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The Collision theory, proposed by Max Trautz
Max Trautz

Max Trautz was a Germany chemist. He was very productive with over 190 scientific publications especially in the field of chemical kinetics. He was first investigating the activation energy of molecules by light by connecting Max Planck new results concerning light with observations in chemistry....
 and William Lewis
William Lewis

William Lewis was involved in England Football in various capacities in the early 20th century. He was first a referee , then a director and later manager of Brentford F.C....
 in 1916 and 1918, qualitatively explains how chemical reactions occur and why reaction rate
Reaction rate

The reaction rate or rate of reaction for a reactant or product in a particular chemical reaction is intuitively defined as how fast a reaction takes place....
s differ for different reactions. This theory is based on the idea that reactant particles must collide for a reaction to occur, but only a certain fraction of the total collisions have the energy to connect effectively and cause the reactants to transform into products.






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The Collision theory, proposed by Max Trautz
Max Trautz

Max Trautz was a Germany chemist. He was very productive with over 190 scientific publications especially in the field of chemical kinetics. He was first investigating the activation energy of molecules by light by connecting Max Planck new results concerning light with observations in chemistry....
 and William Lewis
William Lewis

William Lewis was involved in England Football in various capacities in the early 20th century. He was first a referee , then a director and later manager of Brentford F.C....
 in 1916 and 1918, qualitatively explains how chemical reactions occur and why reaction rate
Reaction rate

The reaction rate or rate of reaction for a reactant or product in a particular chemical reaction is intuitively defined as how fast a reaction takes place....
s differ for different reactions. This theory is based on the idea that reactant particles must collide for a reaction to occur, but only a certain fraction of the total collisions have the energy to connect effectively and cause the reactants to transform into products. This is because only a portion of the molecules have enough energy and the right orientation (or "angle") at the moment of impact to break any existing bonds and form new ones. The minimal amount of energy needed for this to occur is known as activation energy
Activation energy

In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius, that is defined as the energy that must be overcome in order for a chemical reaction to occur....
. Particles from different elements react with each other by releasing activation energy as they hit each other. If the elements react with each other, the collision is called successful, but if the concentration of at least one of the elements is too low, there will be fewer particles for the other elements to react with and the reaction will happen much more slowly.

Collision theory is closely related to chemical kinetics
Chemical kinetics

Chemical kinetics, also known as reaction kinetics, is the study of reaction rate of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction mechanism and transition states, as well as the construction of ma...
.

Rate constant

The rate constant for a bimolecular gas phase reaction, as predicted by collision theory is:

.

  • Z is the collision frequency
    Collision frequency

    Collision frequency is defined in chemical kinetics, in the background of theoretical kinetics, as the average number of collisions between reacting molecules per unit of time....
    .
  • is the steric factor
    Steric factor

    Steric factor, P is a term used in collision theory.It is defined as the ratio between the experimental value of the rate constant and the one predicted by collision theory....
    .
  • Ea is the activation energy
    Activation energy

    In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius, that is defined as the energy that must be overcome in order for a chemical reaction to occur....
     of the reaction.
  • T is the temperature
    Temperature

    In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
    .
  • R is gas constant
    Gas constant

    The gas constant is a physical constant which is featured in a large number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation....
    .


And the collision frequency is:

  • NA is Avogadro's number
    Avogadro's number

    The Avogadro constant , also called Avogadro's number, is the number of "elementary entities" in one mole , that is , the number of atoms in exactly 12 grams of carbon-12....
  • sAB is the reaction cross section
    Cross section (physics)

    In nuclear physics and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles.When particles are thrown against a foil made of a certain substance, the cross section is a hypothetical area measure around the target particles that represents a surface....
  • kB is Boltzmann's constant
  • µAB is the reduced mass
    Reduced mass

    Reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. This is a quantity with the Units_of_measurement of mass, which allows the two-body problem to be solved as if it were a one-body problem....
     of the reactants


Quantitative insights


Derivation

Collision theory can only be applied quantitatively to bimolecular reactions, of the kind:

A + B ? C

In collision theory it is considered that two particles A and B will collide if their nuclei get closer than a certain distance. The area around a molecule A in which it can collide with an approaching B molecule is called the cross section (sAB) of the reaction and is, in principle, the area corresponding to a circle whose radius (rAB) is the sum of the radii of both reacting molecules, which are supposed to be spherical. A moving molecule will therefore sweep a volume per second as it moves, where is the average velocity of the particle.

From kinetic theory
Kinetic theory

Kinetic theory attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecule composition and motion ....
 it is known that a molecule of A has an average velocity
Maxwell–Boltzmann distribution

The Maxwell?Boltzmann distribution is a probability distribution with applications in physics and chemistry. The most common application is in the field of statistical mechanics....
 (different from root mean square
Root mean square

In mathematics, the root mean square , also known as the quadratic mean, is a statistics measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids....
 velocity) of . Where is Boltzmann constant
Boltzmann constant

The Boltzmann constant is the physical constant relating energy at the particle level with temperature observed at the bulk level. It is the gas constant R divided by the Avogadro constant NA:...
 and is the mass of the molecule.

The solution of the two body problem states that two different moving bodies can be treated as one body which has the reduced mass
Reduced mass

Reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. This is a quantity with the Units_of_measurement of mass, which allows the two-body problem to be solved as if it were a one-body problem....
 of both and moves with the velocity of the center of mass
Center of mass

The center of mass of a system of wiktionary:Particles is a specific point at which, for many purposes, the system's mass behaves as if it were concentrated....
, so, in this system must be used instead of .

Therefore, the total collision frequency, of all A molecules, with all B molecules, is:

From Maxwell Boltzmann distribution it can be deduced that the fraction of collisions with more energy than the activation energy is . Therefore the rate of a bimolecular reaction for ideal gases will be:

Where:
  • Z is the collision frequency.
  • is the steric factor
    Steric factor

    Steric factor, P is a term used in collision theory.It is defined as the ratio between the experimental value of the rate constant and the one predicted by collision theory....
    , which will be discussed in detail in the next section.
  • Ea is the activation energy
    Activation energy

    In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius, that is defined as the energy that must be overcome in order for a chemical reaction to occur....
     of the reaction.
  • T is the absolute temperature.
  • R is gas constant
    Gas constant

    The gas constant is a physical constant which is featured in a large number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation....
    .


The product Z? is equivalent to the preexponential factor of the Arrhenius equation
Arrhenius equation

The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of the rate constant, and therefore, rate of a chemical reaction....
.

Validity of the theory and steric factor

Once a theory is formulated, its validity must be tested, that is, compare its predictions with the results of the experiments.

When the expression form of the rate constant is compared with the rate equation
Rate equation

The rate law or rate equation for a chemical reaction is an equation which links the reaction rate with concentrations or pressures of reactants and constant parameters ....
 for an elementary bimolecular reaction, , it is noticed that .

That expression is similar to the Arrhenius equation
Arrhenius equation

The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of the rate constant, and therefore, rate of a chemical reaction....
, and gives the first theoretical explanation for the Arrhenius equation on a molecular basis. The weak temperature dependence of the preexponential factor is so small compared to the exponential factor that it cannot be measured experimentally, that is, "it is not feasible to establish, on the basis of temperature studies of the rate constant, whether the predicted T˝ dependence of the preexponential factor is observed experimentally"

Steric factor
If the values of the predicted rate constants are compared with the values of known rate constants it is noticed that collision theory fails to estimate the constants correctly and the more complex the molecules are, the more it fails. The reason for this is that particles have been supposed to be spherical and able to react in all directions; that is not true, as the orientation of the collisions is not always the right one. For example in the hydrogenation
Hydrogenation

Hydrogenation is the chemical reaction that results from the addition of hydrogen . The process is usually employed to a redox or Saturation organic compounds....
 reaction of ethylene
Ethylene

Ethylene is the chemical compound with the formula C2H4. It is the simplest alkene. Because it contains a carbon-carbon double bond, ethylene is called an unsaturated hydrocarbon or an olefin....
 the H2 molecule must approach the bonding zone between the atoms, and only a few of all the possible collisions fulfill this requirement.

A new concept must be introduced: the steric factor, . It is defined as the ratio between the experimental value and the predicted one (or the ratio between the frequency factor and the collision frequency, and it is most often less than unity.

Usually, the more complex the reactant molecules, the lower the steric factor. Nevertheless, some reactions exhibit steric factors greater than unity: the harpoon reaction
Harpoon reaction

Harpoon reactions are a type of chemical reaction between two substances one of them prone to form a cation, generally a metal, and the other one prone to form an anion, generally a halogen....
s, which involve atoms that exchange electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
s, producing ion
Ion

An ion is an atom or molecule which has lost or gained one or more electrons, giving it a positive or negative electrical charge. According to the Bohr_model this will be from or in the outer shield 'n'....
s. The deviation from unity can have different causes: the molecules are not spherical, so different geometries are possible; not all the kinetic energy is delivered into the right spot; the presence of a solvent (when applied to solutions), etc.

Experimental rate constants compared to the ones predicted by collision theory for gas phase reactions
Reaction A (Azra frequency factor) Z (collision frequency
Collision frequency

Collision frequency is defined in chemical kinetics, in the background of theoretical kinetics, as the average number of collisions between reacting molecules per unit of time....
)		 Steric factor
2ClNO ? 2Cl + 2NO 9.4 1095.9 1010 0.16
2ClO ? Cl2 + O2 6.3 1072.5 1010 2.3 10-3
H2 + C2H4 ? C2H6 1.24 1067.3 1011 1.7 10-6
Br2 + K ? KBr + Br 10122.1 1011 4.3


Collision theory can be applied to reactions in solution; in that case, the solvent cage has an effect on the reactant molecules and several collisions can take place in a single encounter, which leads to predicted preexponential factors being too large. ? values greater than unity can be attributed to favorable entropic
Entropy

In many branches of science, entropy is a measure of the disorder of a system. The concept of entropy is particularly notable as it is applied across physics, information theory and mathematics....
 contributions.

Experimental rate constants compared to the ones predicted by collision theory for reactions in solution
Reaction Solvent A 10-11 Z
Collision frequency

Collision frequency is defined in chemical kinetics, in the background of theoretical kinetics, as the average number of collisions between reacting molecules per unit of time....
 10-11		 Steric factor
C2H5Br
Bromoethane

Bromoethane, also known as ethyl bromide is a chemical compound of the haloalkanes group. It is abbreviated by chemists as EtBr. This volatile compound has an ether-like odour....
 + OH- 		C2H5OH
Ethanol

Ethanol, also called ethyl alcohol, pure alcohol, grain alcohol, or drinking alcohol, is a volatility , flammable, colorless liquid....
 4.303.86 1.11
C2H5O-
Ethanol

Ethanol, also called ethyl alcohol, pure alcohol, grain alcohol, or drinking alcohol, is a volatility , flammable, colorless liquid....
 + CH3I
Iodomethane

Iodomethane, commonly called methyl iodide and commonly abbreviated "MeI", is the Organoiodine compound with the formula CH3I. This Density Vapor pressure liquid is related to methane by replacement of one hydrogen atom by an atom of iodine and its Dipole#Molecular dipoles is 1.59 D....
 C2H5OH2.421.93 1.25
ClCH2CO2- + OH- water
Water

Water is a common chemical substance that is essential for the survival of all known forms of life. In typical usage, water refers only to its liquid form or States of matter, but the substance also has a solid state, ice, and a gaseous state, water vapor or steam....
4.552.86 1.59
C3H6Br2 + I- CH3OH
Methanol

Methanol, also known as methyl alcohol, carbinol, wood alcohol, wood naphtha or wood spirits, is a chemical compound with chemical formula carbonhydrogen3oxygenhydrogen ....
1.071.39 0.77
HOCH2CH2Cl + OH- water25.52.78 9.17
4-CH3C6H4O-
Cresol

Cresols are organic compounds which are methyl groupphenols. They are a widely occurring natural and manufactured group of aromatic organic compounds which are categorized as phenols ....
 + CH3I		 ethanol8.491.99 4.27
CH3(CH2)2Cl + I- (CH3)2CO
3-Pentanone

3-Pentanone is a colorless liquid ketone with an odor like that of acetone. Its formula is carbon5hydrogen10oxygen. It is soluble in about 25 parts water, and miscible with ethanol and diethyl ether....
0.0851.57 0.054
C5H5N
Pyridine

Pyridine is a simple and important heterocyclic aromatic organic compound with the formula CarbonHydrogenNitrogen. This colorless liquid with a distinctive fish-like odor is structurally related to benzene, wherein one CH group in the six-membered ring is replaced by a nitrogen atom....
 + CH3I		 C2H2Cl4-- 2.0 10-6


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