Oxoacid Formulas

For a thorough review of acid/base behavior, see Chapter 13 of Concepts of Chemistry

The formulas for the oxoacids of the p-block elements, shown in Table 1, do not seem to "make sense" in the same way that do formulas of halides and hydrides (with the exception of boron hydrides). For example, it is easy to see that the hydride and halides of carbon should be CH₄ and CX₄, respectively. However, the connection between these formulas, which follow directly from the positions of C, H, and X in the periodic table, and that of carbonic acid, H₂CO₃, is not clear. Similarly, it is puzzling that the highest-oxidation-state oxoacid of N is HNO₃, whereas that of P, in the same family as N, is H₃PO₄. Although oxoacid formulas may be rationalized in terms of Lewis structures, VSEPR, and orbital hybridization ideas, to predict the formulas in Table 1 is more challenging. In this section, we present a procedure for predicting oxoacid formulas. The method is based on the concept of the total coordination number (TCN) of the central atom in a molecule or ion. The TCN is defined as the total number of other atoms and non-bonding electron pairs around the central atom. For example, in CO₃^2-, C has a TCN of 3; and in PO₄^3-, P has a TCN of 4.

Consider a p-block element, E, in oxidation state n+ and with m pairs of valence electrons. We will adopt the shorthand designation (:)_mEⁿ⁺ for this species. What is the formula for the oxoacid of (:)_mEⁿ⁺? The first step in obtaining this is to write the formula for the neutral hydroxide of (:)_mEⁿ⁺. This will be (:)_mE(OH)_n, in exact correspondence with the halide/hydride formulas. This may be called the parent formula. Since it has the same stoichiometry as the halide/hydride formulas, the parent formula provides the bridge between the latter and the final oxoacid formula. The TCN of E in the parent formula is n + m, which may or may not be an acceptable value for Eⁿ⁺. Acceptable TCN values for oxo species of p-block elements, according to Wulfsberg (see references at end of section), are given in Table 2. If n + m differs from the acceptable TCN, the parent formula is altered by removing (or occasionally adding) a sufficient number of water molecules to bring the coordination number into agreement with the acceptable value. Of course, the removal (addition) of each water molecule removes (adds) one oxygen atom from (to) the coordination sphere of E, and reduces (increases) the TCN by 1. Addition or removal of x water molecules gives the oxoacid formula, H_n+2xEO_n+x, where n+m+x is an acceptable TCN. An example is provided by the oxoacid of P5+. The parent formula is P(OH)₅, with n = 5, m = 0, and n+m = 5. This exceeds the acceptable TCN of 4. So one H₂O is removed to give H₃PO₄. Removal of water molecules insures that only neutral species are generated from the neutral parent hydroxide. There is thus no need to worry about charge at all. Given below are a number of examples of the use of this procedure to determine oxoacid formulas.

Note that although there are no halides or hydride of P¹⁺, the parent formula still "makes sense" in terms of the charge balance rule for writing formulas. Note also that although the procedure gives the correct formula, it does not predict the locations of the hydrogen atoms in this molecule.

Successful use of the procedure above requires 1), the ability to determine the likely positive oxidation states of the p-block elements; and 2), memorization of the acceptable TCN values in Table 2. The values of TCN correlate with size (radius) of the central element in the appropriate oxidation state. For example, the radii in picometers of the 3+ ions of group 13 are B, 41; Al, 68; Ga, 76; In, 94; and Tl,103. The relative increments in radius between successive elements, in percent, are 66, 12, 24, and 10, respectively. This pattern of alternation suggests that the period 2 element will differ substantially from the elements of periods 3 and 4, which are similar in size; and that the elements of periods 5 and 6, also similar, should differ from those in the preceding periods. This grouping based on radius corresponds with that in Table 2, based on TCN. A simple statement to the effect that the number of groups that can be attached to an ion increases with its radius then provides some justification for what may at first appear to be an arbitrary listing of TCN values. (Of course, TCN depends not only on radius, but also on polarizing ability (a function of charge-to-radius ratio and electronegativity) and the number of available valence orbitals.

Example: Titanium Ti⁴⁺ Ti(OH)₄ TCN expected to be 6, giving H₈TiO₆.
Because #H > #O, the hydroxide formula is preferred.

Aluminum The "oxoacid" is probably better represented as Al(OH)₃ rather than as in the table.

Also, formulas for possible oxo cations can be obtained by partially dehydrating the hydroxide (recall that complete dehydration gives the oxide).

The following references may be consulted for more on this subject.