The Heat of Neutralization and Quantum Theory

(Adolf Heydweiller. Neutralisationswärme u. Quantentheorie, Annalen der Physik (48) p. 681, 1915).

Heydweiller uses the expression for the energy of a system of \(N\) oscillators (frequency \(\nu\)) in Planck’s second form:

\[ \epsilon = N h\nu \left\{ \frac{1}{2} + \frac{1}{e^{\frac{h\nu}{kT}} - 1} \right\} \ldots \ldots \ldots \ldots \ldots \ldots (1) \]

From the work of Stark and Haber it has been shown that, in chemical transformations, the frequency determining the energy of the transformation is very close to the dispersion frequency. For room temperature (\(T \sim 300^\circ\)) and frequencies of the order \(10^{-15}\)—\(10^{-16}\), equation (1) takes the form:

\[ \epsilon = N \frac{h\nu}{2} \ldots \ldots \ldots \ldots \ldots \ldots \ldots (1') \]

The thermal effect of a reaction accompanied by the appearance of a bond of only one electron must, according to formula (1′), be proportional to the change in frequencies, the proportionality factor being \(N\frac{h}{2}\). Heydweiller examines the case of the combination of the ions \(H\) and \(OH\). The heat of combination in this case has been measured accurately and is so considerable that one may expect a large change in \(\nu\). Denoting the natural frequencies of \(H_2O\) by \(\nu_m\) and of \(OH\) by \(\nu_i\), one can calculate, on the basis of (1′), the change in frequencies that must occur if Planck’s theory is valid:

\[ \nu_m - \nu_i = 0.2895 \cdot 10^{15}\ \mathrm{sec}^{-1} \]

with an accuracy of up to \(1\%\).

If Drude’s theory is used, then the quantity \(\nu_m - \nu_i\) may be found from molecular refraction and magneto-optical constants. In doing so it is necessary to make the following assumptions: 1) the water molecule contains a fairly considerable number of strongly bound electrons of large

and of approximately identical frequency, and one weakly bound valence electron, which determines the phenomena of dispersion and magneto-optical rotation.

2) In electrolytic dissociation only the frequency of the valence electron changes. 3) All electrons are characterized by the normal value

\[ \frac{e}{m}=5.30\cdot 10^7 \]

(e.s.u.).

To calculate the molecular refractivity of the ion \(OH\), Heydweiller takes the results of his earlier works, which connect the electrical conductivity and density of alkaline hydroxides with their refraction. The corresponding measurements were made anew.

The change in frequencies found in this way is

\[ \nu_m-\nu_1=0.292\cdot 10^{15}\ \mathrm{sec}^{-1}\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ (3) \]

Formula \((1')\) is excellently confirmed. From this Heydweiller draws the conclusion that the hypotheses laid at the basis of the calculation of (2) and (3) are valid.

S. Vavilov.