Name: collision theory and reaction speed
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 55 s
Channel: JoVE

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Chemistry and Physics

IPC.7

IPC.7.F

Temperature Dependence on Reaction Rate

Chemical reaction rates are sensitive to changes in temperature. A rise in 10 &#176;C can accelerate the reaction rate by 3 to 4 times, but why?
A reaction&#8217;s rate law defines the relationship between a reactant concentration and the reaction rate. Since the concentration is temperature independent, only the rate constant remains to influence the reaction rate depending on the temperature. Thus, in 1889 the Swedish chemist Svante Arrhenius concluded that a reaction rate&#8217;s temperature dependence is encompassed in the rate constant.
The rate constant describes the relationship between temperature and kinetic parameters relating to the collision, orientation, and activation energy of reacting molecules via the Arrhenius equation. A is a constant called the Arrhenius factor or frequency factor, e is an exponential factor integrating activation energy measured in joules-per-mole, the gas constant, and the temperature in kelvin.
The parameters&#8217; temperature dependence can be explained with the collision model, which states that reacting molecules should collide with sufficient energy in the correct orientation to initiate a chemical reaction.
The frequency factor constitutes two components&#8212;the collision frequency and the orientation factor. The collision frequency is the number of molecular collisions per unit time, whereas the orientation factor describes the probability of collisions with a favorable orientation.
Still, only a small fraction of collisions leads to a reaction. This is because the reacting molecules have to overcome an energy barrier, called the activation energy, to transform into products.
Only those molecules colliding with sufficient kinetic energy will have enough potential energy to bend, stretch, or break bonds, to transform into a high-energy intermediate called the transition state, or the activated complex. The short-lived, unstable activated complex loses energy to form stable products, whose total energy is lower than that of the reactants.
The exponential factor in the Arrhenius equation represents the fraction of successful collisions resulting in products. An increase in temperature influences both the frequency factor and the exponential factor.
At elevated temperatures, molecules move faster, more forcefully, and with higher thermal energies, leading to more favorable collisions.
Thus, a temperature increase results in higher frequency and exponential factors leading to a rise in the rate constant, consequently translating to an accelerated reaction rate.

temperature dependence on reaction rate

The Collision Theory
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. This premise is the basis for a theory that explains many observations regarding chemical kinetics, including factors affecting reaction rates.
The collision theory is based on the postulates that (i) the reaction rate is proportional to the rate of reactant collisions, (ii) the reacting species collide in an orientation allowing contact between the atoms that become bonded together in the product, and (iii) the collision occurs with adequate energy to permit mutual penetration of the reacting species&#8217; valence shells so that the electrons can rearrange and form new bonds (and new chemical species).
For example, in a gas-phase reaction between carbon monoxide and oxygen, occurring at high temperature and pressure, the first step is a collision between the two molecules.
<img alt="Static equilibrium diagram; &#931;Fx=0, MA=0; free body analysis, equilibrium forces study" src="/files/ftp_upload/11379/11379_Equation_1.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
However, there could be many different possible relative orientations in which the two molecules collide. Hence, the orientation of the colliding molecules has great significance in partially determining the feasibility of a reaction occurring between them.
In one instance, the oxygen side of the carbon monoxide molecule may collide with the oxygen molecule. In another instance, the carbon side of the carbon monoxide molecule can collide with the oxygen molecule. The second case is more likely to result in the formation of carbon dioxide, with a central carbon atom bonded to two oxygen atoms (O = C = O).
<img alt="Chemical bond formation diagram; CO and O2 form CO2; molecular reaction process illustrated." src="/files/ftp_upload/11379/11379_Image_1.png" style="text-align: center; height: 250px;" data-altupdatedat="1761830439000" data-alt="Image1" />
Yet, even if the collision does take place in the correct orientation, the guarantee that the reaction will proceed to form carbon dioxide is limited. This is because, in addition to the proper orientation, the collision must also occur with sufficient energy called activation energy to result in product formation. When reactant species collide with both correct orientation and enough activation energy, they combine to form an unstable species called an activated complex or a transition state. These species are short-lived and usually undetectable by most analytical instruments. In some cases, sophisticated spectral measurements can observe transition states.
Collision theory explains why most reaction rates increase as temperature increases; with an increase in temperature, the frequency of collisions increases. More collisions mean a faster reaction rate, assuming the energy of the collisions is adequate.
Activation Energy
The minimum energy necessary to form a product during a collision between reactants is called the activation energy (Ea). The difference in activation energy required and the kinetic energy provided by colliding reactant molecules is a primary factor affecting the rate of a chemical reaction. If the activation energy is much larger than the average kinetic energy of molecules, the reaction will occur slowly, since only a few fast-moving molecules will have enough energy to react. If the activation energy is much smaller than the molecules' average kinetic energy, a large fraction of molecules will be adequately energetic, and the reaction will proceed rapidly.
Reaction diagrams are widely used in chemical kinetics to illustrate various properties of a reaction of interest. It shows how a chemical system's energy changes as it undergoes a reaction, converting reactants to products.
For instance, consider the following reaction diagram for an exothermic reaction: A + B &#8594; C + D;
<img alt="Static equilibrium diagram; &#931;Fx=0, &#931;Fy=0 equations with forces, moments, and weight distribution." src="/files/ftp_upload/11379/11379_Image_2.png" style="text-align: center; height: 350px;" data-altupdatedat="1761830439000" data-alt="Image2" />
The diagram is viewed from left to right. Initially, the system consists of reactants (A + B) only. Once the reactant molecules with sufficient energy collide, they form a high-energy activated complex or transition state. The unstable transition state then subsequently decays to yield stable products (C + D).
The diagram depicts the reaction's activation energy, Ea, as the energy difference between the reactants and the transition state. The energy difference between the reactants and products corresponds to the enthalpy change of the reaction (&#916;H). In this case, the reaction is exothermic (&#916;H &#60; 0), since it yields a decrease in the system enthalpy.
Arrhenius Equation
The Arrhenius equation, k = Ae&#8722;Ea/RT relates the activation energy and the rate constant, k, for many chemical reactions.
In this equation, R is the ideal gas constant, which has a value 8.314 J/mol&#183;K, T is the temperature in kelvin, Ea is the activation energy in joules per mole, e is the constant 2.7183, and A is a constant called the frequency factor, which is related to the frequency of collisions and the orientation of the reacting molecules. The Arrhenius equation nicely accommodates the postulates of collision theory. The frequency factor, A, reflects how well the reaction conditions favor correctly oriented collisions between reactant molecules. An increased probability of effectively oriented collisions results in larger values for A and faster reaction rates.
The exponential term, e&#8722;Ea/RT, describes the effect of activation energy on the reaction rate. According to kinetic molecular theory, the temperature of matter is a measure of the average kinetic energy of its constituent atoms or molecules&#8212;a lower activation energy results in a more significant fraction of adequately energized molecules and a faster reaction.
The exponential term also describes the effect of temperature on the reaction rate. A higher temperature represents a correspondingly greater fraction of molecules possessing sufficient energy (RT) to overcome the activation barrier (Ea). This yields a higher value for the rate constant and a correspondingly faster reaction rate.
<img alt="Dynamic equilibrium concept with normal distribution histogram illustrating spatial variations." src="/files/ftp_upload/11379/11379_Image_3.png" style="text-align: center; height: 280px;" data-altupdatedat="1761830439000" data-alt="Image3" />
Molecular energy distributions showing numbers of molecules with energies exceeding two different activation energies at a given temperature, and a given activation energy at two different temperatures.
This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/12-5-collision-theory">Openstax, Chemistry 2e, Section 12.5: Collision Theory.</a>

The Collision Theory
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. ...

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KEY TERMS AND CONCEPTS

collision theory and reaction speed

Collision theory explains why reaction speed depends on how particles collide. Atoms, molecules, or ions must come close together before they can react. The theory says the reaction rate depends on the collision rate, the orientation of the colliding species, and whether the collision has enough energy for bonds to change.

A gas-phase reaction between carbon monoxide and oxygen shows why orientation matters. The molecules can collide in more than one way. If the oxygen side of carbon monoxide hits oxygen, the collision is less likely to form carbon dioxide. If the carbon side of carbon monoxide hits oxygen, the arrangement is more favorable for making O = C = O.

Even a correctly oriented collision may not react if it does not have enough energy. The minimum energy needed to form products is called activation energy, or Ea. When reactants collide with the right orientation and enough energy, they form an unstable activated complex, also called a transition state. This state is very short-lived and usually cannot be detected with standard instruments, although some advanced spectral methods can observe it.

Temperature affects reaction rate because higher temperature increases collision frequency. More collisions usually means a faster reaction, as long as the collisions also have enough energy. If the activation energy is much larger than the average kinetic energy of the molecules, only a small number of fast-moving particles can react, so the reaction is slow. If the activation energy is much smaller, many molecules have enough energy, and the reaction is faster.

Reaction diagrams help show how energy changes as reactants become products. In an exothermic reaction such as A + B → C + D, the system starts with reactants, reaches the high-energy transition state, and then forms stable products. The activation energy is the energy gap between the reactants and the transition state. The enthalpy change, ΔH, is the energy difference between the reactants and products, and it is negative for an exothermic reaction.

The Arrhenius equation links activation energy and reaction rate: k = Ae−Ea/RT. In this equation, R is the ideal gas constant, T is temperature in kelvin, Ea is activation energy in joules per mole, e is 2.7183, and A is the frequency factor. The frequency factor reflects how often collisions occur and how well the molecules are oriented. The exponential term shows that higher temperature and lower activation energy increase the rate constant and speed up the reaction.

Collision Theory and Reaction Speed

reaction rate

Measuring Reaction Rates

Measuring reaction rates shows how fast reactants are used up or products are formed over time. The rate of reaction is the change in the amount of a reactant or product per unit time. Because of that, scientists measure how a property changes as the reaction proceeds and connect that change to reactant or product amounts. For reactions that make or use a gas, the rate can be followed by changes in volume or pressure. A rate expression is the mathematical way to write how concentration changes...

measuring reaction rates

Tracking Reaction Kinetics with Light and Pressure

Reaction kinetics can be tracked with polarimetry, spectrometry, and pressure measurements. These methods let scientists follow a reaction without disturbing the sample. They also help determine how reactant or product concentrations change over time. Polarimetry is used for optically active substances. These substances rotate the plane of polarized light, which is called optical rotation. The effect comes from molecular structure. Normal monochromatic light is unpolarized, but after it passes...

concentration and rate law

Reaction Order from Concentration

Reaction order from concentration shows how reactant amounts affect reaction rate. Rate laws, also called differential rate laws or rate equations, are mathematical expressions that connect reaction rate with the concentrations of reactants. For a generic reaction a A + b B → products, the rate law can be written using the reactant concentrations [A] and [B] and a rate constant k. In a rate law, k is the rate constant for one specific reaction at one specific temperature. The exponents m and n...

determining order of reaction

Finding Rate Law from Initial Rates

Rate laws connect the speed of a chemical reaction to the concentration of its reactants. The rate constant, k, and the reaction orders are not taken from the chemical equation. They are found experimentally by watching how the rate changes when the reactant concentrations change. One common way to do this is the method of initial rates. In this method, several trials are run with different starting concentrations. The measured rates are then compared to determine the reaction orders and,...

the integrated rate law: the dependence of concentration on time

the-integrated-rate-law-the-dependence-of-concentration-on-time

Reading Reaction Progress with Integrated Laws

Integrated rate laws connect reaction concentration to time. They help show how much reactant or product is present after a certain period. They can also help estimate how long a reaction must run to reach a given extent. A common use is finding how long radioactive material must be stored before its radioactivity drops to a safe level. These equations come from the differential rate law after it is integrated with respect to time. For a first-order reaction, where rate = k[A], the integrated...

half-life of a reaction

Reaction Half-Life in Kinetics

Reaction half-life is the time needed for half of a reactant to be consumed. After each half-life, half of the remaining reactant is used up. A hydrogen peroxide decomposition example shows this pattern clearly. The concentration drops from 1.000 M to 0.500 M in the first 6.00 hours, then to 0.250 M in the next 6.00 hours, and then to 0.125 M in the third period. Each later 6.00-hour interval removes half of what is left. For first-order reactions, the half-life does not depend on the reactant...

Collision theory explains why reaction speed depends on how particles collide. Atoms, molecules, or ions must come close together before they can react. The theory says the reaction rate depends on the collision rate, the orientation of the colliding species, and whether the collision has enough energy for bonds to change. A gas-phase reaction between carbon monoxide and oxygen shows why orientation matters. The molecules can collide in more than one way. If the oxygen side of carbon monoxide...

arrhenius plots

Determining Activation Energy from Temperature

The Arrhenius equation links activation energy and the rate constant, k, for chemical reactions. It is written as k = Ae−Ea/RT. In this equation, R is the ideal gas constant with a value of 8.314 J/mol·K, T is the temperature on the kelvin scale, Ea is the activation energy in J/mole, e is the constant 2.7183, and A is the frequency factor. The frequency factor depends on collision frequency and the orientation of reacting molecules. Experimental kinetic data can be used to find the activation...

reaction mechanisms

Elementary Steps in Reaction Mechanisms

Chemical reactions can happen in steps, and a balanced equation does not show the full path at the molecular level. A reaction mechanism, also called a reaction path, gives the step-by-step process that explains how reactants become products. The decomposition of ozone is one example of a reaction that can be described by a sequence of steps. Each step in a mechanism is an elementary reaction. These elementary reactions happen in order, and when they are added together, they give the balanced...

rate-determining steps

Reaction Bottlenecks in Chemical Kinetics

Reaction bottlenecks help explain rate-determining steps in multistep reaction mechanisms. In a mechanism with several elementary steps, one step is often much slower than the others. That slowest step is called the rate-limiting step, or rate-determining step. A reaction cannot move faster than its slowest step, so this step controls the overall reaction rate. The idea is like traffic on a four-lane freeway with one lane closed. Cars can only move as fast as the bottleneck allows. In the same...

catalysis

Catalyst Action in Reaction Rates

Catalysts change the rate of a chemical reaction by giving it a faster path. A catalyst increases reaction rate without being consumed during the process. Its effect is often explained with reaction mechanisms and energy diagrams. For an endothermic reaction, the reactants and products start and end at the same energies in both cases. The uncatalyzed path is a one-step mechanism with one transition state. The catalyzed path follows a different mechanism with two transition states and a lower...

enzymes

Enzyme Action and Inhibition

Enzymes are biological catalysts that speed up many reactions in living organisms. They help control cellular metabolism by lowering the activation energy needed for biochemical reactions. When activation energy drops, reaction rates can increase. Enzyme problems can also lead to serious disease. A genetic abnormality that causes G6PD, or glucose-6-phosphate dehydrogenase, deficiency can disrupt the pathway that supplies NADPH to cells. In red blood cells, this can reduce glutathione and...

key terms and concepts

Learn how collision theory, activation energy, and the Arrhenius equation explain why higher temperature can speed up chemical reactions in high school chemistry.

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Collision and Transition State Theory

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Collision Theory and Reaction Speed

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