Which factors determine the reactivity of halogens in the subsitution reaction ?

Explanation

Reactivity order of halogens in the substitution reaction of alkane is:
`F_(2)gtC1_(2)gtBr_(2)gtI_(2)`
Two factor that are responsible:
a. Low energy of activation for the chain-propagating steps.
b. More negative heat of reaction `(Delta H_(r)^(@)` of the overall reaction.
`E_(activation)` for the chain-propagation step `(X + CH_(4) rarr HX + CH_(3))` for `F_(2), C1_(2), Br_(2)`, and is `+5.1, +15.9, +77.8`, and `+140.2` kJ `mol^(-1)` , respectively, and `Delta H_(r)^(@)` of overall reaction for flurination, chlorination, brominatikon, and iodination is `-426.8, -102.5, -31.4`, and `+60.0` kJ `mol^(-1)`, respectively. Therefore, it is clear that the chain-intiating step is not responsible for the observed order of reactities, but the two factors discussed above are responsible. As `E_(activation)` for the chain-propagataing step increases from F to I, the fraction of collisions with energies greater than `E_(activation)` decreases and, consequently, the reactivity dereases as shown belown in the plot of `E_(activation)` versus fraction of the collision with the given energy.