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Evaporation rates of K2O, Na2O, and FeO from chondrule-like liquids and the associated potassium isotopic fractionation of the evaporation residues were measured to help understand the processes and conditions that affected the chemical and isotopic compositions of olivine-rich Type IA and Type IIA chondrules from Semarkona. Both types of chondrules show evidence of having been significantly or totally molten. However, these chondrules do not have large or systematic potassium isotopic fractionation of the sort found in the laboratory evaporation experiments. The experimental results reported here provide new data regarding the evaporation kinetics of sodium and potassium from a chondrule-like melt and the potassium isotopic fractionation of evaporation residues run under various conditions ranging from high vacuum to pressures of one bar of H2+CO2, or H2, or helium. The lack of systematic isotopic fractionation of potassium in the Type IIA and Type IA chondrules compared with what is found in the vacuum and one-bar evaporation residues is interpreted as indicating that they evolved in a partially closed system where the residence time of the surrounding gas was sufficiently long for it to have become saturated in the evaporating species and for isotopic equilibration between the gas and the melt. A diffusion couple experiment juxtaposing chondrule-like melts with different potassium concentrations showed that the diffusivity of potassium is sufficiently fast at liquidus temperatures (DK>2-10-4cm2/s at 1650-C) that diffusion-limited evaporation cannot explain why, despite their having been molten, the Type IIA and Type IA chondrules show no systematic potassium isotopic fractionation.