exists as a reactant and the state in which it exists as a product.When the transition state occurs, an activated complex forms, a higher-energy species.Three main factors determine whether or not a reaction takes place according to TST.Among them are:

In a sense, this third postulate qualifies what we discussed in our section on collision theory.Collisions involving molecules with sufficient energy and the right orientation result in reactions, according to collision theory.In transition state theory, however, a successful collision won't necessarily result in the formation of products, but rather the activation of the complex.After the activated complex is formed, it can be used to make products or reverted back to reactants.

Applications in Biochemistry

Biochemistry is most often used to model enzyme-catalyzed processes in the body by using transition state theory.The knowledge of the possible transition states which can form in a given reaction, together with information on the activation energies of the transition states, can be used to predict the course of a biochemical reaction, as well as to determine its reaction rate and rate constant.