A steady-state elimination of a reaction intermediate in 1904 (C. L. Jungius) and a general statement of the condition in 1905 (E. Brunner)

The steady-state approximation of chemical kinetics is usually traced to Bodenstein (1913) and to Chapman and Underhill (1913), and is also called the "Bodenstein approximation". It sets the net rate of change of a low-concentration intermediate to zero and eliminates the intermediate algebraically. This note documents an earlier instance of that operation, in a reaction proceeding through consecutive chemical steps, and an early general statement of the condition. Related ideas had already been stated in words. Pringsheim (1887) wrote "es beginnt der stationäre Zustand" of the state in which an intermediate is formed as fast as it is consumed, and Nernst's textbook, citing him, said that its concentration becomes stationary; Ostwald (as reported by Jungius) held that an immediately consumed intermediate stays very small; and Bancroft (1900), within an equilibrium argument, noted that an intermediate used up as fast as formed changes the apparent order. In April 1904 C. L. Jungius, a doctoral candidate in Amsterdam, treated the decomposition of carbon monoxide as two reversible steps, CO ⇄ C + O and O + CO ⇄ CO₂. He argued that after a short initial period the rates of the two steps are equal, which here means that the net rate of change of [O] is zero. He solved for [O], substituted it, obtained an overall rate law free of the intermediate, and gave its two limiting forms. The paper appeared in Dutch (Amsterdam Academy, meeting of 23 April 1904) and in German (Z. phys. Chem. 49, 1904). In 1905 E. Brunner stated the condition for a general two-step reaction with one intermediate, together with the conditions under which it holds, and discussed its limiting cases. He did not solve the general case for the intermediate. He cites Jungius twice and notes that some of his considerations are found in similar form there. Within the sources listed in this note, Jungius's paper is the earliest I have found in which the steady-state condition is used algebraically to remove an intermediate from a rate law, rather than being stated in words or applied only at equilibrium. The claim concerns consecutive chemical steps (§3). Jungius's paper was read at the time: Brunner cited it; Mittasch, while claiming priority for the general content of two of its conclusions, wrote that Jungius's merit for a mathematical treatment was in no way diminished; and Bancroft abstracted it as showing "that the apparent reaction velocity may be abnormal even in cases where equilibrium is reached", adding "There is nothing new about this". Search snippets show it later listed in handbooks as a reference on stepwise reactions. In the accounts of the origin of the steady-state approximation that I examined (§5, including a full-text index search), neither Jungius nor Brunner is named. I claim no influence on Bodenstein or on Chapman and Underhill.