The main reason why anti-periplaner conformation is preferred in E2 reactions is because the conformation of the hydrogen that is anti to the leaving group provides for a staggered transition state,which is lower in free energy.

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The anti-periplanar conformation creates a staggered transition state, which leads to a lower free energy of activation and therefore a preferred pathway for E2 reactions. This is a basic concept in organic chemistry.

The Main Reason Why Anti-Periplaner Conformation Is Preferred in E2