# pH range outside conventional 0-14 [duplicate]

Is a pH value outside 0 - 14 possible? I asked my teacher who said: yes, it is, but very difficult to achieve.

Then on the internet, I found multiple answers, one saying it is but because of a fault in the pH glass meter we can't be sure, the other said that it is not possible because of the intrinsic value of water to ionize. As you can see, I'm getting mixed answers from different sources and I'm really confused now. Could somebody here give a concise answer whether or not it is possible? A deep argument will be valuable.

Let me add a bit more to the answers already given. As has been said, $\mathrm{pH}$ is nothing but a measure of the activity of protons ($\ce{H+}$) in a solvent - $\displaystyle\mathrm{pH} = -\log_{10} \ce{\ a_{H_{\text{solvated}}^{+}}}$. In dilute solutions, a solute's activity is approximately equal to its concentration, and so you can get away with saying $\mathrm{pH} = -\log_{10} \ce{[H_{solvated}^{+}]}$.

The "normal" aqueous $\mathrm{pH}$ scale that goes from 0-14 delimits the region where both $\ce{[H^{+}]}$ and $\ce{[OH^{-}]}$ are lower than $\pu{1 mol L^{-1}}$, which is about the upper limit where concentrations and activities of solutes in solution are approximately the same and they can be used interchangeably without introducing too much error.

(The reason this is true is because a solute in a very dilute solution behaves as if it surrounded by an infinite amount of solvent; there are so few solute species that they interact very little with each other on average. This view breaks down at high concentrations because now the solute species aren't far enough apart on average, and so the intermolecular interactions aren't quite the same.)

Not only is it rarer to talk about pH for very highly concentrated solutions, because activity has a much more subtle definition than concentration, but also because you have to produce quite concentrated solutions to get unusual values of pH. For example, very approximately, to get a litre of an aqueous solution of $\mathrm{pH} = -1$ using hydrogen perchlorate ($\ce{HClO4}$, a very strong monoprotic acid) you would need to dissolve around $\pu{1 kg}$ of $\ce{HClO4}$ in a few hundred $\pu{mL}$ of water. A litre of $\mathrm{pH} = 15$ aqueous solution using potassium hydroxide ($\ce{KOH}$) would also require several hundred grams of the hydroxide in about as much water. It's so much acid/base in a small amount of solvent that many acids/bases can't even dissolve well enough to reach the required concentrations.

There is also another way to come across unusual values of pH. We almost always talk about acids in bases in water, but they also exist in other media. Notice that in the definition of pH, no direct reference is made to water. It just happens that, for water, we have:

$$\ce{H2O (l) <=> H^+ (aq) + OH^{-} (aq)} \\ K^{\pu{25^\circ C}}_{\text{autodissociation}}=k^{\pu{25^\circ C}}_\mathrm{w}=a_{\ce{H^+(aq)}} \times a_{\ce{OH^- (aq)} } \simeq \ce{[H^{+}]} \times \ce{[OH^{-}]} = 1.01\times 10^{-14}$$ $$\mathrm{pH}+\mathrm{pOH}=-\log\ k_\mathrm{w} \simeq 14 \ (25^\circ C)$$

However, for liquid ammonia, one has:

$$\ce{NH3{(l)} <=> H^+{(am)} + NH2^{-}{(am)}} \\ K^{\pu{-50^\circ C}}_{\text{autodissociation}}=k^{\pu{-50^\circ C}}_\mathrm{am}=a_{\ce{H^+(am)}} \times a_{\ce{NH2^- (am)} } \simeq \ce{[H^{+}]} \times \ce{[NH2^{-}]} = 10^{-33}$$ $$\mathrm{pH}+\mathrm{p}\ce{NH2}=-\log\ k_{\mathrm{am}} \simeq 33 \ (-\pu{50^\circ C})$$

($\ce{(am)}$ stands for a substance solvated by ammonia). Hence, in liquid ammonia at $-50^\circ C$, the pH scale can easily go all the way from 0 to 33 (of course, it can go a little lower and higher still, but again now activities become important), and that neutral pH is actually 16.5.

For pure liquid hydrogen sulfate (some difficulties arise as $\ce{H2SO4}$ is a diprotic acid and tends to decompose itself when pure, but putting that aside and looking only at the first dissociation):

$$\ce{H2SO4{(l)} <=> H^+{(hs)} + HSO4^{-}{(hs)}}\\ K^{\pu{25^\circ C}}_{\text{autodissociation}}=k^{\pu{25^\circ C}}_\mathrm{hs}=a_{\ce{H^+(hs)}} \times a_{\ce{HSO4^- (hs)} } \simeq \ce{[H^{+}]} \times \ce{[HSO4-]} \simeq 10^{-3}$$ $$\mathrm{pH}+\mathrm{p}\ce{HSO4}=-\log\ k_{\mathrm{hs}} \simeq 3 \ (\pu{25^\circ C})$$

($\ce{(hs)}$ stands for a substance solvated by hydrogen sulfate). Thus, the pH in liquid hydrogen sulfate has a much smaller range than in water and ammonia, not going much further than interval from 0 to 3.

Notice also that not only does the range of $\mathrm{pH}$s change in each solvent, but there is no direct relationship between the values of pH between different solvents; formic acid in ammonia would behave as a strong acid and as such a $\pu{1 M}$ solution in ammonia would have a pH close to 0, but formic acid is actually a base in liquid hydrogen sulfate, and as such a $\pu{1 M}$ solution would have a pH above 1.5. An approximate comparison between the pH ranges and their relative positions in different solvents can be found in the figure below, from A Unified pH Scale for All Phases.

• WOW! Never thought about pH in this way. This really enlightens me! I always thought pH is simply the acidity of something, but apparently acidity is determined by other factors and pH itself is not always good. I especially like the example you gave with pH and pNH2, never knew that was even possible! – user209347 Nov 20 '13 at 18:43
• @user209347 One of the best easy ways I've seen to define acidity is to calculate how willing a substance $A$ is to accept $H^+$. The less willing it is, the stronger an acid the substance $HA^+$ is. For example, $NH_3$ can somewhat easily accept $H^+$ forming $NH^+_4$, so $NH^+_4$ isn't a very strong acid. Meanwhile, $He$ is notoriously unreactive, so it would very weakly accept $H^+$ to form $HeH^+$. This in turn means that $HeH^+$ is a fantastically strong acid, around $10^{50}$ times stronger than sulphuric acid. – Nicolau Saker Neto Nov 20 '13 at 19:34
• Using the same concept, a strong base can be determined by how much energy would be released when a substance absorbs $H^+$ (the more energy released, the more willing it is). A common example of a superbase is the methide anion, $CH^-_3$ (in other words, methane ($CH_4$) is an exceptionally weak acid). There are other ways to analyse acidity and basicity via the Hammett acidity function and others, though in this case it's more difficult because again activity has to be used instead of concentrations. – Nicolau Saker Neto Nov 20 '13 at 19:40
• A small errata: $HeH^+$ is approximately $10^{60}$ times stronger than sulphuric acid. That's a trillion trillion trillion trillion trillion times stronger! More information can be found here. – Nicolau Saker Neto Nov 20 '13 at 19:46

In short, it is possible to have pH outside of this range. However, in such cases, pH fails to be a useful or even meaningful measure. In concentrated solutions, one should use concentration directly.

From a practical point of view, pH helps to bring extremely small H+ concentrations to a more familiar range of numbers, but as the concentrations become larger this practice loses its value and becomes counterproductive instead.

From a theoretical point of view, pH as an acidity measure is based on the assumption that water does not have a varying concentration. However in concentrated solutions, because of the lowering concentration of H2O itself you may find H+ concentration decrease as more acid is added.

Further complicating this, in water H+ is a simplified notation for H3O+ as H+ by itself actually ever exist in any solution, in concentrated solutions, it becomes ambiguous what H+ may refer.

For example, the notation "98%(w/w) sulfuric acid" would be much more practically useful than "a sulfuric acid with a pH of -2.25". Not to mention there is no such thing as a "H+" concentration in that situation because it is not clear which one of the many species (H3O+, H3SO4+, HSO3+,...) would be referred to as H+, and anyway you choose that H+ concentration will most likely turn out to be even lower than a 50% sulfuric acid solution.

• I imagine that all solvated protons contribute to the acidity of a mixture, rather than picking one form as representative for a pH calculation. Of course, figuring out the exact quantities of each species and their activity coefficients must be a demanding task. – Nicolau Saker Neto Nov 19 '13 at 22:47
• @NicolauSakerNeto Yes, summation over all solvated proton species would make the most sense. And it would be demanding indeed! I imagine one particular difficulty is that theories for predicting activity coefficients only work well toward high dilutions, and even those corrected for higher concentration will usually only treat binary mixtures of a single salt(or acid) and water, and also fail for some binary systems. – Xiaolei Zhu Nov 20 '13 at 2:00

From its definition:

pH = -log [H+]

If [H+] is greater than 1, the pH will be negative. For example, HCl at 40% minimum.

For a pH greater than 14 are necessary highly concentrated basic solutions.

• So it is possible? Could you elaborate more? – user209347 Nov 19 '13 at 18:47