Oxoacid structures and acid strength

Reading an acid like a map

Phosphoric acid is in a cola. Sulphuric acid is in a car battery. Chloric(I) acid, HOCl, is in a swimming pool. All of them are oxoacids: acids where an atom from the p-block is bonded to oxygen atoms, and some of the oxygen atoms carry a hydrogen atom.

In the free courses of this chapter you met the simple oxoacids. Here we go deeper. The skill is to draw the structure from the formula, and then to read off everything else. Use these rules.

• The central atom (P, S or Cl) makes the bonds. We write each oxygen atom as one of four kinds: a double bond X=O, a hydroxyl group X-OH, a bridge X-O-X, or part of a peroxo link, O-O.
• A hydrogen atom on an oxygen atom, X-O-H, is acidic. A hydrogen atom bonded straight to the central atom, X-H, is not acidic. So the basicity of the acid is the number of X-OH groups.
• Oxygen counts as $-2$ and hydrogen as $+1$. In a peroxo link each oxygen atom counts as $-1$. A bond between two identical central atoms, X-X, does not change the oxidation state, because the two atoms share the electrons equally.
• The sum of all the oxidation states is zero for a molecule. If the acid has two central atoms, we get the average oxidation state of one atom.

The acids of phosphorus

Three acids you already know are $\text{H}_{3}\text{PO}_{2}$, $\text{H}_{3}\text{PO}_{3}$ and $\text{H}_{3}\text{PO}_{4}$. The picture shows four more.

• $\text{H}_{4}\text{P}_{2}\text{O}_{6}$, hypophosphoric acid, has a P-P bond. Each phosphorus atom has one P=O and two OH groups. Phosphorus is $+4$, and the acid is tetrabasic.
• $\text{H}_{4}\text{P}_{2}\text{O}_{5}$, pyrophosphorous acid, has a P-O-P bridge, and each phosphorus atom has one P-H bond. It is $+3$ and only dibasic, because the P-H hydrogen atoms are not acidic.
• $\text{H}_{4}\text{P}_{2}\text{O}_{7}$, pyrophosphoric acid, has a P-O-P bridge and four OH groups. It is $+5$ and tetrabasic. It forms when two molecules of $\text{H}_{3}\text{PO}_{4}$ lose one molecule of water.
• $(\text{HPO}_{3})_{3}$, trimetaphosphoric acid, is a ring of three phosphorus atoms joined through three oxygen atoms. Each phosphorus atom has one P=O and one OH group. The acid is tribasic and phosphorus is $+5$.

Count the average oxidation state of phosphorus in $\text{H}_{4}\text{P}_{2}\text{O}_{6}$. There are 6 oxygen atoms ($-12$) and 4 hydrogen atoms ($+4$). The two phosphorus atoms together must give $+8$, so each is $+4$. The P-P bond has no effect on the count.

The acids of sulphur

• $\text{H}_{2}\text{SO}_{3}$, sulphurous acid, has the structure S(=O)(OH)2 with a lone pair on sulphur. Sulphur is $+4$. The acid exists only in solution.
• $\text{H}_{2}\text{SO}_{4}$, sulphuric acid, has two S=O bonds and two OH groups. Sulphur is $+6$.
• $\text{H}_{2}\text{S}_{2}\text{O}_{7}$, disulphuric acid (pyrosulphuric acid), is the main part of oleum. It has an S-O-S bridge. Sulphur is $+6$. It gives two molecules of sulphuric acid with water: $\text{H}_{2}\text{S}_{2}\text{O}_{7}\ +\ \text{H}_{2}\text{O}\ \rightarrow \ 2\text{H}_{2}\text{SO}_{4}$.
• $\text{H}_{2}\text{S}_{2}\text{O}_{6}$, dithionic acid, has an S-S bond and sulphur at $+5$.
• $\text{H}_{2}\text{SO}_{5}$, peroxomonosulphuric acid (Caro's acid), has an O-O link. Sulphur is $+6$, and the two oxygen atoms of the link are $-1$ each.
• $\text{H}_{2}\text{S}_{2}\text{O}_{8}$, peroxodisulphuric acid (Marshall's acid), has an O-O link between two sulphate groups. Sulphur is $+6$.
• $\text{H}_{2}\text{S}_{2}\text{O}_{3}$, thiosulphuric acid, is sulphuric acid with one oxygen atom replaced by sulphur. The average state of sulphur is $+2$. One sulphur atom is $+6$ and the other, the added one, is $-2$.

Peroxodisulphate is a very strong oxidising agent. It oxidises manganese(II) to permanganate when a little silver ion is present: $2\text{Mn}^{2+}\ +\ 5\text{S}_{2}\text{O}_{8}^{2-}\ +\ 8\text{H}_{2}\text{O}\ \rightarrow \ 2\text{MnO}_{4}^{-}\ +\ 10\text{SO}_{4}^{2-}\ +\ 16\text{H}^{+}$. The acid also hydrolyses to hydrogen peroxide: $\text{H}_{2}\text{S}_{2}\text{O}_{8}\ +\ 2\text{H}_{2}\text{O}\ \rightarrow \ 2\text{H}_{2}\text{SO}_{4}\ +\ \text{H}_{2}\text{O}_{2}$. This was once a way to make hydrogen peroxide.

A rule for the nature of an acid. An O-O link makes an oxidising acid, because the peroxide oxygen atoms ($-1$) can fall to $-2$. A P-H bond or a low oxidation state, as in $\text{H}_{3}\text{PO}_{2}$, makes a reducing acid, because phosphorus can rise to $+5$.

Acid strength and Pauling's rules

Why is sulphuric acid so much stronger than sulphurous acid? Linus Pauling found a pattern. Write the acid as $\text{XO}_\text{n}(\text{OH})_\text{m}$. Here $n$ is the number of non-hydroxyl oxygen atoms, the oxygen atoms with no hydrogen. Then:

• the first pKa is about $8 - 5n$;
• each next hydrogen is weaker by about 5 pKa units, which is a factor of about 100 000.

Look at the graph. HOCl has $n = 0$ and pKa about 7.5. $\text{H}_{3}\text{PO}_{4}$ has $n = 1$ and pKa 2.15. Nitric acid has $n = 2$ and pKa about $-1.4$. Perchloric acid has $n = 3$ and pKa about $-10$. The real values lie within a few units of the line. The rule is a guide, not a law. Ethanoic acid, CH3COOH, also has $n = 1$, but its pKa is 4.76.

The second and third pKa values of phosphoric acid are 7.20 and 12.35. They go up by about 5 units each time, as the rule says. The reason is charge. It is harder to take a proton from an ion that is already negative.

Why do the extra oxygen atoms make the acid stronger? There are two reasons. First, each oxygen atom pulls electron density from the central atom, and that pulls the bonding electrons of the O-H bond. The hydrogen leaves more easily. Second, after the proton leaves, the negative charge of the anion is spread over several oxygen atoms by resonance. In $\text{ClO}_{4}^{-}$ it is spread over four. A spread charge is more stable, so the anion is a weak base and the acid is strong.

The central atom matters too. For the halogen oxoacids HOX, the pKa rises from HOCl (about 7.5) to HOBr (about 8.6) and to HOI (about 10.6). A more electronegative central atom pulls the electrons more, so the acid is stronger.

Start with $n = 1$ and the first hydrogen. The rule gives 3. Now move $n$ to 3: the acid is 15 powers of ten stronger than at $n = 0$. Then set the hydrogen to the second and the third. Each step adds 5.

Practise with new numbers

Try it in Python

The program counts the oxygen and hydrogen atoms from the structure of each acid. Then it finds the average oxidation state of the central atom.

Common mistakes

• Counting every hydrogen as acidic. The hydrogen atoms on P (or S) are not acidic. $\text{H}_{4}\text{P}_{2}\text{O}_{5}$ is dibasic, not tetrabasic.
• Treating the X-X bond as a change of state. A P-P or S-S bond between equal atoms does not change the oxidation state.
• Giving the peroxo oxygen atoms $-2$. In $\text{H}_{2}\text{S}_{2}\text{O}_{8}$ and $\text{H}_{2}\text{SO}_{5}$ the O-O link has oxygen at $-1$.
• Counting all oxygen atoms for $n$. Only the oxygen atoms without hydrogen count.
• Using the rule as exact. It is within about 2 or 3 units.

Remember these

• Basicity is the number of X-OH groups. X-H hydrogen atoms are not acidic.
• Peroxo links give oxidising acids. P-H bonds give reducing acids.
• Pauling: the first pKa is about $8 - 5n$, and each next hydrogen is about 5 units weaker.
• More oxygen atoms on the central atom, and more electronegative central atom, make a stronger acid.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. What is the oxidation state of sulphur in $\text{H}_{2}\text{S}_{2}\text{O}_{6}$? Does the S-S bond change it?

2. Why is $\text{H}_{2}\text{SO}_{5}$ a stronger oxidising agent than $\text{H}_{2}\text{SO}_{4}$?

3. By the rule, what is the first pKa of an acid with 2 non-hydroxyl oxygen atoms? Which acid in the list has about this strength?

4. How many moles of sodium hydroxide neutralise one mole of $\text{H}_{4}\text{P}_{2}\text{O}_{6}$?

References

• NCERT, Chemistry Part I for Class XII, the chapter The p-Block Elements, on the oxoacids of phosphorus, sulphur and chlorine.
• OpenStax, Chemistry 2e, Chapter 18 (the nonmetals), and Chapter 14, the section on the relative strengths of acids and bases, for the oxoacid trend.