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I have confused myself when thinking about vapor-liquid equilibrium. The typical way that I saw PV diagrams explained is that the left edge of the two-phase region is the boiling point of the liquid (bubble point is the same as boiling point for pure liquids?). But as we know, liquids will always generate some vapor pressure when sitting in a container even well below its boiling point. So what is different about existing inside the two-phase part of the diagram?

Is the description of bubble point = boiling point incorrect, and the only way to land in the region from A to B in the picture is to compress the liquid so that there is simply no room for gas to exist?

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  • $\begingroup$ In the curve AB, you have all liquid. $\endgroup$ Commented Sep 22 at 10:01
  • $\begingroup$ All liquid? Or just negligible amounts of vapor? I still don't understand what it means to exist in the two-phase region. $\endgroup$ Commented Sep 22 at 11:57
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    $\begingroup$ The two phase region is BD $\endgroup$ Commented Sep 22 at 12:24
  • $\begingroup$ AB is all liquid in a closed container under a pressure higher than the equilibrium vapor pressure. $\endgroup$ Commented Sep 22 at 12:47
  • $\begingroup$ @ChetMiller Under pressure of an inert gas, say? That doesn't seem right. Is the point that inside a container not totally full of liquid, I'm supposed to include the entire container for the molar volume, which will always put me inside the two-phase region? If so, why do they refer to two-phase region as "boiling"? $\endgroup$ Commented Sep 22 at 21:40

3 Answers 3

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Let's see how this can be quantified.

For an equilibrium (saturated) mixture of liquid water and water vapor in the tank (2 phase region), let

$m=\mathrm{mass\ of\ water\ in\ tank}$
$x=\mathrm{mass\ fraction\ vapor\ in\ tank}$
$V=\mathrm{tank\ volume}$
$T=\mathrm{temperature}$
$P(T)=\mathrm{equilibrium\ vapor\ pressure\ at temperature}\ T$
$v_L(T)=\mathrm{specific\ volume\ of\ saturated\ liquid\ water\ at\ temperature}\ T$
and
$v_V(T)=\mathrm{specific\ volume\ of\ saturated\ water\ vapor\ at\ temperature}\ T$

then you can calculate the mass fraction of vapor of in the tank by writing: $$m(1-x)v_L+m(x)v_V=V$$ That is, the volume of saturated water vapor in the tank plus the volume of saturated liquid water in the tank must equal the (constant) tank volume. If you change the temperature, the fraction of vapor, the fraction of liquid, and the masses of vapor and liquid will change in order to preserve to total volume of the rigid container.

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  • $\begingroup$ This is not what the diagram is attempting to describe. $\endgroup$
    – jimchmst
    Commented Sep 24 at 21:25
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It would help to label the axes appropriately: the x-axis is volume at a given temperature for each isothermal line [A-B-D and N]; the y-axis is pressure of the gas, of the gas on the liquid or the mechanical force on the liquid from right to left. There is no air or inert gas present. This diagram is explained nicely in Maron and Prutton, "Principles of Physical Chemistry" pp 48 f.

At the right low gas pressure means no liquid; increasing pressure below the critical T eventually induces liquid formation in equilibrium; attempts to increase pressure simply increase liquid while decreasing vapor at constant pressure. Eventually there is no more vapor and pressure on the liquid measures the compressibility of the liquid.

Above the critical T the curves show the behavior of the gas to the various gas laws [whether empirical or actual laws depends on the author] eventually Boyles or the Ideal Gas Law. Again this is explained understandably in M&P.

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Following the orange arrow as the volume is reduced along the isotherm in the diagram below: enter image description here

We start with vapor which increases in pressure at constant T as it is compressed. At point D the substance begins to condense into liquid (therefore dew point). The amount of liquid increases between D and B as described in Chet Miller's answer until at point B only liquid is present. Further reduction in the volume results in a rapid increase in p as liquids are relatively incompressible.

If the direction of the process is reversed the liquid expands and pressure drops at constant T until point B is encountered and vapor begins to form (fittingly named the bubble point).

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  • $\begingroup$ Maybe my issue is more with terminology. This picture helps me: hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/vappre.html So in the two-phase region, you're describing the "volume" boiling phenomenon in that third picture? $\endgroup$ Commented Sep 26 at 3:50
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    $\begingroup$ Yes, the transition to increased vapor is described by the boiling picture since there is a disequilibrium between the pressure within the fluid and outside (the external or applied pressure). This is not the same as saying that the vapor pressure is not at equilibrium (which it isn't, but that alone will not lead to bubbles within the liquid). "Bubble point" is a historical label based on this observation of bubbles. $\endgroup$
    – Buck Thorn
    Commented Sep 26 at 10:27

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