Wikipedia:Reference desk/Archives/Science/2018 October 22

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October 22

Question on Solvent Levelling

I am attempting this question on solvent levelling from my inorganic chem textbook. Firstly, the reference to figure 4.2 appears to be incorrect. That figure has nothing to do with solvent levelling, so I'm assuming they meant Figure 4.4. Part a) of the question is straight forward; perchloric acid and nitric acid are both fully dissociated in water, so they are too strong i.e. their conjugate bases are too weak to be studied; O^2- in water would be immediately protonated to form OH^-, the strongest possible base in water, so it is too strong to be studied, and; bicarbonate is a weak acid in water, hence carbonate is a weak base and is in the range where it can be studied. This can be quantitatively confirmed by showing that the pK_a values of the conjugate acids given in Table 4.1 are outside of the range for water given in Figure 4.4 for all except bicarbonate.

Part b) of the question is not so straight forward for me though. Referring to Figure 4.4 and Table 4.1, sulfuric acid has a very narrow range for acid-base discrimination. The pK_a value of perchloric acid is within the range, so it should be possible to study it in this medium, but both nitric and sulfuric acid appear to be too weak or, stated differently, their conjugate bases are too strong. This section of the textbook appears to back up my conclusions on nitric and perchloric acids by showing that perchloric is a weak acid in sulfuric medium, and that nitric acid is not simply protonated by sulfuric acid, but actually loses OH^- to it.

But how can HSO₄^- be too strong to be studied in sulfuric acid? After all, the autoprotolysis of sulfuric acid involves the formation of HSO₄^-. Thinking about this by analogy to water, would we say that OH^- is too strong a base to be studied in water? It is the strongest possible base, so I suppose in a sense you could say it's right on the borderline. But you can use an aqueous solution of very strong base to determine if any other base is stronger than hydroxide (increases its concentration) or weaker than it (reduces its concentration). With anhydrous sulfuric, we could add a strong base to get a large concentration of HSO₄^-, and then to test whether any other base was stronger or weaker than HSO₄^-, we add it and note the change in HSO₄^- concentration. What's more, the pH range for acid-base discrimination for sulfuric acid in Figure 4.4 wouldn't even place HSO₄^- on the borderline. It would have it 8 pH units away. The only other explanation I can think of is that the autoionization of sulfuric acid is complicated, and involves more than just the autoprotolysis reaction. This is unsatisfying though, as it amounts to me saying "oh well...stuff is complicated and whatever therefore the answer is the answer". I cannot actually draw out any conclusions as to how the complicated array of autoionization reactions influence the acid-base discrimination pH range.

The answer guide however, disagrees with my answer. In fact, it has it exactly backwards to what I reasoned. It does give the intuitive conclusion that HSO₄^- is not too strong. It doesn't actually answer the question with regard to whether perchloric is too strong or too weak though. Handschuh-^{talk to me} 04:53, 22 October 2018 (UTC)

Our article on perchloric acid says it is a stronger acid than sulfuric acid (your table says -10; our article says "-10,-15" citing two different sources). Sulfuric acid is -2 in your table, "-3, 1.99" in our article (but at least this one has two protons!). So clearly there's no protonating perchlorate to any large degree in sulfuric acid. But your figure gives the sulfuric acid range from -13 to -10 as the "effective pH in water" - I don't know why though I am suspicious maybe they meant to write perchloric there ?? (Except our article leveling effect has the same range on the same kind of table!) I would assume the conjugate base of any solvent ought to be a "strong base" in it just like KOH in water ... I mean, you can put a stronger base in a solvent and measure some slight difference from total dissociation, but it would take extra precision. I don't like the question because the whole philosophy of whether something "can be studied" is of course pretty absurd... it's amazing what people can study with a sufficiently roundabout mechanism. Wnt (talk) 13:58, 22 October 2018 (UTC)

I agree the question is not worded well, but reading between the lines, including the text's section on solvent leveling, I take "can be studied" to mean you must be able to determine its pK_a by titrating a solution of it in the solvent. You can only do that if the pK_a falls within the discriminating range of the solvent. Anyhow, as usual thanks for the very helpful answer Wnt. Handschuh-^{talk to me} 03:59, 23 October 2018 (UTC)

@Bobby1011: It still bothers me that the sulfuric acid "effective pH" range in our article matches your book. Is your book Schriver and Atkins 5th edition by any chance? Otherwise, I think there's something important I didn't understand about this. Wnt (talk) 12:37, 24 October 2018 (UTC)

Yes, that's the one. Shriver & Atkins 5th edition. Handschuh-^{talk to me} 21:15, 24 October 2018 (UTC)

Thinking about this further, it stands to reason that the acid-base discriminating range of water will be between the pK_a of H₃O⁺ (0) and the pK_a of water (or equivalently, the pK_b of OH^-) (14). If an acid has a pK_a within the range 0-14 it can be determined by titration in water, and likewise for a base that has a pK_b in that range. That range of 0-14 is reflected in Figure 4.4. If we apply the same reasoning to ammonia, then the pK_a of ammonium (9.26) and the pK_b of amide ion (38) also gives the range shown in the table of 9-38. Although it's tempting here to apply the equation pK_a + pK_b = pK_sol, which would show that the pK_sol for ammonia is ~47, I don't think that is correct. The literature value of pK_sol for ammonia is 33. The reason I think the equation fails is because it is meant for the autoprotolysis reaction in the pure solvent, but we are using the reaction constant for the protonation in water. So if we then apply the same reasoning to sulfuric acid, the range should be from the pK_a of H₃SO₄⁺ to the pK_a of H₂SO₄ (-2). I don't have a value for the lower bound (either the pK_a of H₃SO₄⁺ or the pK_b of H₂SO₄). But what I do have is the autoprotolysis constant from the article sulfuric acid which is given as 2.7×10⁻⁴ or pK_sol = 3.6. That confirms the narrow range of the sulfuric acid solvent's ability to discriminate, so we could guess at a range of about -6 to -2. Handschuh-^{talk to me} 09:39, 25 October 2018 (UTC)

For what it's worth, the "effective pH in water" appears to be based on the Hammett acidity function. This isn't just some typo - there's clearly some significant part of this story I don't understand. Wnt (talk) 04:31, 26 October 2018 (UTC)

I think what bobby1011/Handschuh says above makes sense. "The reason I think the equation fails is because it is meant for the autoprotolysis reaction in the pure solvent, but we are using the reaction constant for the protonation in water" Concepts like pH and pKa are based on an aqueous solvent system. While an analogous set of concepts exists for any protic solvent system (like ammonia or sulfuric acid), those values do not necessarily have a nice, easy relationship to the water based values. That is, whatever the analogue for pH is in sulfuric acid, those numbers probably don't have a nice linear relationship to the pH scale. That means that concepts like "pH-analogue in pure sulfuric acid" are going to be hard to translate to "what the pH would be in water". --Jayron32 11:16, 26 October 2018 (UTC)