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| [[Image:Molecular-collisions.jpg|thumb|right|525px|[[Reaction rate]] tends to increase with [[concentration]] phenomenon explained by '''collision theory''']]
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| '''Collision theory''' is a theory proposed independently by <ref>Trautz, Max. ''Das Gesetz der Reaktionsgeschwindigkeit und der Gleichgewichte in Gasen. Bestätigung der Additivität von Cv-3/2R. Neue Bestimmung der Integrationskonstanten und der Moleküldurchmesser'', Zeitschrift für anorganische und allgemeine Chemie, Volume 96, Issue 1, Pages 1 - 28, 1916, [http://www3.interscience.wiley.com/cgi-bin/abstract/109795783/ABSTRACT]</ref> [[Max Trautz]] in 1916 and [[William Lewis (physical chemist)|William Lewis]] in 1918, that qualitatively explains how [[chemical reactions]] occur and why [[reaction rate]]s differ for different reactions.<ref>{{GoldBookRef | file = C01170 | title = collision theory}}</ref> The collision theory states that when suitable particles of the reactant hit each other, only a certain percentage of the collisions cause any noticeable or significant chemical change; these successful changes are called successful collisions. The successful collisions have enough energy, also known as [[activation energy]], at the moment of impact to break the preexisting bonds and form all new bonds. This results in the products of the reaction. Increasing the concentration of the reactant particles or raising the temperature, thus bringing about more collisions and therefore many more successful collisions, increases the rate of reaction.
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| When a catalyst is involved in the collision between the reactant molecules, less energy is required for the chemical change to take place, and hence more collisions have sufficient energy for reaction to occur. The reaction rate therefore increases.
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| Collision theory is closely related to [[chemical kinetics]].
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| ==Rate constant==
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| The [[rate constant]] for a bimolecular gas phase reaction, as predicted by collision theory is:
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| :<math>k(T) = Z \rho \exp \left( \frac{-E_{a}}{RT} \right)</math>.
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| where:
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| *''Z'' is the [collision frequency].<ref name="frequency">{{GoldBookRef | file = C01166| title = collision frequency}}</ref>
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| * <math>\rho</math> is the [[steric factor]]. <ref name="steric">{{GoldBookRef | file = S05998 | title = steric factor}}</ref>
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| *''E<sub>a</sub>'' is the [[activation energy]] of the reaction.
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| *''T'' is the [[temperature]].
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| *''R'' is [[gas constant]].
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| The collision frequency is:
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| :<math>Z = N_A \sigma_{AB} \sqrt \frac{8 k_B T}{\pi \mu_{AB}}</math>
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| where:
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| *''N<sub>A</sub>'' is the [[Avogadro constant]]
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| *''σ<sub>AB</sub>'' is the reaction [[cross section (physics)|cross section]]
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| *''k<sub>B</sub>'' is [[Boltzmann's constant]]
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| *''μ<sub>AB</sub>'' is the [[reduced mass]] of the reactants.
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| ==Quantitative insights ==
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| ===Derivation===
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| Consider the reaction:
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| :A + B → C
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| 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<sub>AB</sub>) of the reaction and is, in principle, the area corresponding to a circle whose radius (<math>r_{AB}</math>) is the sum of the radii of both reacting molecules, which are supposed to be spherical.
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| A moving molecule will therefore sweep a volume <math>\scriptstyle \pi r^{2}_{AB} c_A</math> per second as it moves, where <math>\scriptstyle c_A</math> is the average velocity of the particle.
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| From [[kinetic theory]] it is known that a molecule of A has an [[Maxwell–Boltzmann distribution|average velocity]] (different from [[root mean square]] velocity) of <math>c_A = \sqrt \frac{8 k_B T}{\pi m_A}</math>, where <math>\scriptstyle k_B</math> is [[Boltzmann constant]] and <math>\scriptstyle m_A</math> is the mass of the molecule.
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| 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 <math>\mu_{AB}</math> must be used instead of <math>m_A</math>.
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| Therefore, the total '''collision frequency''',<ref name="frequency"/> of all A molecules, with all B molecules, is:
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| :<math>N_A^{2} \sigma_{AB} \sqrt \frac{8 k_B T}{\pi \mu_{AB}}[A][B] =N_A^{2} r^{2}_{AB} \sqrt \frac{8 \pi k_B T}{ \mu_{AB}}[A][B] = Z [A][B] </math>
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| From Maxwell Boltzmann distribution it can be deduced that the fraction of collisions with more energy than the activation energy is <math>e^{\frac{-E_a}{k_BT}}</math>. Therefore the rate of a bimolecular reaction for ideal gases will be:
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| :<math>r = Z \rho [A][B] \exp \left( \frac{-E_{a}}{RT} \right)</math>
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| Where:
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| *''Z'' is the collision frequency.
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| *<math>\scriptstyle \rho</math> is the [[steric factor]], which will be discussed in detail in the next section.
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| *''E<sub>a</sub>'' is the [[activation energy]] of the reaction.
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| *''T'' is the absolute temperature.
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| *''R'' is [[gas constant]].
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| The product Zρ is equivalent to the [[preexponential factor]] of the [[Arrhenius equation]]. | |
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| ===Validity of the theory and steric factor===
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| Once a theory is formulated, its validity must be tested, that is, compare its predictions with the results of the experiments.
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| When the expression form of the rate constant is compared with the [[rate equation]] for an elementary bimolecular reaction, <math>\scriptstyle r =k(T) [A][B]</math>, it is noticed that <math>k(T) = N_A^{2} \sigma_{AB} \sqrt \frac{8 k_B T}{\pi m_A} \exp \left( \frac{-E_{a}}{RT} \right)</math>.
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| 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<sup>½</sup> dependence of the preexponential factor is observed experimentally"''{{Citation needed|date=February 2010}}
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| ====Steric factor ====
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| 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 H<sub>2</sub> molecule must approach the bonding zone between the atoms, and only a few of all the possible collisions fulfill this requirement.
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| To alleviate this problem, 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 (chemistry)|frequency factor]] and the collision frequency, and it is most often less than unity.<ref name="steric"/>
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| :<math>\rho = \frac{A_{observed}}{Z_{calculated}}</math>
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| Usually, the more complex the reactant molecules, the lower the steric factor. Nevertheless, some reactions exhibit steric factors greater than unity: the [[harpoon reaction]]s, which involve atoms that exchange [[electron]]s, producing [[ion]]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.
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| {| class="toccolours" border="1" style="float: center; clear: center; margin: 0 0 1em 1em; border-collapse: collapse;"
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| ! colspan="4" align="center" style="background:#ffdead;"|Experimental [[rate constant]]s compared to the ones predicted by collision theory for gas phase reactions
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| | width="180" align="center" bgcolor="E0E0E0"| Reaction
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| | width="180" align="center" bgcolor="E0E0E0"| A (Azra [[frequency factor (chemistry)|frequency factor]])
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| | width="140" align="center" bgcolor="E0E0E0"| Z ([[collision frequency]])
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| | width="100" align="center" bgcolor="E0E0E0"| Steric factor
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| |-
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| |align="center"| 2ClNO → 2Cl + 2NO ||align="center"| 9.4 10<sup>9</sup>|| align="center"|5.9 10<sup>10</sup>||align="center"| 0.16
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| |-
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| |align="center"| 2ClO → Cl<sub>2</sub> + O<sub>2</sub> ||align="center"| 6.3 10<sup>7</sup>|| align="center"|2.5 10<sup>10</sup>||align="center"| 2.3 10<sup>−3</sup>
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| |align="center"| H<sub>2</sub> + C<sub>2</sub>H<sub>4</sub> → C<sub>2</sub>H<sub>6</sub> ||align="center"| 1.24 10<sup>6</sup>|| align="center"|7.3 10<sup>11</sup>||align="center"| 1.7 10<sup>−6</sup>
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| |align="center"| Br<sub>2</sub> + K → KBr + Br ||align="center"| 10<sup>12</sup>|| align="center"|2.1 10<sup>11</sup>||align="center"| 4.3
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| |-
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| |}
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| 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 [[entropy|entropic]] contributions.
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| {| class="toccolours" border="1" style="float: center; clear: center; margin: 0 0 1em 1em; border-collapse: collapse;"
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| ! colspan="5" align="center" style="background:#ffdead;" |Experimental rate constants compared to the ones predicted by collision theory for reactions in solution<ref>Moelwyn-Hughes</ref>
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| |-
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| | width="180" align="center" bgcolor="E0E0E0"| Reaction
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| | width="100" align="center" bgcolor="E0E0E0"| Solvent
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| | width="120" align="center" bgcolor="E0E0E0"| [[Preexponential factor|A]] 10<sup>−11</sup>
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| | width="120" align="center" bgcolor="E0E0E0"| [[Collision frequency|Z]] 10<sup>−11</sup>
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| | width="120" align="center" bgcolor="E0E0E0"| Steric factor
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| |-
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| |align="center"| [[Bromoethane|C<sub>2</sub>H<sub>5</sub>Br]] + OH<sup>-</sup> ||align="center"| [[Ethanol|C<sub>2</sub>H<sub>5</sub>OH]]||align="center"| 4.30|| align="center"|3.86||align="center"| 1.11
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| |-
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| |align="center"| [[Ethanol|C<sub>2</sub>H<sub>5</sub>O<sup>-</sup>]] + [[Iodomethane|CH<sub>3</sub>I]]||align="center"| C<sub>2</sub>H<sub>5</sub>OH||align="center"|2.42|| align="center"|1.93||align="center"| 1.25
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| |-
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| |align="center"| ClCH<sub>2</sub>CO<sub>2</sub><sup>-</sup> + OH<sup>-</sup>||align="center"| [[water]]||align="center"|4.55|| align="center"|2.86||align="center"| 1.59
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| |-
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| |align="center"| C<sub>3</sub>H<sub>6</sub>Br<sub>2</sub> + I<sup>-</sup>||align="center"| [[methanol|CH<sub>3</sub>OH]]||align="center"|1.07|| align="center"|1.39||align="center"| 0.77
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| |-
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| |align="center"| HOCH<sub>2</sub>CH<sub>2</sub>Cl + OH<sup>-</sup>||align="center"| water||align="center"|25.5|| align="center"|2.78||align="center"| 9.17
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| |-
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| |align="center"| [[cresol|4-CH<sub>3</sub>C<sub>6</sub>H<sub>4</sub>O<sup>-</sup>]] + CH<sub>3</sub>I||align="center"| ethanol||align="center"|8.49|| align="center"|1.99||align="center"| 4.27
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| |-
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| |align="center"| CH<sub>3</sub>(CH<sub>2</sub>)<sub>2</sub>Cl + I<sup>-</sup>||align="center"| [[Acetone|(CH<sub>3</sub>)<sub>2</sub>CO]]||align="center"|0.085|| align="center"|1.57||align="center"| 0.054
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| |-
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| |align="center"| [[pyridine|C<sub>5</sub>H<sub>5</sub>N]] + CH<sub>3</sub>I||align="center"| C<sub>2</sub>H<sub>2</sub>Cl<sub>4</sub>||align="center"|-|| align="center"|-||align="center"| 2.0 10<sup>−6</sup>
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| |-
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| |}
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| ==See also==
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| * [[Two-dimensional gas]]
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| ==References==
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| {{Reflist}}
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| == External links ==
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| *[http://www.chemguide.co.uk/physical/basicrates/introduction.html Introduction to Collision Theory]
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| {{Reaction mechanisms}}
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| {{DEFAULTSORT:Collision Theory}}
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| [[Category:Chemical kinetics]]
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The son of the , is aware patience and perseverance are key elements when it comes to a prosperous career- . His very first album, Continue to be Me, produced the most notable hits “All My Girlfriends Say” and “Country Guy,” although his work, Doin’ Factor, identified the vocalist-three straight No. 2 single people: In addition Getting in touch with Is often a Fantastic Point.”
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