Benzene Continued

So, the reagent with an appropriate functional group is cooled and sprayed in the way of benzene in a warmer spray of mist.  At what specific temperatures depend on the interpretation of $E$,

$E=E_{ph}=\cfrac{n.hc}{2\pi a_{\psi}}$

where $a_{\psi}\approx 139\,pm$  and  $n=3$

and the specific reagent.  The point is to mitigate the energy difference between the temperature particles clouds on the two reacting compounds.

What is $E_{ph}$ on the Celsius temperature scale?

In experiments freezing water and benzene, at the temperature at approximately $-22^oC$, a large expansion occurs in contrast with the gradual contraction found with temperature above  $-22^oC$.  This might be due to the temperature particle clouds on water and benzene aligning themselves and both molecules form into a hyper-lattice.

The temperature clouds have to be attractive to from into a lattice.  Benzene freezes at $5.5^oC$; water freezes at $0^oC$.

What happens at $-22^oC$?

The temperature around a containment is due to temperature charge on its surface.  So it is the temperature charge around the mixture of water and benzene that give a temperature reading of $-22^oC$.  Is this charge that mitigate the energy level difference between the two temperature particle clouds?  That the charge equivalent to $-22^oC$ makes both temperature clouds on the reacting compounds neutral and is attractive.

If, we mix benzene and the reagent with a functional group to be substituted for an hydrogen on the benzene and lowers the temperature of the mixture in porous porous Vycor Glass till similar expansion occurs at say, $T_{ex}$.  Does a temperature difference of $T_{ex}$, the hotter spray being benzene, encourages the substitution reaction?

Water dissolves benzene, but a reagent that provides a functional group for substitution might react quickly.

Note:  $T_{ex}$ can be negative, but the hot spray is benzene when the other reagent is expected to have a smaller temperature particle cloud.  Two running streams when the reagents are liquid will work as well as two sprays of mist.  The point of both set up is to encourage collisions between the reacting molecules.