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What does phase change from liquid to gas have to do with equality of vapor pressure and ambient pressure? I understand that at higher pressures more kinetic energy is needed for molecules in liquid to spread out to form bubbles of vapor since vapor has lower density than liquid which means that higher temperature is needed. But why should equality of vapor pressure and ambient pressure determine when phase change takes place?

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When the vapor pressure equals the applied ambient pressure the liquid can form vapor in the bulk liquid hence "boiling". To accurately measure this care must be taken to mix the liquid well and to prevent overheating. At lower vapor pressures evaporation is only from the exposed surfaces.

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