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Direct measurements of the phase separation relative humidity (RH) and morphology of aerosol particles consisting of liquid organic and aqueous inorganic domains are presented. Single droplets of mixed phase composition are captured in a gradient force optical trap, and the evolving size, refractive index (RI), and morphology are characterized by cavity-enhanced Raman spectroscopy. Starting at a RH above the phase separation RH, the trapped particle is dried to lower RH and the transition to a phase-separated structure is inferred from distinct changes in the spectroscopic fingerprint. In particular, the phase separation RHs of droplets composed of aqueous solutions of polyethylene glycol (PEG-400)/ammonium sulfate and a mixture of C6-diacids/ammonium sulfate are probed, inferring the RH from the RI of the droplet immediately prior to phase separation. The observed phase separation RHs occur at RH marginally higher (at most 4%) than reported in previous measurements made from studies of particles deposited on hydrophobic surfaces by brightfield imaging. Clear evidence for the formation of phase-separated droplets of core-shell morphology is observed, although partially engulfed structures can also be inferred to form. Transitions between the different spectroscopic signatures of phase separation suggest that fluctuations in morphology can occur. For droplets that are repeatedly cycled through the phase separation RH, the water activity at phase separation is found to be remarkably reproducible (within ±0.0013) and is the same for the 1-phase to 2-phase transition and the 2-phase to 1-phase transition. By contrast, larger variation between the water activities at phase separation is observed for different droplets (typically ±0.02).