The ethylene glycol (EG) molecule, HOCH2CH2OH, adopts a conformation where the central OCCO dihedral is exclusively gauche in the gaseous and crystalline states, but in the liquid state, for close to 20% of the molecules, the central OCCO adopts the energetically unfavorable trans conformation. Here we report calculations, based on ab initio molecular dynamics simulations, on the thermodynamics associated with hydrogen bond formation in the liquid state of EG between donor-acceptor pairs with different molecular conformations. We establish an operational, geometric definition of hydrogen bonds in liquid EG from an analysis of the proton NMR data and show that the key feature, irrespective of the conformation, is marked directionality with almost linear angle HO center dot center dot center dot O angles. The free energy for hydrogen bond formation estimated as the potential of mean force for the reversible work associated with the passage from a hypothetical state where hydrogen bonding is absent and donor-acceptor pairs are randomly oriented to the hydrogen-bonded state where the pairs are oriented showed comparable magnitudes irrespective of the molecular conformation of either the donor or acceptor. The results suggest that the presence of the trans conformer in liquid EG would require an understanding of its role in the extended hydrogen-bonded network of the liquid.