explain why 2,4,6-trinitro-N,N-dimethylaniline is 40,000 times strong base than 2,4,6-trinitro aniline?

This is due to the fact that the NMe, group is sufficiently large to interfere sterically with the very large NO, groups in both o-positions. Rotation about ring-carbon to nitrogen bonds allows the 0 atoms of NO, and the Me groups of NMe, to move out of each other's way, but the p orbitals on the N atoms are now no longer parallel to the p orbitals of the ring-carbon atoms. As a consequence, mesomeric shift of the unshared electron pair on NMe, to the oxygen atoms of the NO, groups, via the p orbitals of the ring-carbon atom, is inhibited, and the expected base-weakening-by mesomeric electron-withdrawal-does not take place . The base-weakening influence of the three nitro