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The pH of pure liquid water depends on temperature. It is about pH = 7.0 at room temperature, pH = 6.1 at 100 °C, and pH = 7.5 at 0 °C. What happens to the pH (or to the ion product) of pure water when it freezes?

I assume that the proton transfer reactions $$\ce{2H2O <=> H3O+ + OH-}$$ $$\ce{H3O+ + H2O <=> H2O + H3O+}$$ $$\ce{H2O + OH- <=> OH- + H2O}$$ are too fast, so that any present $\ce{H3O+}$ and $\ce{OH-}$ cannot be easily trapped in the solid ice crystal when it grows. Does that mean that pure ice crystals are free of $\ce{H3O+}$ and $\ce{OH-}$ ions?

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According to Martin Chaplin's Water Dissociation and pH:

In ice, where the local hydrogen bonding rarely breaks to separate the constantly forming and re-associating ions, the dissociation constant is much lower (for example at $-4~\mathrm{^\circ C}$, $K_\mathrm{w} = 2 \times 10^{-20}~\mathrm{mol^2~L^{-2}}$).

So $[\ce{H+}] = 1.4 \times 10^{-10}~\mathrm{mol\ L^{-1}} \Longrightarrow \mathrm{p[\ce{H+}]} = 9.9$

For more information see Self-Dissociation and Protonic Charge Transport in Water and Ice Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences Vol. 247, No. 1251 (Oct. 21, 1958), pp. 505-533

This is a review article by Nobel Prize winner Manfred Eigen , after whom hydrated $\ce{H3O+}$ is sometimes referred to as the Eigen Ion.

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    $\begingroup$ Is pH even defined when you aren't dealing with an aqueous solution? $\endgroup$ – bon May 5 '16 at 14:03
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    $\begingroup$ @bon I would say "yes", the hydrogen ion has an activity in solvents other than water. denverinstrument.com/denverusa/media/pdf/… $\endgroup$ – DavePhD May 5 '16 at 14:11
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    $\begingroup$ I'd like to know how this was measured, since usually $\mathrm{pH}$ is a measure of a solution's conductivity. $\endgroup$ – ringo May 5 '16 at 20:00
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    $\begingroup$ @ringo The article is discussing 7 methods, one of which is d.c. conductivity measurement of ice. Hall effect and NMR are two of the others. One involves a.c. current. Some are related to dielectric constant. I can't say I fully understand the article. $\endgroup$ – DavePhD May 5 '16 at 20:20
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    $\begingroup$ I think it's worth remembering that in this case, pH + pOH = 14 doesn't apply anymore; we would have p[H+] + p[OH-] ~= 20, and so a p[H+] of 9.9 is actually just as neutral as pH 7 at 25°C. $\endgroup$ – Roberto May 6 '16 at 2:21
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$\mathrm{pH}$ is the aqueous concentration of $\ce{H3O+}$ or $\ce{H+}$ ions in soution. I would not say that ice lacks $\ce{H3O+}$ and $\ce{OH-}$ ions as ice's structure would allow for such, however, since the ions are not in aqueous solution, the material cannot rightfully have a "$\mathrm{pH}$" as we know it.

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    $\begingroup$ Why can't any material with a well defined hydrogen ion activity have a defined pH? $pH = -\log_{10}{a_H}$ $\endgroup$ – Curt F. May 6 '16 at 9:31
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    $\begingroup$ @CurtF. Because this "pH" does not compare against the pH as we know it. That is like comparing acidities of different compounds in different solvents. Hardly quantiatively useful. $\endgroup$ – Karl May 6 '16 at 14:46
  • $\begingroup$ I think when you say "as we know it", you probably meant "as I know it". With that substitution your argument gets to be a bit circular, doesn't it? And despite your claim, hydrogen ion activities are in fact "quantitatively" useful in non-aqueous solvents. $\endgroup$ – Curt F. May 6 '16 at 14:54
  • $\begingroup$ Of course you can transfer the principle to solids (see other answer), and use it as a new concept in its own right. But I'm not sure if the whole thing is sufficently similar to justify using the same names. (Which is the case for non-aqueous solutions.) $\endgroup$ – Karl May 6 '16 at 14:54
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    $\begingroup$ @CurtF. : A.K.'s claim doesn't seem to be impossibility of interpretation in other settings. It is the much more practical incomparability of these numbers in other settings. As the comments to the other answer point out, a "pH" of 9.9 in ice is approximately equivalent to a "pH" of 7 in water because the sum "pH + pOH = 20" approximately holds in ice (in specific conditions). So, is ice more basic that water because 9.9 > 7? If we were to put ice in contact with water, would ion exchange occur making the water more basic? What use is that number? $\endgroup$ – Eric Towers May 6 '16 at 20:10

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