NationMaster - Encyclopedia: Collision theory

Collision theory is a theory, proposed by Max Trautz and William Lewis in 1916 that qualitatively explains how chemical reactions occur and why reaction rates differ for different reactions.^[1] It assumes that for a reaction to occur the reactant particles must collide, but only a certain fraction of the total collisions, the effective collisions, cause the transformation of reactant molecules into products. This is due to the fact that only a fraction of the molecules have sufficient energy and the right orientation at the moment of impact to break the existing bonds and form new bonds. The minimal amount of energy needed so that the molecule is transformed is called activation energy. Collision theory is closely related to chemical kinetics. Chemical reactions are also known as chemical changes. ... Iron rusting - a chemical reaction with a slow reaction rate. ... The sparks generated by striking steel against a flint provide the activation energy to initiate combustion in this Bunsen burner. ... In physical chemistry, chemical kinetics or reaction kinetics is the study of reaction rates in a chemical reaction. ...

Reaction rate tends to increase with concentration - a phenomenon explained by collision theory

1 Rate constant
2 Qualitative overview
3 Quantitative insights
4 References
5 External links

Image File history File links Molecular-collisions. ... Image File history File links Molecular-collisions. ... Iron rusting - a chemical reaction with a slow reaction rate. ... For other uses, see Concentration (disambiguation). ...

Rate constant

The rate constant for a bimolecular gas phase reaction, as predicted by collision theory is: In chemical kinetics a reaction rate constant quantifies the speed of a chemical reaction. ...

$k(T) = Z rho exp left( frac{-E_{a}}{RT} right)$ .

Z is the collision frequency.^[2]
$scriptstyle rho$ is the steric factor.^[3]
E_a is the activation energy of the reaction.
T is the temperature.
R is gas constant.

And the collision frequency is: Steric effects arise from the fact that each atom within a molecule occupies a certain amount of space. ... The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ...

$Z = N_A sigma_{AB} sqrt frac{8 k_B T}{pi mu_{AB}}$

N_A is Avogadro's number
σ_AB is the reaction cross section
k_B is Boltzmann's constant
μ_AB is the reduced mass of the reactants

Avogadros number, also called Avogadros constant (NA), named after Amedeo Avogadro, is formally defined to be the number of carbon-12 atoms in 12 grams (0. ... In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles. ... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... Reduced mass is an algebraic term of the form that simplifies an equation of the form The reduced mass is typically used as a relationship between two system elements in parallel, such as resistors; whether these be in the electrical, thermal, hydraulic, or mechanical domains. ...

Qualitative overview

Fundamentally collision theory is based on kinetic theory and therefore it can only be applied strictly to ideal gases, otherwise approximations are used. Qualitatively, it assumes that the molecules of the reactants are rigid, uncharged spheres that physically collide prior to reacting. Moreover, it postulates that the majority of collisions do not lead to a reaction, but only those in which the colliding species have: Kinetic theory or kinetic theory of gases attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecular composition and motion. ... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ...

A kinetic energy greater than a certain minimum, called the activation energy, E_a
The correct spatial orientation (steric factor) with respect to each other.

These collisions which lead to reaction are called effective collisions. The reaction rate, may be defined as the number of effective collisions per unit time. The sparks generated by striking steel against a flint provide the activation energy to initiate combustion in this Bunsen burner. ... Steric effects arise from the fact that each atom within a molecule occupies a certain amount of space. ... Iron rusting - a chemical reaction with a slow reaction rate. ...

According to collision theory, two significant factors determine reaction rates:

Concentration: Increase in concentration of reactants increases the collision frequency between the reactants. Thus the effective collision frequency also increases.
Temperature: The kinetic energy of particles follows the Maxwell-Boltzmann distribution. An increase in temperature not only increases the average speed of the reactant particles and the number of collisions, but also the fraction of particles having kinetic energy higher than the activation energy. Thus, the effective collision frequency increases.

If a heterogeneous reaction takes place, then the surface area of the solid is also important: the more reactive centers exposed on the surface (due to the porosity of the solid and how finely divided it is), the more collisions with reacting molecules. The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

Quantitative insights

Derivation

Collision theory can only be applied quantitatively to bimolecular reactions, of the kind:^[4]

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 (σ_AB) of the reaction and is, in principle, the area corresponding to a circle whose radius (r_AB) is the sum of the radii of both reacting molecules, which are supposed to be spherical. A moving molecule will therefore sweep a volume $scriptstyle pi r^{2}_{AB} c_A$ per second as it moves, where $scriptstyle c_A$ is the average velocity of the particle.

From kinetic theory it is known that a molecule of A has an average velocity (different from root mean square velocity) of $c_A = sqrt frac{8 k_B T}{pi m_A}$ . Where $scriptstyle k_B$ is Boltzmann constant and $scriptstyle m_A$ is the mass of the molecule. Kinetic theory or kinetic theory of gases attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecular composition and motion. ... The Maxwellâ€“Boltzmann distribution is a probability distribution with applications in physics and chemistry. ... In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ...

The solution of the two body problem states that two different moving bodies can be treated as one body which has the reduced mass of both and moves with the velocity of the center of mass, so, in this system $μ A B$ must be used instead of $m A$ . In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other. ... Reduced mass is an algebraic term of the form that simplifies an equation of the form The reduced mass is typically used as a relationship between two system elements in parallel, such as resistors; whether these be in the electrical, thermal, hydraulic, or mechanical domains. ... In physics, the center of mass of a system of particles is a specific point at which, for many purposes, the systems mass behaves as if it were concentrated. ...

Therefore, the total collision frequency,^[2] of all A molecules, with all B molecules, is:

$N_A sigma_{AB} sqrt frac{8 k_B T}{pi mu_{AB}}[A][B] =N_A r^{2}_{AB} sqrt frac{8 pi k_B T}{ mu_{AB}}[A][B] = Z [A][B]$

From Maxwell Boltzmann distribution it can be deduced that the fraction of collisions with more energy than the activation energy is $e^{frac{-E_a}{k_BT}}$ . Therefore the rate of a bimolecular reaction for ideal gases will be:

$r = Z rho [A][B] exp left( frac{-E_{a}}{RT} right)$

Where:

Z is the collision frequency.
$scriptstyle rho$ is the steric factor, which will be discussed in detail in the next section.
E_a is the activation energy of the reaction.
T is the temperature.
R is gas constant.

The product Zρ is equivalent to the preexponential factor of the Arrhenius equation. Steric effects arise from the fact that each atom within a molecule occupies a certain amount of space. ... The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ... In chemical kinetics, the preexponential factor or A factor is the pre-exponential constant in the Arrhenius equation, an empirical relationship between temperature and rate coefficient. ... The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of a chemical reaction rate, more correctly, of a rate coefficient, as this coefficient includes all magnitudes that affect reaction rate except for concentration. ...

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 the rate constant is compared with the rate equation for an elementary bimolecular reaction, $scriptstyle r =k(T) [A][B]$ , it is noticed that $k(T) = N_A sigma_{AB} sqrt frac{8 k_B T}{pi m_A} exp left( frac{-E_{a}}{RT} right)$ . For a chemical reaction, the rate law or rate equation is an equation which links the reaction rate with concentrations or pressures of reactants. ...

That expression is similar to the Arrhenius equation, 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^½ dependence of the preexponential factor is observed experimentally"^[4] The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of a chemical reaction rate, more correctly, of a rate coefficient, as this coefficient includes all magnitudes that affect reaction rate except for concentration. ...

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 reaction of ethylene the H₂ molecule must approach the bonding zone between the atoms, and only a few of all the possible collisions fulfill this requirement. Hydrogenation is a class of chemical reactions which result an addition of hydrogen (H2) usually to unsaturated organic compounds. ... Ethylene (or IUPAC name ethene) is the chemical compound with the formula C2H4. ...

A new concept must be introduced: the steric factor, $ρ$ . 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.^[3] $rho = frac{A_{observed}}{Z_{calculated}}$ In chemical kinetics, the frequency factor or A factor is the pre-exponential constant in the Arrhenius equation, which indicates how many collisions between reactants have the correct orientation to lead to the products. ...

Usually, the more complex the reactant molecules, the lower the steric factor. Nevertheless, some reactions exhibit steric factors greater than unity: the harpoon reactions, which involve atoms that exchange electrons, producing ions. 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)... Unfortunately, steric factors cannot be calculated theoretically, so the applicability of collision theory is greatly diminished. Harpoon reactions[1] 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. ... For other uses, see Electron (disambiguation). ... This article is about the electrically charged particle. ...

Experimental rate constants compared to the ones predicted by collision theory for gas phase reactions
Reaction	A (Arrhenius frequency factor)	Z (collision frequency)	Steric factor
2ClNO → 2Cl + 2NO	9.4 10⁹	5.9 10¹⁰	0.16
2ClO → Cl₂ + O₂	6.3 10⁷	2.5 10¹⁰	2.3 10^-3
H₂ + C₂H₄ → C₂H₆	1.24 10⁶	7.3 10¹¹	1.7 10^-6
Br₂ + K → KBr + Br	10¹²	2.1 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. ρ values greater than unity can be attributed to favorable entropic contributions. In chemical kinetics a reaction rate constant quantifies the speed of a chemical reaction. ... In chemical kinetics, the frequency factor or A factor is the pre-exponential constant in the Arrhenius equation, which indicates how many collisions between reactants have the correct orientation to lead to the products. ... 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. ... For a less technical and generally accessible introduction to the topic, see Introduction to entropy. ...

Experimental rate constants compared to the ones predicted by collision theory for reactions in solution^[5]
Reaction	Solvent	A 10^-11	Z 10^-11	Steric factor
C₂H₅Br + OH^-	C₂H₅OH	4.30	3.86	1.11
C₂H₅O^- + CH₃I	C₂H₅OH	2.42	1.93	1.25
ClCH₂CO₂^- + OH^-	water	4.55	2.86	1.59
C₃H₆Br₂ + I^-	CH₃OH	1.07	1.39	0.77
HOCH₂CH₂Cl + OH^-	water	25.5	2.78	9.17
4-CH₃C₆H₄O^- + CH₃I	ethanol	8.49	1.99	4.27
CH₃(CH₂)₂Cl + I^-	(CH₃)₂CO	0.085	1.57	0.054
C₅H₅N + CH₃I	C₂H₂Cl₄	-	-	2.0 10^-6

In chemical kinetics, the preexponential factor or A factor is the pre-exponential constant in the Arrhenius equation, an empirical relationship between temperature and rate coefficient. ... 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. ... R-phrases , , S-phrases , Flash point âˆ’20 Â°C Autoignition temperature 511 Â°C Explosive limits 6. ... â€œGrain alcoholâ€ redirects here. ... â€œGrain alcoholâ€ redirects here. ... Iodomethane, commonly called methyl iodide, is a dense volatile liquid. ... Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ... Methanol, also known as methyl alcohol, carbinol, wood alcohol, wood naptha or wood spirits, is a chemical compound with chemical formula CH3OH. It is the simplest alcohol, and is a light, volatile, colourless, flammable, poisonous liquid with a distinctive odor that is somewhat milder and sweeter than ethanol (ethyl alcohol). ... Cresols are organic chemical compounds which are methylphenols. ... 3-Pentanone, also known as diethyl ketone, is a colorless liquid ketone with an odor like that of acetone. ... Pyridine is a chemical compound with the formula C5H5N. It is a liquid with a distinctively putrid odour. ...

Conclusion

Simple collision theory does not give a clear interpretation of the activation energy, nor a way to theoretically calculate it, but, in spite of its simplicity, it provides a basis for defining a "typical" kinetic behavior, which allows us to focus on more particular cases.

References

^ International Union of Pure and Applied Chemistry. "collision theory". Compendium of Chemical Terminology Internet edition.
^ ^a ^b Template:GoldBookRef = file = C01166
^ ^a ^b International Union of Pure and Applied Chemistry. "steric factor". Compendium of Chemical Terminology Internet edition.
^ ^a ^b Kenneth Connors, Chemical Kinetics, 1990, VCH Publishers
^ Moelwyn-Hughes

IUPAC logo The International Union of Pure and Applied Chemistry (IUPAC) (Pronounced as eye-you-pack) is an international non-governmental organization established in 1919 devoted to the advancement of chemistry. ... Compendium of Chemical Terminology (ISBN 0-86542-684-8) is a book published by IUPAC containing internationally accepted definitions for terms in chemistry. ... IUPAC logo The International Union of Pure and Applied Chemistry (IUPAC) (Pronounced as eye-you-pack) is an international non-governmental organization established in 1919 devoted to the advancement of chemistry. ... Compendium of Chemical Terminology (ISBN 0-86542-684-8) is a book published by IUPAC containing internationally accepted definitions for terms in chemistry. ...

External links

Introduction to Collision Theory

Category: Chemical kinetics

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