A Procedure for Determining Formulas for the Simple p-Block Oxoacids Nicholas K. Kildahl Worcester Polytechnic Institute, Worcester. MA 01609

The formulas for the oxoacids of the p-block elements, shown in Table 1, baffle many high school and undergrad- uate students. This is understandable because these for- mulas, unlike those of halides and hydrides, do not seem to "make sense". (Boron hydrides are exceptions.)

Table 1. Formulas of the p-Block Oxoacids by Group

Group 13(3A) 14(4A) 15(5A) 16(6A) 17(7A) 18(8A)

ti3603 ti2C03 H N G HOF HNOz

H5Ga04 H4Ge04 H3AsD4 HzSe04 HBr04 H3As03 HzSeCb HBr03

HBrOz HBrO

For example, students readily predict that the hydride and halides of carbon should be CHd and C&, respectively, because these formulas follow directly from the positions of C, H, and X on the periodic table. However, students often see no clear connection between these formulas and the formula of carbonic acid, HzC03. Similarly, students are generally puzzled that the nitrogen oxoacid with the high- est oxidation state is HNOs, whereas for phosphorus, which is nitrogen's congener, it is H3POa.

Although students can learn to rationalize oxoacid for- mulas in terms of Lewis structures. VSEPR. and orbital hybridization ideas, very few could predict thk formulas in Table 1. Conswuentlv. thev havedifficultvevenrcmembcr- ". "

ing the formulas. Previous articles in this Journal have addressed the strengths (1) and nomenclature (2, 3) of oxoacids. Auseful mnemonic for remembering the formulas and charges of oxoanions has also appeared (4). However, no simple method for determining the formulas has been published. Similarly, most textbooks of general and inor- ganic chemistry start with the formulas and focus on the nomenclature and strendhs of oxoacids ( 5 4 . -

In his recent text (91, Wulfsberg eves an excellent discus- sionofaciditvand basicitvinauueoussolution. Hc Drcsents a procedure ibr developing the formulas of oxoaniok of the p-block elements that is based on the concept of the total coordination number (TCN) of the central atom in the molecule or ion. The TCN is defined as the total number of other atoms and nonbonding electron pairs around the central atom. For example, in C03'-, carbon has a TCN of three; and in PO4", phosphorus has a TCN of four. Al- though Wulfsberg's procedure is very useful and easy to

apply,it shedsnolight on the problem discussed above: The apparent lackofwnnection between the hydndennd halide f&ulas on the one hand, and the oxo&id and qxoanion formulas on the other. In this paper, I present a modifica- tion of Wulfsbere's urocedure that establishes the missine

- A .- connection.

Consider u-block element E in oxidation state n+ with m pairs of noibonding valence electrons. I will indicate this suedes bv the shorthand (:),En+. What is the formula for tke oxoahd of (:),E"+?

The first steo in obtaining this is to write the formula for the neutral hidroxide of (:),E"+. This will be (:),E(OH)., in exact correspondence with the halide and hydride formu- las. I call this hydroxide formula the parent formula. Since it has the same stoichiometry as the halide and 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 valves for 0x0 species of p-block elements, according to Wulfsberg, 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 mol- ecules to bring the coordination number into agreement with the acceptable value.

Table 2. Acceptable TCNs for the p-Block Elements in Oxoacids and Oxoanions

Period TCN

5,s 6 (highest oxidation state) 4 (lower oxidation states)

Of course, the removal of each water molecule entails the removal of one oxygen atom from the coordination sphere of E, and reduces the TCN by one. Likewise, the addition of each water molecule entails the addition of one oxygen atom to the coordination sphere of E, and increases the TCN by one. Additionor removalofx water molecules gives the oxoacid formula. H,. + .mEOi. +A. where n + m i x is an , ~ ,.--, ~,.-",. acceptable TCN.

An example is provided by the oxoacid of p+. The parent formula is P(OH16, with n = 5, m = 0, and n + m = 5. This exceeds the accentable TCN of four. so one H90 is removed to give H3P04.

It is to be noted that removal of water molecules insures that only neutral species are generated from the neutral parent hydroxide. Thus, there is no need for the student to worry about charge.

Below are a number of examples of the use of this proce- dure to determine oxoacid formulas.

1. 'Ib determine the axoacid of N5*

The parent formula is N(OHIS. The TCN in the parent formula is 5. The acceptable TCN is 3.

Volume 68 Number 12 December 1991 1001

Remove two H20 molecules. The oxoacid is HN03.

2. To determine the oxoacid of (:I2Cl3+

The oarent formula is (:)LXOH)r. . ." The ~ C N in the parent formula 5. The acceptable TCN is 4. Remove one Hz0 molecule The axoacid is HClO2.

3. 'Ib determine the oxoacid of (:IzP+

The parent form& is (:)zP(OH). The TCN in the narent formula is 3. The acceptable l ? 2 ~ is 4. Add one H20 molecule. The oxoacid is H3POz.

Althoueh there are no halides or hvdride of F. the ~ a r e n t fnnnuls still '.makes sense" in ten& of the charge-balance rule for writineformulas.Althwah the ~rocedurcaves the correct f o d a , i t does not prebiet the locatio& of the hydrogen atoms in this molecule.

4. To determine the oxoacid of 17+

The parent formula is I(OHI7. The TCN in the parent formula is 7. An acceptable TCN is 6. Remove one Hz0 molecule. The oxoacid is H5106.

Some chemists may object to writing the f o r m ~ l a N ( 0 H ) ~ because the analogous halides and hvdride are unknown. This objection mayhave some validity. However, two points may be made. First, N(OH)S is written only as an initial step in a procedurethat ultimately produces the correct formula. Second, if asked to predict the formula, for exam- ple, of the fluoride of N5+, studen& would correctly indicate NF5. The fact that this substance has not yet been made in no way invalidates the value of using this formula for predictions. The formula N(OH)S is similarly a very reason- able prediction.

Successful use of the procedure above requires two things from the students. They must be able to determine the positive oxidation states that are likely for the p-block elements, and they must memorize the acceptable TCN values in Table 2. Determining possible oxidation states of an element fmm its ~osi t ion in the wriodic table is nor- mally taught in high Hchool and then;epeated early in the college curriculum, and thus should present no problem.

The values of TCN correlate with the size (radius) of the central element in the appropriate oxidation state. For example, the radii in picometers of the trivalent cations of group 13 are B, 41; Al, 68; Ga, 76; In, 94; and T1,103. The relative increments in radius between successive elements are 66, 12,24, and lo%, respectively. This pattern of alter- nation suggests that the elements of period 2 will differ substantif;iiy in their chemistry from the elements of peri- ods 3 and 4 that are similar in size. In the same way, the elements of periods 5 and 6 that are also similar should differ from those in the preceding periods.

This gmuping based i n radius~omesponds with that in Table 2. based on TCN. A simple statement can provide some j;stification for what may a t first appear to the student to be an arbitrary listing of TCN values: The number of groups that can be attached to an ion increases with its radius. Of course, TCN depends not only on radius, but also on polarizing ability, which is a function of electro- negativity and of the ratio of charge to radius. TCN also depends on the number of available valence orbitals. How- ever, a t the high school and introductory college levels, discussion of these additional factors is u~eces&ry .

I h o ~ e that the orocedure developed in this Daper will prov~de a framewo;kthat helps studentsand traihfrsalike to understand nxoacid formulai. Althoueh it is essentiallv a modification of the approach develope$by ~ u l f s b e r ~ , thk procedure provides a connection between oxoacid formulas and formulas of halides and hydrides that has not been previously made

Acknowledgment I thank Ladislav H. Berka and Gary Wulfsberg for many

helpful comments on the manuscript.

Literature Cited 1. Mmme. M.; Abrams, K. J. Chem. Edvc 1985.62.4143. 2. Rodgers,G. E.; Stste,H. M.:Bivens,R. L. J Chrm. Educ 1987, €4,409-410, 3. Ferndim, W. C.: Loening, K; Adam, R, J. Chem. Educ 1978, 55, 3W1, and

references therein. 4. Hawkes,S. J. J. CkamEduc. 1990,67,149. 5. Cotlon.F.A.: Wikinson. GAduondIwnronl f Chemishu.5th Ed.: Wl1ev:NewYork. . . . .

pter3. .: Atkina, P. w ; Lsngfmd. C. H. InogMC Chemlrtry: Freeman: New

i, 1990: Chapter 5. W.;Beail. H. Ckamlslry fwEngineesandSriantists: Ssmders:Philadelphis,

);Chapter 4. 8. Brown, T. L.: LeMay, H. E. Chemistry, The Central Seieie, 4th Ed.; Rentice-Hall:

EnglewoodCIiffs, NJ, 1988; Chapter 17. 9. Wulbberg, G. P~imiples ofLkscriptiue Inorganic Ckamistry: BmaLsiCole: Monferey,

CA. 1987: Chapter 2.

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1002 Journal of Chemical Education