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Vapor Pressure and Atmospheric Pressure

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From what I have read so far, the vapor pressure of a liquid is temperature dependent while it is independent of the atmospheric pressure. I am not sure why atmospheric pressure would have no effect of the vapor pressure though. For example, if a highly volatile liquid is placed in a sealed container, and I increase the pressure inside the container to an extremely high value, wouldn't the high pressure make it harder for the volatile liquid to evaporate?

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