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:

\[ \varepsilon = Nh\nu \left\{\frac{1}{2}+\frac{1}{e^{\frac{h\nu}{kT}}-1}\right\}\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ . \tag{1} \]

By the works 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:

\[ \varepsilon = N \frac{h\nu}{2}\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ .\ . \tag{1'} \]

The thermal effect of a reaction accompanied by a change in the bond of only one electron should, according to formula (1′), be proportional to the change in frequency, with the proportionality factor \(N \frac{h}{2}\). 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 may calculate, on the basis of (1′), the change in frequencies which should 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 one uses Drude’s theory, then the quantity \(\nu_m - \nu_i\) can be found from the molecular refraction and the 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 the same 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

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

(electrostatic units).

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

The change in frequencies found in this way is

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

Formula \((1')\) is excellently confirmed. From this Heydweiller concludes that the hypotheses underlying the calculation of (2) and (3) are valid.

S. Vavilov.