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Triple points and triple lines for pure substances and mixtures

My understanding is that pure substances can have triple points. But mixtures of substances have triple lines, i.e. there isn't a single point but a one-dimensional path in $PT$ space where three phases can coexist.

This is understanding comes from the Gibbs phase rule that $F = C - P + 2$, where $F$ is the degrees of freedom, $C$ is the number of components, and $P$ is the number of phases. At a triple point (or triple line) $P = 3$. For a two-component system like a mixture of ethanol and water, $C = 2$. If we apply the equation, then we find that in this case, $F = 1$, i.e. there is one degree of freedom. If we pick $P$ then $T$ is defined for us by the constraints of any two-component, three-phase system. That's a "triple line". For a one-component system, the equation says that if $C = 1$ and $P = 3$, then $F = 0$. A triple point. We don't get to pick either $P$ or $T$.

Water isn't exactly a pure substance

But, ordinary water is not actually a pure substance. It is a mixture of different isotopologues, e.g. $\ce{HDO}$ and $\ce{H2^{18}O}$, etc. It is also a mixture of para- and ortho-isomers that differ only in the relative spin states of the two $\ce{H}$ atoms, as I learned from reading this very site the other day.

Does ordinary water have a triple point?

Pure $\ce{D2O}$ has a triple point distinct from that of $\ce{H2O}$. For example, one web site says that $\ce{H2O}$ has a triple point of 612 Pa and 0.01 °C, while $\ce{D2O}$ reportedly has a triple point of 661 Pa and 3.82 °C. But most (all?) water samples in the world are not 100% isotopically pure. And very little work has been done separating para- and ortho spin isomers of water.

So given that water isn't a pure substance, how does it have a well-defined triple point? "The" triple point of water was until recently fixed by the definition of SI units, so it seems that for most practical purposes the impurities in water don't matter much. Why not? What is the triple point of para-$\ce{H2O}$? Of ortho-$\ce{H2O}$? Of para-$\ce{H2^{18}O}$? Etc. etc. etc. Why doesn't the phase rule apply to these species?

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    $\begingroup$ Interesting question. The Comité International des Poids et Mesures (CPIM) defines the triple point of water using VSMOW (en.wikipedia.org/wiki/Vienna_Standard_Mean_Ocean_Water), and VSMOW has multiple components. So essentially you're asking, given the Gibbs phase rule, how the international standard for water's triple point can be based on a substance with multiple components. $\endgroup$ – theorist Jun 15 at 1:00
  • $\begingroup$ When a solution of glucose in water boils or freezes, the composition of the solution changes because glucose stays in the liquid phase. I'm not aware that it is possible to enrich isotopologues of water by freezing or boiling (e.g. ice can accommodate the different isotopes and does not crystallize into separate crystal lattices). If that is the case, the composition of "pure" water does not change, so maybe the number of components is one after all. $\endgroup$ – Karsten Theis Jun 15 at 1:37
  • $\begingroup$ @theorist From the wikipedia article you quote: "Fresh distilled VSMOW water is also used for making high accuracy measurement of water's physical properties and for defining laboratory standards since it is considered to be representative of average ocean water, in effect representing all water on Earth." So they remove the solutes first before doing any measurements. $\endgroup$ – Karsten Theis Jun 15 at 1:38
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    $\begingroup$ @KarstenTheis The OP's concern about 'multiple components' referred not to solutes, but to the multiple isotopic (and other) components of pure water itself. And VSMOW's own definition (see, specifically, en.wikipedia.org/wiki/…) provides a perfect example of this. So yes, the solutes are removed (as much as possible) from VSMOW but this still leaves, by the VSMOW specification itself, its multiple isotopic components, each with different physical properties. $\endgroup$ – theorist Jun 15 at 1:55
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Summarizing the relevant point (pun intended) of my answer to a related post: a mixture does not exhibit a "triple line" if its composition is constant. It is only a "triple line" insofar as you get to vary the proportion (mole fractions) of the components. Therefore different samples of water with different isotopic composition will differ in the value of the TP, but for a given sample the TP is just that, a single constant point (not a line).

This question however does point out a very important problem for the implementation of the standards adopted during establishment of an absolute temperature scale based on the triple point of water. A good discussion of this is provided in white papers (1,2) from Isotech (manufaturers of triple point measurement apparatuses):

There are 3 main sources of error in a water triple point cell[6, 7] (excluding errors associated with measurement):

  • The isotopic composition of the cell’s water may not be that of SMOW.

  • There may be air trapped inside the cell.

  • There will be impurities in the water.

Isotopic composition can be measured to great accuracy from a small sample of the cell’s contents.

SMOW and V-SMOW are water samples of standard composition (this is amply discussed in Isotech white papers, referring also to the documentation behind the International Temperature Scale established in 1990 (ITS-90)):

\begin{array} {|r|r|} \hline \text{Component} & \text{Mole Fraction} \\ \hline \ce{^1H} & 0.999 842 \\ \ce{^2H} (\text{deuterium}) & 0.000 158 \\ \ce{^3H} (\text{tritium}) & 0 \\ \ce{^{16}O} & 0.997 640 \\ \ce{^{17}O} & 0.000 371 \\ \ce{^{18}O} & 0.001 989 \\ \hline \end{array}

A second white paper provides guidelines on consideration of these effects (see the section "Isotopic Composition"):

We think of water as $\ce{H2O}$, more precisely we should write $\ce{^1H2^{16}O}$. This has been termed ‘light’ water and is unobtainable. If it were obtainable it’s triple point would be approximately +0.008°C. In practice what we drink from the tap, and what is in the ocean is a soup of $\ce{^1H}$, $\ce{^2H}$ with $\ce{^{16}O}$, $\ce{^{17}O}$ and $\ce{^{18}O}$. This means real water does not have a single triple point temperature. Its ‘combination triple point’ will vary as the isotopic composition varies. This was understood more than 50 years ago and after much analysis of water from different sources recent temperature scales state that the water in a triple point cell shall have the isotopic composition of ocean water. Although not explicitly stated, there is a Standard Mean Ocean Water (SMOW) and it is assumed that the isotopic content of SMOW fulfils the ITS-90 requirements.

concluding:

Analysing the cell contents for isotopic composition is a useful and valid addition to the usual techniques of intercomparing cells and gives an accurate indication of the cells ideal triple point value. [...] Such cells, complete with isotopic analysis provide the closest association to the ITS-90 value of the water triple point and hence the KTTS Scale. It is now possible to produce cells, based on Stimpson’s original design which can be associated to V-SMOW within ±3mK and this is a smaller uncertainty than can be provided by traditional measurements.

References

  1. The Establishment of ITS-90 Water Triple Point References to ±2μK, and the Assessment of 100 Water Triple Point Cells Made Between 2001 and 2006, John P. Tavener and Nick Davies, Isothermal Technology Ltd. (England).

  2. The Water Triple Point - A Reference Cell Close to the ITS-90 Value. John P. Tavener & Anne Blundell. Northern Temperature Primary Laboratory, Pine Grove, Southport, Merseyside, PR9 9AG, England.

  3. Supplementary Information for the International Temperature Scale of 1990, BIPM. ISBN 92-822-2111-3.

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  • $\begingroup$ Very nice answer, thank you. For the mixture composition to be constant, doesn't that mean the composition of each phase at the triple point (ice, steam, and liquid water) must be the same as the other two? At the triple point, would that really be true? Or am I misinterpreting what you are saying? $\endgroup$ – Curt F. Jun 17 at 3:19
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    $\begingroup$ @CurtF. Basically all the phases have to remain at constant composition but they don't have to be equivalent, only each component has to have balanced chemical potential across phases according to Raoult's law or equivalent (for practical purposes). In practice you can have problems (see the isotech white papers) with preferential evaporation or freezing of a particular isotopic consituent, so that you essentially deplete that component from your solution (same principle as in distillation). If you operate in a closed chamber apparently there are ways around this, to obtain reproducibility. $\endgroup$ – Buck Thorn Jun 17 at 8:07

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