# 5.7: Collision Theory (2023)

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Learning Objectives

• Molecules must collide in order to react.
• In order to effectively initiate a reaction, collisions must be sufficiently energetic (kinetic energy) to break chemical bonds; this energy is known as the activation energy.
• As the temperature rises, molecules move faster and collide more vigorously, greatly increasing the likelihood of bond breakage upon collision.

Collision theory explains why different reactions occur at different rates, and suggests ways to change the rate of a reaction. Collision theory states that for a chemical reaction to occur, the reacting particles must collide with one another. The rate of the reaction depends on the frequency of collisions. The theory also tells us that reacting particles often collide without reacting. For collisions to be successful, reacting particles must (1) collide with (2) sufficient energy, and (3) with the proper orientation.

## Requirement 1: Molecules Must Collide to React

Collision Theory provides a qualitative explanation of chemical reactions and the rates at which they occur. A basic principal of collision theory is that, in order to react, molecules must collide. This fundamental rule guides any analysis of an ordinary reaction mechanism. Consider a simple bimolecular step:

$A + B \rightarrow Products$

If the two molecules $$A$$ and $$B$$ are to react, they must approach closely enough to disrupt some of their existing bonds and to permit the creation of any new ones that are needed in the products. Such an encounter is called a collision. The frequency of collisions between $$A$$ and $$B$$ in a gas is proportional to the concentration of each; if [A] is doubled, the frequency of $$A-B$$ collisions will double, and doubling $$[B]$$ will have the same effect. If all collisions lead to products, then the rate of a bimolecular process is first-order in A and in B, or second-order overall:

$rate = k[A][B]$

The need for collisions fundamental to any analysis of an ordinary reaction mechanism and explains why termolecular processes (three species colliding and reaction) are so uncommon. The kinetic theory of gases states that for every 1000 binary collisions, there will be only one event in which three molecules simultaneously come together. Four-way collisions are so improbable that this process has never been demonstrated in an elementary reaction.

The frequency of collisions between A and B in a gas is proportional to the concentration of each.

Consider the reaction in the Haber process for making ammonia:

$\ce{N_2 (g) + 3 H_2 (g) } \rightleftharpoons \ce{2NH_3} (g) \label{eq3}$

the collision theory says that $$\ce{H_2}$$ and $$\ce{N_2}$$ will only react when they collide. Hence, the more frequently they collide, the faster the rate of reaction. This can be achieved easily by either increasing the pressure on the gasses to bring $$\ce{H_2}$$ and $$\ce{N_2}$$ closer together on average or by increasing the temperature to makes molecules move faster.

(Video) Collision Theory and Chemical Reaction Rate experiment for Physical Science 12

Car damage can be very expensive, especially if the person hitting your car does not have insurance. Many people have had the experience of backing up while parallel parking and hearing that "bump". Fortunately, there is often no damage because the cars were not going fast enough. But every once in a while there is a rearrangement of the body parts of a car when it is hit with sufficient speed. Then things need to be fixed - this akin to a reaction, albeit on a macroscopic scale.

## Requirement 2: Not all Collisions are Sufficiently Energetic

In the Haber process (Equation $$\ref{eq3}$$) at 300 K only 1 in $$10^{11}$$ collisions between $$H_2$$ and $$N_2$$ results in a reaction! At 800 K, this increases to 1 in $$10^4$$ collisions resulting in a reaction. Hence, while the collisions are needed for a reaction, other aspects contribute. Reacting particles can form products when they collide with one another provided those collisions have enough kinetic energy and the correct orientation. Particles that lack the necessary kinetic energy may collide, but the particles will simply bounce off one another unchanged. Figure $$\PageIndex{1}$$ illustrates the difference. In the first collision, the particles bounce off one another and no rearrangement of atoms has occurred. The second collision occurs with greater kinetic energy, and so the bond between the two red atoms breaks. One red atom bonds with the other molecule as one product, while the single red atom is the other product. The first collision is called an ineffective collision, while the second collision is called an effective collision.

For a gas at room temperature and normal atmospheric pressure, there are about 1033 collisions in each cubic centimeter of space every second. If every collision between two reactant molecules yielded products, all reactions would be complete in a fraction of a second. For example, when two billiard balls collide, they simply bounce off of each other. This is the most likely outcome if the reaction between A and B requires a significant disruption or rearrangement of the bonds between their atoms. In order to effectively initiate a reaction, collisions must be sufficiently energetic (or have sufficient kinetic energy) to bring about this bond disruption.

A reaction will not take place unless the particles collide with a certain minimum energy called the activation energy of the reaction. Activation energy is the minimum energy required to make a reaction occur. This can be illustrated on an energy profile for the reaction. An energy profile for a simple exothermic reaction is given in the Figure $$\PageIndex{2}$$.

If the particles collide with less energy than the activation energy, nothing interesting happens. They bounce apart. The activation energy can be thought of as a barrier to the reaction. Only those collisions with energies equal to or greater than the activation energy result in a reaction.

Any chemical reaction results in the breaking of some bonds (which requires energy) and the formation of new ones (which releases energy). Some bonds must be broken before new ones can be formed. Activation energy is involved in breaking some of the original bonds. If a collision is relatively gentle, there is insufficient energy available to initiate the bond-breaking process, and thus the particles do not react.

Energetic collisions between molecules cause interatomic bonds to stretch and bend, temporarily weakening them so that they become more susceptible to cleavage. Distortion of the bonds can expose their associated electron clouds to interactions with other reactants that might lead to the formation of new bonds.

Chemical bonds have some of the properties of mechanical springs: their potential energies depend on the extent to which they are stretched or compressed. Each atom-to-atom bond can be described by a potential energy diagram that shows how its energy changes with its length. When the bond absorbs energy (either from heating or through a collision), it is elevated to a higher quantized vibrational state (indicated by the horizontal lines) that weakens the bond as its length oscillates between the extended limits corresponding to the curve in Figure $$\PageIndex{3}$$.

When the bond absorbs energy (either from heating or through a collision), it is elevated to a higher quantized vibrational state (indicated by the horizontal lines) that weakens the bond.

(Video) AP Chem Unit 5.1 -- Collision theory

A particular collision will typically excite a number of bonds in this way. Within about 10–13 seconds, this excitation is distributed among the other bonds in the molecule in complex and unpredictable ways that can concentrate the added energy at a particularly vulnerable point. The affected bond can stretch and bend farther, making it more susceptible to cleavage. Even if the bond does not break by pure stretching, it can become distorted or twisted so as to expose nearby electron clouds to interactions with other reactants that might encourage a reaction.

Example $$\PageIndex{1}$$

1. Draw a simple energy profile for an exothermic reaction in which 100 kJ mol-1 is evolved, and which has an activation energy of 50 kJ mol-1 .
2. Draw a simple energy profile for an endothermic reaction in which 50 kJ mol-1 is absorbed and which has an activation energy of 100 kJ mol-1
3. Explain why all reactions have an activation energy, using your knowledge of collision theory.

c: All reactions have an activation energy because energy is required to make the reactants combine in a way that will cause the reaction. No chemical process can take place without having at least a little energy to get things started.

Exercise $$\PageIndex{1}$$

To increase the rate of a reaction, there must be (select one):

1. Decrease in the frequency of collisions
2. An Increase in the frequency of collisions.
3. A decrease in the frequency of effective collisions
4. An increase in the frequency of effective collisions

D

The Maxwell-Boltzmann Distribution

Because of the key role of activation energy in deciding whether a collision will result in a reaction, it is useful to know the proportion of the particles present with high enough energies to react when they collide. In any system, the particles present will have a very wide range of energies. For gases, this can be shown on a graph called the Maxwell-Boltzmann distribution, a plot showing the number of particles with each particular energy.

The area under the curve measures of the total number of particles present. Remember that for a reaction to occur, particles must collide with energies equal to or greater than the activation energy for the reaction. The activation energy is marked on the Maxwell-Boltzmann distribution with a green line:

(Video) 14.5 The Orientation Factor

Notice that the large majority of the particles have insufficient energy to react when they collide. To enable them to react, either the shape of the curve must be altered, or the activation energy shifted further to the left to lower energies.

## Requirement 3: Not all Collisions are Sufficiently Oriented

Even if two molecules collide with sufficient activation energy, there is no guarantee that the collision will be successful. In fact, the collision theory says that not every collision is successful, even if molecules are moving with enough energy. The reason for this is because molecules also need to collide with the right orientation, so that the proper atoms line up with one another, and bonds can break and re-form in the necessary fashion. However, because molecules in the liquid and gas phase are in constant, random motion, there is always the probability that two molecules will collide in just the right way for them to react.

Consider a simple reaction involving a collision between two molecules: for example, ethene, $$\ce{CH_2=CH_2}$$, and hydrogen chloride, $$HCl$$. These react to give chloroethane as shown:

$\ce{ H_2C=CH_2 + HCl \rightarrow CH_3CH_2Cl}$

As a result of the collision between the two molecules, the double bond in ethene is converted into a single bond. A hydrogen atom is now attached to one of the carbons and a chlorine atom to the other. The reaction can only happen if the hydrogen end of the H-Cl bond approaches the carbon-carbon double bond. No other collision between the two molecules produces the same effect. The two simply bounce off each other.

With no knowledge of the reaction mechanism, one might wonder why collision 2 would be unsuccessful. The double bond has a high concentration of negative charge around it due to the electrons in the bonds. The approaching chlorine atom is also partially negative due to dipole created by the electronegativity difference between it and hydrogen. The repulsion simply causes the molecules to bounce off each other. In any collision involving unsymmetrical species, the way they hit each other is important in determining whether a reaction occurs.

Unimolecular processes also begin with a Collision

Until about 1921, chemists did not understand the role of collisions in unimolecular processes. It turns out that the mechanisms of such reactions are actually quite complicated, and that at very low pressures they do follow second-order kinetics. Such reactions are more properly described as pseudounimolecular. The cyclopropane isomerization described in Example 1 is typical of many decomposition reactions found to follow first-order kinetics, implying that the process is unimolecular.

Consider, for example, the isomerization of cyclopropane to propene, which takes place at fairly high temperatures in the gas phase:

(Video) 5.5-5.7 AP Chem

The collision-to-product sequence can be conceptualized in the following [grossly oversimplified] way:

Note that

• For simplicity, the hydrogen atoms are not shown here. This is reasonable because C–C bonds are weaker then C–H bonds, which are less likely to be affected.
• The collision at 1 is most likely with another cyclopropane molecule, but because no part of the colliding molecule gets incorporated into the product, it can in principle be a noble gas or some other non-reacting species;
• Although the C–C bonds in cyclopropane are all identical, the instantaneous localization of the collisional energy can distort the molecule in various ways (2), leading to a configuration sufficiently unstable to initiate the rearrangement to the product.

Of course, the more critical this orientational requirement is, like it is for larger or more complex molecules, the fewer collisions there will be that will be effective. An effective collision is defined as one in which molecules collide with sufficient energy and proper orientation, so that a reaction occurs.

Exercise $$\PageIndex{2}$$

According to collision theory, what three criteria are needed to be met before a bimolecular reaction can take place?

1. The orientation probability factor must be 1.
2. The collision energy must be greater than the activation energy for the reaction.
3. The collision must occur in the proper orientation.
4. The collision frequency must be greater than the frequency factor for the reaction.
5. A collision between the reactants must occur.

Exercise $$\PageIndex{3}$$

How will the given change affect the rate of an elementary reaction.

1. An increase in temperature.
2. An increase in the activation energy for the reaction
3. An increase in the reactant concentration.
4. An increase in the size of one of the reactants in a bimolecular reaction

## Summary

Collision Theory provides a qualitative explanation of chemical reactions and the rates at which they occur. For a chemical reaction to occur, an energy threshold must be overcome, and the reacting species must also have the correct spatial orientation. Factors that increase the rate of a reaction must influence at least one of the following:

• How often collisions occur - more frequent collisions will mean a faster rate.
• More effective collisions in terms of collisions occurring with sufficient energy
• More effective collisions in terms of collisions occurring with the proper orientation.

Two more topics must be examined before these can be discussed in depth: reaction mechanisms and the concept of threshold energy.

(Video) Unit 5.5 - Collision Model

## FAQs

### What is the collision theory equation? ›

ZPQ = collision frequency of reactants P and Q. Ea = Activation Energy.

What are the 3 parts of collision theory? ›

Three things must happen for a reaction to occur.
• Molecules must collide.
• Molecules must collide with enough energy to begin to break the old bonds so new bonds can form. ( Remember activation energy)
• Molecules must collide with the correct orientation.

Why does higher temperature increase the reaction rate? ›

Increasing the temperature increases the average speed of the reactant molecules. As more molecules move faster, the number of molecules moving fast enough to react increases, which results in faster formation of products.

How do you calculate collision rate? ›

Show that the number of collisions a molecule makes per second , called the collision frequency , f , is given by f=vˉ/lm , and thus f=42 πr2vˉN/V.

How do you calculate collision force? ›

FAQ
1. Measure the velocity at the moment of the impact, v .
2. Measure the mass of the subject of the collision, m .
3. Either use: The stopping distance d in the formula: F = mv²/2d ; or. The stopping time t in: F = mv/t.
4. If you want to measure the g-forces, divide the result by mg , where g = 9.81 m/s² .
Dec 29, 2022

What are the 4 factors of collision theory? ›

The collision energy must be greater than the activation energy for the reaction. The collision must occur in the proper orientation. The collision frequency must be greater than the frequency factor for the reaction. A collision between the reactants must occur.

What are the 4 factors that can affect the rate of reaction? ›

The rate of a chemical reaction is influenced by many different factors, including reactant concentration, surface area, temperature, and catalysts.

What are the 5 rates of reaction? ›

There are five general properties that can affect the rate of a reaction:
• The concentration of the reactants. The more concentrated the faster the rate.
• Temperature. ...
• Physical state of reactants. ...
• The presence (and concentration/physical form) of a catalyst (or inhibitor). ...
• Light.

What are the five 5 Factors affecting the rate of reaction? ›

We can identify five factors that affect the rates of chemical reactions: the chemical nature of the reacting substances, the state of subdivision (one large lump versus many small particles) of the reactants, the temperature of the reactants, the concentration of the reactants, and the presence of a catalyst.

What are 6 types of reactions? ›

Six common types of chemical reactions are discussed below.
...
Different Types of Chemical Reactions
• Combination reaction.
• Decomposition reaction.
• Displacement reaction.
• Double Displacement reaction.
• Precipitation Reaction.

### How does temperature affect collision theory? ›

Extending the collision theory of reactions

Increasing the temperature makes molecules move faster, increasing the frequency of collisions. How much more frequently do molecules collide, when temperatures rise? The average speed of molecules is proportional to the square root of the absolute temperature.

How does increasing the temperature affect collisions? ›

When the temperature is increased, the average velocity of the particles is increased. The average kinetic energy of these particles is also increased. The result is that the particles will collide more frequently, because the particles move around faster and will encounter more reactant particles.

What is the relationship between temperature and reaction rate? ›

An increase in temperature typically increases the rate of reaction. An increase in temperature will raise the average kinetic energy of the reactant molecules. Therefore, a greater proportion of molecules will have the minimum energy necessary for an effective collision (Figure. 17.5 “Temperature and Reaction Rate”).

What is average collision rate? ›

Collisional Frequency is the average rate in which two reactants collide for a given system and is used to express the average number of collisions per unit of time in a defined system.

How is crash severity calculated? ›

The severity index (SI) of a crash is equal to the total equivalent property damage only (EPDO) divided by the number of crashes.

How do you calculate accident speed? ›

To calculate the velocity or speed of the car when it collided with the pedestrian we use the same formula v² = u² +2as. To find the point of collision with the pedestrian we have to measure from the centre of the front wheels back to where the skid mark deviates slightly indicating where the contact took place.

What is the force of impact at 30 mph? ›

In a 30 mph crash, a 100 pound adult becomes a 3,000 pound force against the child. That is why it's important for each passenger in a vehicle to be independently and properly restrained with a seatbelt or a child restraint.

What are the 3 forces of impact in a collision? ›

The three types of impact that occur (in succession) are those involving the vehicle, the body of the vehicle occupant, and the organs within the body of the occupant.

How much G force can a human take in a crash? ›

Most of us can withstand up to 4-6G. Fighter pilots can manage up to about 9G for a second or two. But sustained G-forces of even 6G would be fatal.

What are the 7 most common causes of collisions? ›

There is a long list of factors, but the most common include:
• Distracted driving.
• Speeding.
• Alcohol-impaired driving.
• Aggressive driving.
• Drowsy driving.
• Dangerous weather conditions.

### What are the five main causes of collisions? ›

Here are 5 common causes of auto collisions and how to avoid them.
• Distracted Driving. Distracted driving is the leading cause of auto collisions. ...
• Exceeding the Speed Limit. Speed limits exist and are enforced for a reason. ...
• Impaired Driving. ...
• Inclement Weather. ...
• Tailgating.
Sep 24, 2021

What is the collision theory quizlet? ›

What is the collision theory? It is the idea that particles have to collide in order to react and they have to collide hard enough (with enough energy to break the bonds - activation energy).

What are the two most important points of collision theory? ›

1. The reactants must collide with each other. 2. The molecules must have sufficient energy to initiate the reaction (called activation energy).

What are the 2 conditions needed to have an effective collision? ›

According to the collision theory, the molecules must collide with enough energy, known as the activation energy, to prevent the chemical bonds from breaking, in order for a chemical reaction to occur. Additionally, the molecules must collide in the proper orientation.

What are the failures of collision theory? ›

This theory is only applicable to simple gaseous molecules. Collision theory does not explain energy activation barriers. This theory considers atoms/ molecules to be hard spheres and ignores the structural aspect of atoms/molecules. This theory is not applicable to reversible reactions.

What are the 5 factors that affect the rate of reaction quizlet? ›

Terms in this set (20)
• Nature of Reactants.
• Surface Area (more = faster)
• Temperature (higher = faster)
• Concentration (larger = faster)
• Catalyst (present = faster)

What is collision theory in equilibrium? ›

In terms of collision theory, the number of successful collision between the reactants to produce products and between products to produce reactants are equal at equilibrium. This would mean that the rate of forward and reverse reaction is equal at equilibrium.

Which is the formula for collision cross section? ›

CollisionalCrossSection=π(rA+rB)2=π[(1.12×10−10)+(9.6×10−11)]2=1.36×10−19 1.36 x 10-11 m is the furthest the two molecules can be and still get a collision. Since 2.00 x 10-11 m is larger than that distance, the center of one molecule is not in the collisional cross section of the other molecule.

WHAT IS A in collision theory? ›

What is Collision Theory? The collision theory states that a chemical reaction can only occur between particles when they collide (hit each other). The collision between reactant particles is necessary but not sufficient for a reaction to take place. The collisions also have to be effective.

What is the formula before collision? ›

An object's momentum before collision is given by P = mv. In the absence of external force, its motion and momentum do not vary before the collision.

### What are the 4 points of collision theory? ›

The collision energy must be greater than the activation energy for the reaction. The collision must occur in the proper orientation. The collision frequency must be greater than the frequency factor for the reaction. A collision between the reactants must occur.

What are the 2 factors of collision theory? ›

Collision theory is based on the following postulates:
• Greater the number of collisions between reactants in a given amount of time, faster will be the reaction. ...
• The collision must occur with adequate energy (this minimum energy needed is called activation energy).

What is the formula of collision diameter? ›

The collision diameter of the molecule is computed as the cubic root of A*B*C. The correlation between calculated and experimental values is the following: The correlation coefficient here is 0.977.

How do you calculate cross section reaction? ›

As applications, the reaction cross sections for the rate constant of k(T) = k′ Tne-E0/kT and for the rate constant of the absolute reaction rate theory have been calculated.

How do you calculate before and after collision? ›

Before the collision, one car had velocity v and the other zero, so the centre of mass of the system was also v/2 before the collision. The total momentum is the total mass times the velocity of the centre of mass, so the total momentum, before and after, is (2m)(v/2) = mv.

What are the units of collision? ›

SI unit of Z is the volumetric collision rate (unit m3⋅s1).

How will you explain using the collision theory the factor? ›

There are several factors that affect reaction rates. Their effects can be explained using collision theory. These factors are the nature of the reactants, concentration, surface area, temperature and catalysts. Each of these factors increases reaction rate because they increase the number or energy of collisions.

What is the rate of collision? ›

The rate at which a single particle of radius m collides with particles of mass in the range of (m1, m1 + Δm1) is proportional to the concentration of those particles n(m1) Δm1: where β(m, m1) is the rate constant for collisions between the two particles of masses m and m1 and depends on the process involved.

How do you find V1 and V2 in a collision? ›

How can we derive the equations for V1 and V2 for elastic collisions from scratch (see below): V1: (m1-m2/m1+m2)u1 + (2m2/m1+m2)u2 V2: ( 2m1/m1+m2)u1 + (m2-m1/m1+m2)u2 Assume that u1 is the initial velocity of mass 1, v1 is the final velocity of mass 1, u2 is the initial velocity of mass 2 and v2 is the final velocity ...

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