Monday, November 18, 2019

acid base - Why can't the strength of superacids be measured in water?


I learned about acid strength, that the strength of an acid increases with it's degree of ionization when solvated. So, in water, a strong acid is one where $\ce{[H_3O^+]}$ is large, which is equal to a low pH: $\mathrm{pH=-log[H_3O^+]}$.


Considering extreme cases, such as superacids, I have found out that other methods are used to measure their acidity (methods I don't really understand). My question is why is it impossible to simply get super high concentrations of $\ce{[H_3O^+]}$ in aqueous solutions of superacids, and use this to determine the acid strength. Also, is pH used as a measure of acidity outside of aqueous solutions?


I have come over the leveling effect, but I don't think I fully understand it. The way I understand it (for the case with water as solvent) is that basically any acid in water will protolyze $\ce{H2O}$ to $\ce{H3O+}$, making this the effective acid. I don't understand why this would affect the measured pH, as it is $\ce{[H_3O^+]}$ you are measuring.



Answer



Any acid-base reaction is always an equilibrium:


$$\ce{HA^1 + (A^2)- <=> (A^1)- + HA2}\tag{1}$$


and for each pair of acids $\ce{HA^1}$ and $\ce{HA^2}$ you could calculate a $K_\mathrm{a}$ value to determine one acid’s strength with respect to the other. This $K_\mathrm{a}$ value is typically calculated according to equation $(2)$ if $\ce{(A^2)-}$ (which does not have to feature a negative charge; I just wanted to avoid different descriptions for the two acids) is the solvent.


$$K_\mathrm{a} = \frac{[\ce{HA^2}][\ce{(A^1)-}]}{[\ce{HA^1}]}\tag{2}$$



If $\ce{(A^2)-}$ is $\ce{H2O}$ (i.e. $\ce{HA^2}$ is $\ce{H3O+}$) and the acid $\ce{HA^1}$ is a strong acid or a superacid, then this equation is of little use; the equilibrium $(1)$ will be strongly shifted towards the product side, the concentration $[\ce{HA^1}]$ will be very small and thus $K_\mathrm{a}$ very large. With ‘very small’, I mean that $[\ce{HA^1}]\approx10^{-10}$ — acid $\ce{HA^1}$ is said to be fully dissociated.


Exact measurements of $K_\mathrm{a}$ become very hard if not impossible because you would need to determine extremely minute concentrations. The concentrations $[\ce{HA^2}]$ and $[\ce{(A^1)-}]$ are of little help since:


$$[\ce{HA^2}] = [\ce{(A^1)-}] \approx c_0(\ce{HA^1})\tag{3}$$


This is the levelling effect of water: no matter how strong the acid, there is no acidic species stronger than $\ce{H3O+}$ that can survive in aqueous solution for extended time. Most importantly, consider two very strong acids with different $K_\mathrm{a}$ — e.g. one with $\mathrm{p}K_\mathrm{a} = -15$, the other with $-10$. They have a very different acidity, yet the concentrations of all relevant species in aqueous solutions will be nigh identical.


Therefore, a new, more expandable way to measure and compare the strengths of very strong acids was required.


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