The author replies to Jensen.

Regarding Campbell's Rule

With the exception of the cases for which ∆n_g = 0 in both Tables 1 and 2 of Campbell’s paper (3), the unremarked omission of the Trouton’s rule value in Table 1 (3), and the unremarked correction in the first entry of Table 2 (3), for which ∆_rS° = 64 J (K mol rxn)^–1 for ∆n_g = 0.5, the remaining 18 values from Tables 1 and 2 were incorporated in computing the reported average of 136 J (K mol rxn)^–1 mol^–1. Unfortunately, some errors crept into Table 1 in ref 1. The corrections are:

∆_rS° = 181.8 J (K mol rxn)^–1 and an unchanged ratio for H₂O₂(l) → H₂O(g) + ½O₂(g);

a ratio of 136 J (K mol rxn)^–1 for Fe(c) + 5CO(g) → Fe(CO)₅(l);

and ∆_rS° = 108.3 J (K mol rxn)^–1 for HgO(c) → Hg(l) + ½O₂(g) and a corresponding ratio of 217 J (K mol rxn)^–1 mol^–1.

The average ratio for the data in Table 1 (1) becomes 149 J (K mol rxn)^–1 mol^–1. With these revisions and three revised values from the two tables in Campbell’s paper, the straight line fit to all the data, including reactions for which ∆n_g = 0, becomes ∆_rS° = 1.9 + 130.1∆n_g (R = 0.98). This result gives an estimate of the Campbell’s rule value of 132 J (K mol rxn)^–1 mol^–1, which is the same as the value derived recently from ab initio calculations of molecular properties by Watson and Eisenstein for reactions of gases only (4).

The cause of the discrepancy between the average value of about 140 J (K mol rxn)^–1 mol^–1 reported in ref 1 and Jensen’s value found from fitting a straight line is an overlooked consequence of the averaging process. In the averaging process all of the data were taken as positive. If the same data as used for the fit given above, but made positive, are fit to a straight line, the result is ∆_rS° = 16.8 + 121.3∆n_g (R = 0.96), which is, of course, comparable to averaging to obtain a value of about 140 J (K mol rxn)^–1 mol^–1 reported in ref 1. The big discrepancy arises from the unexpectedly large intercept value of 16.8. Jensen makes a similar observation. When negative values as well as positive values are used in the fitting, a reasonable intercept near zero for ∆n_g = 0 is obtained.

Because Campbell’s rule is numerically approximate with an uncertainty range of about ±40% (23% statistical average), we must be careful not to put a fine point on its value. The numerical value depends on the choice of reactions used in illustrating the rule. In Campbell’s tables (3), species are gases with few exceptions, but the stoichiometry varies. In Table 1 in ref 1, a more varied set of reactions involving solids and liquids along with different stoichiometries is given. Of course, a great number of reactions could be considered to obtain a statistically “more significant” value for the rule. In addition, as Jensen points out, the participation of exceptionally light H₂(g) or H(g) in a reaction makes significant differences in ∆_rS°. In view of these complications, the selection of a value for Campbell’s rule rests on judgment as much as on statistics.

Literature Cited

1. Craig, N. C. J. Chem. Educ. 2003, 80, 1432–1436.
2. Jensen, W. B. J. Chem. Educ. 2004, 81, 1570.
3. Campbell, J. A. J. Chem. Educ. 1985, 62, 231.
4. Watson, L. A.; Eisenstein, O. J. Chem. Educ. 2002, 79, 1269–1277.