I've read that the partial pressure of oxygen in water will be the same as the partial pressure of oxygen in the atmosphere, but that the saturation of oxygen in water is dependent on factors like salinity and temperature. If the partial pressure of oxygen in water is equal to its partial pressure in the atmosphere, how is it possible that the concentration of dissolved oxygen in water can vary?
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Partial pressure in chemistry is only strictly defined for a gas in a mixture of gases. If a chemist were asked for the partial pressure of oxygen dissolved in water, I think the answer would be, "Huh? If it's dissolved in water then it's not in the gas phase any more, so it doesn't really have a partial pressure." Chemistry describes the linear relationship between the partial pressure of a gas above a liquid and the dissolved concentration (not partial pressure) of the gas dissolved in the liquid at equilibrium as Henry's Law.
Other fields, especially biology and medicine, have used the convention for a long time that the partial pressure of a gas dissolved in a liquid can be defined by imagining a liquid/gas interface at equilibrium and then observing the partial pressure of the gas in the gas phase. That's a likely explanation for why "the partial pressure of oxygen in water will be the same as the partial pressure of oxygen in the atmosphere." Under equilibrium conditions, this is true by definition according to this unpleasant and potentially confusing definition used in those other fields.
However, the physical reality is that Henry's law constant varies with temperature and salinity, and equilibrium conditions also often don't exist in the most interesting systems. That's why, for the same partial pressure of oxygen in the gas phase, the concentration of dissolved oxygen in water can vary.
