The untilting to tilting (U-->t) phase transition of amphiphile monolayers at the water-air interface is studied as a distortion of the orthogonally hexagonal orientation of molecules by a competition among entropy, Lennard-Jones potential, and the work done by surface and bulk pressures (Pi,P). The U/t phase portion in the Pi-T diagram is derived as an approximately linear van der Waals equation Pi=kT/2A(0)-Pl(0) with A(0), l(0) being the molecular area and chain length, respectively, at the U phase. A comparison with experiment in monolayers of C-14-C-24 acids [see, e.g., Peterson , Langmuir 8, 2995 (1992)] shows quantitative agreement. Besides two optimal tilting directions, i.e., in the direction to a nearest neighbor (NN) and to a next-nearest neighbor (NNN), an intermediate tilt at the NN-->NNN transition is shown to be physically possible based on Selinger-Nelson theory [Phys. Rev. Lett. 61, 416 (1988)].