IX: More About the Laws of Reaction Rates and of Equilibrium

IN A recent columnZ Mysels has exposed to light the confusion between the laws of reaction rates and of equilibrium existing in most textbooks. It may be appropriate to supplement this article by exposing the falsity of certain statements commonly found in these same textbo~ks ,~ relating to the historical side of these matters. Statements to the effect that Guldberg and Waage in 1867 clearly formulated in the law of mass action the fundamental relationship between velocity and concentration and that according to this law the velocity of a reaction a t constant temperature is proportional to the product of the concentrations of the reacting substances, are frequently found but are incorrect and misleading.

I shall first sketch the early history of kinetics, then the early history of equilibrium. I shall conclude by describing the contribution of Guldberg and Waage.

KINETICS

In 1850 Wilhelmy4 showed that the inversion of su- crose is first order with respect to sucrose and first order with respect to strong acid. It is important to observe that the second fact could not be predicted from the stoichiometric equation for the reaction.

In 1866 Harcourt6 showed that the reaction between HzOz and H I is first order with respect to H,Oz and first order with respect to iodide. Here again it is important that the second fact could not be predicted from the stoichiometric formula

In 1877 van't Hoff6 discussed the esterification

Suggestions of material suitable for this column are eagerly sought and will be acknowledged. They should be sent with as many details aa possible to Karol J. Mysels, Chemistry Deparb ment, University of Southern California, Los Angelea 7, Cali- fornia. Contributors of discussions in a form suitable for pub- lication directly will be acknowledged as guest authors.

MYSELS, I(ARoL J., J. CEEM. EDUC., 33,178 (1956). Since the purpose of this column is to prevent the spread and

continuation of errors and not the evaluation of individual texts, the source of the errors discussed will not be cited. The error must occur in a t least two independent standard books to be pre- sented. ~~ ~~~~~.

WILEELMY, L., Ann. Phgs. & Chem., 157, 413 (1850). HARCOURT, A. V.. J . Chem. Soc., 20,460 (1867).

4 VAN'T HOPF, J. H., Ber., 10, 669 (1877).

E. A. GUGGENHEIM University of Reading. England

equilibrium as a balance betmeen two opposed reac- tions.

In 1884 van't Hoff' quoting Pfaundler, whose puh- lished work I have been unable to trace, gave a kinetic treatment of both rates and equilibrium. After deriv- ing kinetic formulas for rates of all orders he mentions that experimental reaction rates are almost always uni- or bimolecular. He quotes as an example that the rate of

4PH8 - P, + 3H2

is first order. It is possible that there are relevant publications by

van't Hoff between 1877 and 1884, but I have not been able to trace them.

The important point, already stressed in Mysels' article, that the kinetic behavior of a particular reaction muet he determined experimentally and cannot be predicted from the stoichiometric formula was better appreciated by Wilhelmy, Harcourt, and van't Hoff than by many subsequent writers, especially writers of textbooks.

EQUILIBRIUM

In 1873 Horstmanns gave a correct thermodynamic derivation of the equilibrium conditions for the disso- ciation of CaC08 and that of PC&, including their tem- perature dependence, treating the vapor as a perfect gas. In 1877 Horstmanng gave a correct thermo- dynamic derivation of the equilibrium conditions for the dissociation of NH&OzNH4. Horstmann's treat- ment of these equilibria is applicable to any other equilibrium involving perfect gases. It is rather cum- brous because free energy was not yet invented, and the reasoning is in terms of energy and entropy, but apart from this matter of presentation the reasoning cannot be improved on.

There is little to add to Horstmann's exposition except its extension to solutions. This extension is closely tied to van? Hoff's treatment of dilute solutions and Gihbs' more powerful analytical approach.

'VAN'T HOFF, J. H., "Etudes de dynamique chimique," 1884. 8 HORSWNN, A., Ann. Chem. & Pharm., 170, 192 (1873);

Ostwald'~ Klassiker, 137. HORSTMANN, A., Verhand. Naturhist-Med. Ver. Heidelberg

1 ( 5 ) , 465 (1877); Ostwald's Klassiker, 137.

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VOLUME 33, NO. 11. NOVEMBER, 1956 545

CONTRIBUTION OF GULDBERG AND WAAGE

Waage was professor of chemistry in Christiania (Oslo), and his brother-in-law Guldberg was professor of mathematics in the same university. Although they published jointly,1° the chemistry and the mathematics may to a large extent be separated.

The most important contribution was experimental proof that in an incomplete reaction a definite equilib- rium is reached and can be approached from either direction. Almost all the experiments were on hetero- geneous systems containing solid phases and an aqueous solution. No experiments appear to have been made on systems containing gases.

From the outset the authors were confident that the condition for equilibrium a t a given temperature should be expressible mathematically in terms of the concen- trations (which they called" "active masses"). But the formulation of this condition was gradual, em- pirical, and slow. The published papers, spread over the period 1864 to 1879, covered about two hundred pages, and it is possible to give here only a brief outline of the development of the authors' ideas.

In 1865 Guldberg and Waage stated their law of '< mass action," namely, The driving force for a substitu- tion is under otherwise equal conditions directly propor- tional to the product of the masses each raised to some definite power, and, together with it, their law of "volume action," namely, When the same mass of a reacting substance i s present i n different volumes, the efect of this mass is inversely proportional to the volume. There are several comments to be made on this formulation. First, the formulation as two distinct laws is peculiarly abstract and could of course be replaced by a single law of concentration action. Second, the "definite power" to which a concentration was to be raised was, as we shall see, not an integral Dower deducible from

GULDBERG, C. M., AND P. WMGE, Forh. Vid. Selsk. Chris- tiania, 35, 92,111 (1864); "Etudes sur lea affinites chimiques," Christiania, 1867; J. Pmkt. Chem., 19, 69 (1879); Ostwald's Klassiker, 104. " GULDBERG, C. M., AND P. WAAGE, Ostwald's Klassiker, 104,

16.

the equation of the reaction, but an empirically deter- mined, usually irrational, number. They even sug- gested that. effectively complete reactions were due to a high ratio of the indices (for example: 150:l) occurring in the products relating to the forward and backward reactions. Third, the statements are concerned with driving force and do not mention rate of reaction. Guldberg and Waage tentatively suggested that the rate may be proportional to the driving force, but their study of rates was extremely sketchy.

The shifting attitude of Guldberg and Waage toward the mathematical formulation of the equilibrium condi- tion can be illustrated by quoting their successive expressions for the ester hydrolysis equilibrium,

EtOAo + HOH * HOAc + EtOH

'studied experimentally by Berthelot and Saint-Gilles.12 In 1864 they expressed the equilibrium condition as:

In 1867 they replaced this by the more complicated empirical relation: (HOAo)(EtOH) + 0.01843(HOAc)(EtOAc) +

0.00626(HOAc) (HOH) = 0.2372(EtOAc)(HOH) + 0.0372(EtOH)(EtOAc) + 0.00723(EtOH)(HOH)

In 1879 they a t last adopted the simple relation pub- lished by van't Hoff two years earlier:

To sum up, to Guldberg and Waage belongs the credit of being the first to appreciate qualitatively the nature of a balanced reaction. But they did not succeed in correctly formulating a quantitative expres- sion for the equilibrium condition until six years after Horstmann had done so for gases and two years after van't Hoff had done so for the ester hydrolysis. They made no significant contribution either experimental or theoretical to our knowledge of kinetics.

"BERTHELOT, M., AND P. SAINT-GILLES, Ann. ehim. Phys., 68, 225 (1863).

SYMPOSIUM ON THE FOUR-YEAR CURRICULUM IN CHEMISTRY

Tm Committee on Teaching of the Division of Chemical Education has proposed s. symposium , ' on the four-year chemistry curriculum for the fall meeting of the American Chemicd Society in September, 1957, at New York. The Chairman. Leallyn B. Clapp, Chemistry Department, Brawn University, Providence 12, Rhode Island, is anxious to hear from anyone interested in participating in this symposium. Reports of new ideas for the curriculum that are being discussed or tried experimentally are particularly welcome.