Particles can undergo different phase transitions in the atmosphere including deliquescence, liquid-liquid phase separation (LLPS), melting, and freezing. In this study, phase transitions of particles/droplets containing polyethylene glycol with a molar mass of 400 g mol-1 (PEG400) and ammonium sulfate (AS), i.e., PEG400-AS particles/droplets, were investigated at different organic-to-inorganic dry mass ratios (OIRs) under typical tropospheric temperatures and water activities (aw). The investigated droplets (60-100 μm) with or without LLPS in the closed system froze through homogeneous ice nucleation. At temperatures lower than 200 K, multiple ice nucleation events were observed within the same individual droplets at low aw. Droplets with and without LLPS shared similar lambda values at the same OIR according to the lambda approach indicating they form ice through the same mechanism. A parameterization of lambda values was provided which can be used to predict freezing temperature of aqueous PEG400-AS droplets. We found that adding AS reduces the temperature dependence of aw in aqueous PEG400 droplets. Assuming incorrectly that aw is temperature-independent for a constant droplet composition leads to a deviation between the experimental determined ice nucleation rate coefficients for droplets at OIR > 1 and the predicted values by the water-activity-based ice nucleation theory. We proposed a parameterization of temperature dependence of aw to minimize the deviations of the measured melting temperatures and nucleation rate coefficients from the corresponding predictions for aqueous PEG400-AS system.