The Friedel-Crafts alkylation of toluene gives a 54-17-29 ratio of the ortho/meta/para dimethylbenzene isomers at #0^@ "C"#. At #25^@ "C"#, the ratio changes to 3-69-28. Explain?
The isomerization may involve an acid-catalyzed methyl migration.
The overall equation for the reaction is
At 0°C, the mixture consists of the 2-, 3-, and 4-isomers in a 54-17-29 ratio.
At 25°C, the ratio changes to 3-69-28.
At higher temperatures, the proportion of the 3-isomer becomes even higher.
This makes sense if we assume that the 2- and 4-isomers are the kinetic product (that is, they are formed fastest), but the 3-isomer is the thermodynamic product (that is, the most stable).
Thus, if you raise the temperature or allow more time, the first-formed 2- and 4-isomers would rearrange in some equilibrium process to form the more stable 3-isomer.
A possible mechanism
It can protonate the xylenes and initiate methyl migrations on the aromatic ring.
For example, the 4-isomer could rearrange to the 3-isomer as follows.
(Adapted from http://chemistry.umeche.maine.edu/Gould/GouldProbs11a.html)
We could write a similar mechanism for rearrangement of the 2-isomer.