Data are presented for the lifetime and Doppler broadening parameters for positrons annihilating in ethane physisorbed on grafoil. The coverage dependence of these parameters has been investigated up to about 2.5 monolayers at 108 K. Both the positron lifetimes and Doppler broadening parameters reflect significant variations in the surface electron density as a function of adsorbate coverage, with clear evidence for minimum electron density occurring at coverages of ϳ0.8 and 2. The temperature dependencies of the lifetime and Doppler broadening data, studied for coverages of 0.4, 0.9, and 1.5 monolayers, show structural phase transitions in the adsorbate. We propose a mechanism for this structural phase transition at 39 K.