# Phase Equilibrium of Liquid and Vapor Under External Pressure

In summary: The equilibrium is only between vapor and liquid. If you have a gas (air) above the liquid, then the equilibrium is still between vapor and liquid, but the pressure will be greater on the vapor side.
TL;DR Summary
Does the SVP of water vapor depend on external pressure (eg atmospheric pressure)?
Suppose you have a container of water at a given temperature T (say normal room temperature) with a vacuum above it. Presumably water will evaporate until there is sufficient vapor that the pressure of it above the water is the SVP for that temperature.

Now suppose that there is air above the water in a closed system. Is the pressure of the water vapor the same as in the former case? I really don't understand this, because on a phase diagram it would seem that given the pressure of the atmosphere is greater than the SVP of water, and therefore that the vapor, also under the same pressure from the air, cannot be in equilibrium with the water.

You do understand the difference between partial pressure and total pressure? For vapor/liquid equilibrium only the former matters (at least as long as we don't talk about boiling).

Hi Borek. Yes I understand that. But external pressure should affect the equilibrium shouldn't it? Take the famous block of ice at around zero degress Celsius with a heavy weight attached to it by a steel wire. The pressure of the wire on the ice causes some of it to turn to liquid (and the wire eventually moved through the entire blco with the water freezing behind it). Why does not external air pressure change the position of the equlibrium of water with respect to vapor. I think very possibly my conceptual difficulty with this is perhaps a question of the very different properties of molecules solids/liquids/vapors and the rate at which an equilibrium is established.

Is your definition of a closed container 'impervious to external pressure'? Then it ignores external lab conditions of air pressure, e.g., STP, but still is affected by external temperature changes.

There are definitely some effects of the total pressure on the SVP at a given temperature, but as long as we deal with pressures in the several atm range they are negligible.

Lord Jestocost and Chestermiller
Borek said:
There are definitely some effects of the total pressure on the SVP at a given temperature, but as long as we deal with pressures in the several atm range they are negligible.
Yes. The saturation vapor pressure changes by the so-called Poynting correction, which is small at a total pressure of 1 atm.

My definition of closed system was one at constant external pressure, but not thermally insulated.

I have thought more about my conceptual difficulty. Perhaps I can pose my misunderstanding in a different way. Take the phase diagram for water. Assume we have a closed contained with water, and air above it at 1 atmosphere at, say, 20Celsius. The phase diagram seems to suggest that there is a single phase under those conditions: namely water. But we all know that some energetic molecules would escape into the air and eventually there would be an equilibrium (note: not an open container: a closed system). Further, the vapor will increase the pressure on the liquid slightly. So how can the phase diagram suggest that there is only water, no vapor under these conditions? The pressure depicted in the phase diagram isn't just that of vapor is it? The pressure can be due to anything -- in this case the nearly inert components of air. The pressure on the water is one atmosphere, and the pressure on the vapor is one atmosphere.

You are aware that the phase diagram is for pure water, no air, right?

Chester, I think that is/was the nature of my conceptual difficult. If the pressure were applied with a piston in a sealed container, and if that pressure were greater than the SVP, there would be no vapor. If the pressure is due in whole or in part to another gas phase above the liquid, still a sealed system, then the equilibrium is more complex and must take into account another phase/component. I don't think many textbooks make that clear, in part because they immediately start talking about water boiling at 100Celsius under atmospheric pressure.

Thanks for all the replies.

The textbooks I am familiar with (engineering textbooks) make pretty clear what is involved.

## 1. What is phase equilibrium?

Phase equilibrium refers to the state in which two or more phases of a substance coexist in a system without any changes in their relative amounts. This means that the rate of transformation between the phases is equal in both directions, resulting in a stable system.

## 2. How does external pressure affect phase equilibrium?

External pressure can have a significant impact on phase equilibrium, as it can influence the boiling point and vapor pressure of a substance. When the external pressure is increased, the boiling point of a liquid also increases, and the vapor pressure decreases. This can lead to a shift in the equilibrium between the liquid and vapor phases.

## 3. What is the phase diagram of a substance?

A phase diagram is a graphical representation of the different phases of a substance at various combinations of temperature and pressure. It shows the conditions at which a substance exists as a solid, liquid, or gas, as well as the boundaries between these phases.

## 4. How is phase equilibrium affected by temperature?

Temperature plays a crucial role in phase equilibrium, as it determines the energy of the molecules in a substance. As temperature increases, the molecules have more energy and can overcome the intermolecular forces that keep them in a specific phase, resulting in a phase change. At equilibrium, the rate of phase change is equal in both directions, maintaining a stable system.

## 5. What are the factors that influence the phase equilibrium of a substance?

Several factors can affect the phase equilibrium of a substance, including temperature, pressure, and the nature of the substance itself. Other factors such as the presence of impurities, the container's size and shape, and the presence of a catalyst can also influence the equilibrium between phases.

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