Polar stratospheric clouds (PSCs) are important for the chemical activation of chlorine compounds and subsequent ozone depletion. However, how solid PSCs form is still subject to controversial discussion. Recently, the octahydrate of sulfuric acid (H2SO4⋅8H2O) has been proposed as a solid phase for PSC particles. In our experiment single H2SO4/H2O aerosols levitated in an electrodynamic balance are cooled to 158 K along the ice-liquid equilibrium line. This coexistence curve has been measured for the first time in the temperature interval between 200 K and 158 K. Three independent methods are used for measuring the H2SO4 concentration of the aerosol. No phase transition is observed over a time period of 24 hours and longer at these or higher temperatures. There is no indication for the occurrence of the octahydrate in our experiments. Since the product of experimental volume and suspension time is equal to that of stratospheric droplets over an entire winter, the homogeneous formation of the octahydrate at quasi-thermodynamic equilibrium can be practically excluded.