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If I take a half full bottle of water, seal it with a pressure gauge, and wait a few days then it will be at equilibrium. If I observe the pressure, that would be the water vapor's pressure. However, if that water had a lot of dissolved gasses, like a soft drink full of Co2, does that mean the vapor pressure of Coke is more than water?

Restated, I'm wondering if the pressure from dissolved gasses escaping the liquid adds to the total vapor pressure of a liquid, or is there another term that describes the additional pressure that a carbonated soft drink causes beyond just pure water in a sealed container?

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  • $\begingroup$ Of course the vapor pressure of all ingredients contributes to the total vapor pressure (modulo interaction terms between species in the gas or liquid phase). $\endgroup$ – Jon Custer Nov 20 '17 at 23:46
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    $\begingroup$ Vapor pressure is normally defined for a pure component, not mixtures. Vapor-liquid equilibrium is involved for mixtures. For ideal mixtures, each component of the mixture contributes its own vapor pressure, according to its concentration in the liquid, and other components of the mixture do NOT affect each component's vapor pressure. For non-ideal mixtures (which is probably the case here), fugacity must be used to calculate the system pressure. Calculation of fugacity coefficients can be involved, and is associated with chemical engineering thermodynamics. $\endgroup$ – David White Jun 6 '18 at 2:39
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Vapor pressure is a property of a liquid, and depends on two things: temperature, and the presence of solutes or other liquids that interact significantly with the liquid. Temperature is assumed to be the same in both cases, so we compare the vapor pressure of water with the vapor pressure of Coke, which is water plus a bunch of non-volatile solutes and some dissolved CO2.

For a solution with one liquid and non-volatile solutes, Raoult's law states that the vapor pressure of an impure solution is always lower than that of a pure solution. So a non-carbonated drink has lower vapor pressure than pure water.

For carbonated drinks, the CO2 equilibrates inside the bottle according to Henry's Law, dissolving in the water at a concentration dependent on the partial pressure of the CO2 in the bottle. Since it's inert and equilibrated, it also behaves like a non-volatile solute, which further lowers the vapor pressure of the drink. So it turns out that the vapor pressure of Coke is actually lower than both pure water and non-carbonated drinks!

The reason for the counterintuitive answer is that the pressure inside a Coke bottle is mostly the partial pressure of CO2, not the vapor pressure of water.

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  • $\begingroup$ I seriously doubt that CO2 behaves like a non-volatile solute, and the answer above implies an assumption of ideal-solution behavior for every mixture. Most mixtures do not exhibit ideal-solution behavior ... fugacity coefficients need to be used to calculate the system pressure in these cases. $\endgroup$ – David White Jun 6 '18 at 2:45
  • $\begingroup$ @DavidWhite Is the deviation from ideal behavior large enough that this answer is qualitatively incorrect? $\endgroup$ – probably_someone Jun 6 '18 at 3:19
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    $\begingroup$ probably_someone, in my opinion, the answer is "yes". CO2 dissolves in water to make carbonic acid, and there is an equilibrium between CO2 in the vapor phase and carbonic acid in the liquid phase. An ideal solution would not involve this type of chemical reaction between CO2 and water. $\endgroup$ – David White Jun 6 '18 at 14:38

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