In an intrinsic semiconductor, Ef is the fermi energy and sits right in the middle of the band gap. Ec and Ev are the energy of the bottom of the conduction band and the energy of the top of the valence band, respectively.
This means that Ec - Ev = Egap. It also means that since Ef is right in the middle of the gap, Ec - Ef = Egap/2
Egap OR Eg = 1.12 eV