Question

Oxoacids can be formed that involve several central atoms of the same chemical element. An example is ${\mathbf{H}}_{\mathbf{3}}{\mathbf{P}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{9}}$, which can be written ${\mathbf{P}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{6}}{\mathbf{\left(}\mathbf{OH}\mathbf{\right)}}_{\mathbf{3}}$(Sodium salts of these polyphosphoric acids are used as "builders" in detergents to improve their cleaning power.) In such a case, we expect acid strength to correlate approximately with the ratio of the number of lone oxygen atoms to the number of central atoms (this ratio is 6:3 for ${\mathbf{H}}_{\mathbf{3}}{\mathbf{P}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{9}}$, for example). Rank the following in order of increasing acid strength: ${\mathbf{H}}_{\mathbf{3}}{\mathbf{PO}}_{\mathbf{4}}\mathbf{,}{\mathbf{H}}_{\mathbf{3}}{\mathbf{P}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{9}}\mathbf{,}{\mathbf{H}}_{\mathbf{4}}{\mathbf{P}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{6}}\mathbf{,}{\mathbf{H}}_{\mathbf{4}}{\mathbf{P}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{7}}\mathbf{,}{\mathbf{H}}_{\mathbf{5}}{\mathbf{P}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{10}}$. Assume that no hydrogen atoms are directly bonded to phosphorus in these compounds.

Short answer

To increase acid strength, the following are listed.

${\mathrm{HPO}}_4<{\mathrm{H}}_4{\mathrm{P}}_2{\mathrm{O}}_6<{\mathrm{H}}_4{\mathrm{P}}_2{\mathrm{O}}_7<{\mathrm{H}}_3{\mathrm{P}}_3{\mathrm{O}}_{10}<{\mathrm{H}}_5{\mathrm{P}}_3{\mathrm{O}}_9$

Because considering the number of lone oxygen atoms to phosphorus atoms, the strongest acid is not the one with ten oxygen atoms.

Step-by-step solution

Increasing acid strength.

The order of increasing acid strength for the given compounds is shown below:

${\mathrm{H}}_3{\mathrm{PO}}_4,{\mathrm{H}}_3{\mathrm{P}}_3{\mathrm{O}}_9,{\mathrm{H}}_4{\mathrm{P}}_2{\mathrm{O}}_6,{\mathrm{H}}_4{\mathrm{P}}_2{\mathrm{O}}_7,{\mathrm{H}}_5{\mathrm{P}}_3{\mathrm{O}}_{10}$.

Determining the strongest acid.

The number of lone oxygen must be considered while determining which acid is the strongest and which is the weakest.

As a result, when looking at the given acids, see that the acid with the fewest lone oxygen atoms${\mathrm{H}}_3{\mathrm{P}}_3{\mathrm{O}}_9$ is the weakest. More importantly, simply follow this rule to obtain the strongest one:

${\mathrm{HPO}}_4<{\mathrm{H}}_4{\mathrm{P}}_2{\mathrm{O}}_6<{\mathrm{H}}_4{\mathrm{P}}_2{\mathrm{O}}_7<{\mathrm{H}}_3{\mathrm{P}}_3{\mathrm{O}}_{10}<{\mathrm{H}}_5{\mathrm{P}}_3{\mathrm{O}}_9$

Because considering the number of lone oxygen atoms to phosphorus atoms, the strongest acid is not the one with ten oxygen atoms.