Editing Collision theory (section)

===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]] for an elementary bimolecular reaction, <math>r = k(T) [A][B]</math>, it is noticed that
: <math>k(T) = N_A \sigma_{AB}\rho \sqrt \frac{8 k_\text{B} T}{\pi \mu_{AB}} \exp \left( \frac{-E_\text{a}}{RT} \right)</math>
unit M<sup>−1</sup>⋅s<sup>−1</sup> (= dm<sup>3</sup>⋅mol<sup>−1</sup>⋅s<sup>−1</sup>), with all dimension unit dm including ''k''<sub>B</sub>.

This 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>{{sfrac|1|2}}</sup> dependence of the preexponential factor is observed experimentally".<ref name="Connors">Kenneth Connors, Chemical Kinetics, 1990, VCH Publishers.</ref>

==== 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, which is not true, as the orientation of the collisions is not always proper for the reaction. 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.

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):

: <math>\rho = \frac{A_\text{observed}}{Z_\text{calculated}},</math>

and it is most often less than unity.<ref name="steric"/>

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.

:{| class="wikitable"
|+ Experimental [[rate constant]]s compared to the ones predicted by collision theory for gas phase reactions
|-
! Reaction
! [[frequency factor (chemistry)|''A'']], s<sup>−1</sup>M<sup>−1</sup>
! [[collision frequency|''Z'']], s<sup>−1</sup>M<sup>−1</sup>
! Steric factor 
|-
| 2ClNO → 2Cl + 2NO || 9.4{{e|9}} || 5.9{{e|10}} || 0.16
|-
| 2ClO → Cl<sub>2</sub> + O<sub>2</sub> || 6.3{{e|7}} || 2.5{{e|10}} || 2.3{{e|−3}}
|-
| H<sub>2</sub> + C<sub>2</sub>H<sub>4</sub> → C<sub>2</sub>H<sub>6</sub> || 1.24{{e|6}} || 7.3{{e|11}} || 1.7{{e|−6}}
|-
| Br<sub>2</sub> + K → KBr + Br || 1.0{{e|12}} || 2.1{{e|11}} || 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 [[entropy|entropic]] contributions.

:{| class="wikitable"
|+ Experimental rate constants compared to the ones predicted by collision theory for reactions in solution<ref>E.A. Moelwyn-Hughes, [https://archive.org/details/in.ernet.dli.2015.474865/mode/2up ''The kinetics of reactions in solution''], 2nd ed, page 71.</ref>
|-
! Reaction
! Solvent
! [[Preexponential factor|''A'']], 10<sup>11</sup> s<sup>−1</sup>⋅M<sup>−1</sup>
! [[Collision frequency|''Z'']], 10<sup>11</sup> s<sup>−1</sup>⋅M<sup>−1</sup>
! Steric factor 
|-
| [[Bromoethane|C<sub>2</sub>H<sub>5</sub>Br]] + OH<sup>−</sup> || [[ethanol]] || 4.30 || 3.86 || 1.11
|-
| [[Ethanol|C<sub>2</sub>H<sub>5</sub>O<sup>−</sup>]] + [[Iodomethane|CH<sub>3</sub>I]] || ethanol ||2.42 || 1.93 || 1.25
|-
| ClCH<sub>2</sub>CO<sub>2</sub><sup>−</sup> + OH<sup>−</sup> || [[water]] || 4.55 || 2.86 || 1.59
|-
| C<sub>3</sub>H<sub>6</sub>Br<sub>2</sub> + I<sup>−</sup> || [[methanol]] || 1.07 || 1.39 || 0.77
|-
| HOCH<sub>2</sub>CH<sub>2</sub>Cl + OH<sup>−</sup> || water ||25.5 || 2.78 || 9.17
|-
| [[cresol|4-CH<sub>3</sub>C<sub>6</sub>H<sub>4</sub>O<sup>−</sup>]] + CH<sub>3</sub>I || ethanol || 8.49 || 1.99 || 4.27
|-
| CH<sub>3</sub>(CH<sub>2</sub>)<sub>2</sub>Cl + I<sup>−</sup> || [[acetone]] || 0.085 || 1.57|| 0.054
|-
| [[pyridine|C<sub>5</sub>H<sub>5</sub>N]] + CH<sub>3</sub>I || [[Tetrachloroethane|C<sub>2</sub>H<sub>2</sub>Cl<sub>4</sub>]] || — || — || 2.0 10{{e|−6}}
|-
|}