CHEMISTRY AND ELECTRONIC PHENOMENA.

N. N. Semenov.

Introduction.

Perhaps in insufficient accord with the generality and broad title of this article, the sole subject of discussion in it is a certain equation given by Born (M. Born). This equation follows directly from the law of conservation of energy and comprises, on the one hand, purely chemical—or, more precisely, thermochemical—quantities, and, on the other, certain physical quantities from the field of electronic phenomena. It might seem that, since the law of conservation of energy is unquestionably valid and since there is no reason to doubt the correctness of our general electronic conceptions, the equation under consideration must, obviously, be justified, and the whole question is essentially devoid of any practical interest. In what follows I shall attempt to show that the questions connected with this—at first glance—narrow topic are of exceptional interest and great significance.

1) Electronic conceptions have always been the guiding thread that has directed the investigations of physicists during the last quarter of a century; all the results we obtain we interpret and classify by means of these conceptions. However, if we believe in the reality of these conceptions, one cannot fail to acknowledge the possibility of another point of view. For perhaps this is only a more or less successful working hypothesis, applicable only to the circle of phenomena for which it was created; perhaps all our experiments mean something quite different, and do not have the meaning that we ascribe to them. To prove that this is not so, that electronic conceptions have a universal character, it would be necessary to show that, by applying the results we have obtained—in precisely the interpretation of them that we give—to the calculation of quantities encountered in quite other fields, we obtain exact quantitative agreement with the values of these quantities found by the methods of that field, which has no relation whatever to electrons. Born’s energy equation is most suitable for such a test. It makes it possible to connect

the values of reaction heats measured by chemists by means of calorimetric measurements, the values of the heats of dissociation and sublimation measured by physical chemists in investigations of the elasticity of vapors, with purely electronic quantities, such as ionization potentials, electron affinity, and lattice energy. At the same time, the connection between these quantities is established only by the law of conservation of energy, in whose validity physicists and chemists alike have equally little doubt. Herein lies the fundamental importance of the question under consideration. It is precisely the quantitative side of the question that is especially important, and therefore those discrepancies of \(5\)—\(10\%\) which, as we shall see below, do occur, are extremely unpleasant. But nothing can be done here. This is connected with the limits of error of the physical and chemical observations entering into the equation of quantities.

2) The application of classical physics to chemical questions has created, as is well known, an entirely new science—physical chemistry. Physical chemistry consists chiefly of two divisions: chemical statics and the electrochemistry of solutions. It seems to me that there is every reason to suppose that the application of the new electronic physics to chemistry will greatly increase the scope of physical chemistry, creating there new divisions of the electrochemistry of solid and gaseous bodies and developing to the full the already existing, embryonic divisions of chemical kinetics (in particular, the theory of catalysis) and photochemistry. In the present literature there are many attempts to throw a bridge between physics and chemistry; all of them are highly interesting; they open up completely new points of view on chemical phenomena, but almost all of them, being deprived of a rigorous quantitative basis, are rather reminiscent merely of projects for such a future bridge between the new physics and chemistry. Born’s equation, however, is a solid first abutment of this bridge. It is the beginning of the construction itself. Therefore, secondly, I have chosen precisely such content for the article, in preference to other questions from the same field that are highly interesting but still not sufficiently definite.

3) I was also attracted by the thought of collecting all the experimental material that electron physics possesses for the construction of the indicated bridge and of showing the degree of suitability of this material. Although this material is not large, it is very scattered among various articles; it is not in the handbooks. It is most fully collected in the article by Grimm and Herzfeld (ZS. f. Phys. B. 19, p. 141, 1923), yet not everything is collected even there. Therefore I have provided the article abundantly with tables containing numerical material.

In conclusion I shall point out that I assume the reader is acquainted with the contents of Prof. V. R. Bursian’s articles “The Electrical Nature of Molecular Forces in Crystals” (Uspekhi Fizicheskikh Nauk, vol. III, issue 1, p. 65) and my “Ionization Potentials and Spectra of Gases and Vapors” (Uspekhi Fizicheskikh Nauk, vol. III, issue 4, p. 449),

§ 1. Born’s Equation.

According to the data of X-ray analysis, crystals of salts of the type \(NaCl\) or \(CaCl_2\) consist of ions regularly arranged in space: \(\overset{+}{Na}\) and \(\overset{-}{Cl}\) in \(NaCl\), and \(Ca\), \(Cl\), \(\overset{-}{Cl}\) in \(CaCl_2\). Here by the sign \(\overset{+}{Na}\) we denote a singly charged ion \(Na\), i.e. an atom \(Na\) deprived of one electron. Similarly, \(Ca\) is a doubly charged ion \(Ca\), i.e. an atom \(Ca\) deprived of two electrons. By the sign \(\overset{-}{Cl}\) we denote a singly charged negative ion \(Cl\), i.e. a combination of a chlorine atom with one electron. Let us note that when salts are dissolved in water they break up precisely into such ions; moreover, the number of charges on the metallic ion is equal to its positive valency, and the number of charges of the negative ion is equal to its negative valency. The maximum positive valency of an element is equal to the number of the column in Mendeleev’s table, and the maximum negative valency is equal to eight minus the number of the column. Thus, the number of positive valencies is equal to the number of electronic charges, i.e. electrons, which an atom can give up in chemical interactions. The number of negative valencies is equal to the number of electrons which an atom can attach in chemical interactions.

We saw in the article “Ionization and Luminescence Potentials” that the visible and ultraviolet light emitted by excited atoms is produced by their peripheral electrons, which are bound to the nucleus considerably more weakly than the other electrons, called internal ones. It turned out that the number of optical electrons is equal to the positive valency of the element. This proves that in chemical reactions an active role is played only by the peripheral electrons, whose number determines the \(+\)-valency. Born and Kossel (W. Kossel) proved that the number of outer electrons in the zero group, i.e. in the noble gases, is \(8\). However, this group of eight electrons is so firmly bound to the nucleus that, in order to detach one of these electrons, such a large energy is needed that in chemical reactions no such process occurs. Therefore the noble gases do not enter into any chemical reactions. This group of eight electrons is so strong and stable that it has no tendency whatever to attach or give up electrons. Metals of the first group differ from the noble gases in that, in addition to eight electrons arranged in the same way as in the noble gases (here these electrons already belong to the internal ones), they have one outer electron, rather weakly bound to the nucleus. Therefore, by giving up this one electron, the atom of metals of the 1st group, e.g. \(Na\), becomes similar to neon and gives up no more electrons. In accordance with this, the ion \(Na\) is inert (for example, it does not react with water), and the valency of \(Na = 1\). Atoms of the second column, e.g. \(Ca\), already possess two outer electrons, comparatively weakly bound to the nucleus. Giving up 1 electron (\(\overset{+}{Ca}\)), they become similar to—

Na and therefore do not lose activity. Only by giving up two electrons \((\overset{++}{Ca})\) do they become similar to a noble gas. Atoms of metalloids, for example \(Cl\), possess, in accordance with 7 positive valencies of \(Cl\), seven electrons. It is easier for them to become similar to noble gases not by giving up electrons, but by attaching one more, eighth electron. A group of eight electrons is more stable; therefore a free electron combines with a chlorine atom with the liberation of energy. The magnitude of this energy is called the electron affinity. Unfortunately, we cannot dwell in greater detail on these interesting questions. They could constitute the subject of a separate article.

Let the energy which must be expended in order to ionize 1 gram-atom of sodium vapor be \(J_{Na}\). We shall write this as follows: \((Na)=\overset{+}{Na}+e-J_{Na}\), where the parentheses denote the gaseous state, and \(e\) denotes a free electron. Let the energy liberated when a free electron combines with one gram-atom of chlorine be \(E_{Cl}\). We shall write this as follows: \((Cl)+e=\overline{Cl}+E_{Cl}\). Next, let the energy which must be expended in order to break up 1 gram-molecule of crystalline \(NaCl\) into the free ions \(\overset{+}{Na}\) and \(\overline{Cl}\) be \(U_{NaCl}\), i.e. \([NaCl]=\overset{+}{Na}+\overline{Cl}-U_{NaCl}\). Square brackets \([\,]\) denote the solid state. Further, let the heat of reaction, i.e. the energy liberated when one gram-atom of solid sodium \([Na]\) combines with half a gram-molecule of gaseous diatomic chlorine, be \(Q_{NaCl}\), i.e. \([Na]+\tfrac{1}{2}(Cl_2)=[NaCl]+Q_{NaCl}\). Let the energy expended in evaporating one gram-atom \([Na]\) be \(D_{Na}\); then \([Na]=(Na)-D_{Na}\). Finally, let the energy required for the dissociation of \(\tfrac{1}{2}\) gram-molecule of diatomic chlorine into atoms be \(\tfrac{1}{2}D_{Cl_2}\); then \(\tfrac{1}{2}Cl_2=Cl-\tfrac{1}{2}D_{Cl_2}\).

Now let us carry out two processes by means of which, from 1 gram-atom of sodium vapor \((Na)\) and 1 gram-atom of atomic chlorine \((Cl)\), we obtain 1 gram-atom of sodium ions \(\overset{+}{Na}\) and 1 gram-atom of chlorine ions \(\overline{Cl}\).

\[ \begin{aligned} 1)\quad &(Na)=\overset{+}{Na}-J_{Na} \\ 2)\quad &(Cl)+e=\overline{Cl}+E_{Cl}. \end{aligned} \]

\[ \text{Energy expended } J_{Na}-E_{Cl}. \]

\[ \begin{aligned} 1)\quad &(Na)=[Na]+D_{Na} \\ 2)\quad &(Cl)=\left(\tfrac{1}{2}Cl_2\right)+\tfrac{1}{2}D_{Cl_2} \\ 3)\quad &[Na]+\tfrac{1}{2}Cl_2=[NaCl]+Q_{NaCl}, \\ 4)\quad &[NaCl]=\overset{+}{Na}+\overline{Cl}-U_{NaCl}. \end{aligned} \]

\[ \text{Energy expended } U_{NaCl}-D_{Na}-\tfrac{1}{2}D_{Cl_2}-Q_{NaCl}. \]

Since the initial and final results of both processes are the same, the amount of energy expended in both processes must be the same, i.e.

\[ J_{Na}-E_{Cl}=U_{NaCl}-D_{Na}-{}^{1}\!/_{2}D_{Cl_2}-Q_{NaCl}. \tag{1} \]

We shall obtain the same equation if, after the 4th operation of the second process, we carry out two more: 5) \(\overset{+}{Na}=(Na)+J_{Na}\); 6) \(\overset{-}{Cl}=(Cl)+e-E_{Cl}\).

In this case the initial substances of the process, \((Na)\) and \((Cl)\), are the same as the final ones. We have carried out a so-called cyclic process, in which, obviously, the amount of energy expended \(=0\). Adding the effects of all six reactions, we again obtain the same equation (1).

Born represents such a cyclic process symbolically as follows:

\[ \begin{array}{ccc} & -E_{Cl} \qquad\qquad\qquad\qquad {}^{1}\!/_{2}D_{Cl_2} & \\ & \longrightarrow (Na),(Cl) \longrightarrow & \\ J_{Na} & & D_{Na} \\ \overset{+}{Na},\ \overset{-}{Cl} & & [Na];\ ({}^{1}\!/_{2}Cl_2) \\ & & \downarrow \\ & [NaCl] \longleftarrow & \\ & -U_{NaCl} \qquad\qquad\qquad Q_{NaCl} & \end{array} \]

Here the arrows indicate the direction of the process, and on both sides of the arrow are written the quantities of energy released at each stage of the process.

This process is valid for any compound \(MX\), where \(M\) is one of the metals of the first group, and \(X\) is one of the halogens \((F, Cl, Br, J)\). Thus:

\[ U_{MX}=Q_{MX}+D_M+{}^{1}\!/_{2}D_{X_2}+J_M-E_X \tag{1} \]

where \(U_{MX}\) is the lattice energy of the solid salt \([MX]\)
\(Q_{MX}\) is the heat of reaction of \([M]\) with \({}^{1}\!/_{2}X_2\), the gaseous halide
\(D_M\) is the heat of vaporization of the metal
\(D_{X_2}\) is the heat of dissociation of the diatomic molecule \((X_2)\) into atoms
\(J_M\) is the ionization energy of the metal vapor \((M)\)
\(E_X\) is the electron affinity of the atom \(X\), i.e. the energy released when the atom \(X\) combines with an electron.

We shall refer all these quantities to gram-atoms or gram-molecules and express them in large calories.

For a compound of the type \(MX_2\), where \(M\) is one of the divalent metals and \(X\) is a halogen, we can construct an analogous cyclic process; only here there will also enter the energy of detachment of an electron from the ion \(M\), which we shall denote by \(J'_M\).

This energy corresponds to the process \(M^+ = M^{++} + e - J'_M\)

\[ \begin{gathered} \frac{-2E_X}{J_M+J'_M}\ \longrightarrow\ (M),\ (X)_2,\ (X) \quad \xrightarrow[\ D_{X_2}\ ]{D_M}\quad |M|:(X_2)\\[6pt] \overset{++}{M},\ \overline{X},\ \overline{X}\\ \uparrow\\[6pt] \xleftarrow{\ -U_{MX_2}\ }\ [MX_2]\ \xleftarrow{\ Q_{MX_2}\ }\ |M|:(X_2) \end{gathered} \]

whence

\[ U_{MX_2}=Q_{MX_2}+D_M+D_{X_2}+(J_M+J'_M)-2E_X \tag{II} \]

Here also we shall express all quantities in large calories per gram-molecule.

Thus, six quantities enter into equations (I) and (II). Before checking whether their experimental values satisfy these equations, we shall show how these quantities are obtained from experimental data and what the accuracy is with which they are fixed.

§ 2. Lattice energy. With regard to the calculation of this quantity, in Advances in the Physical Sciences, vol. III, issue 1, there is a detailed abstract by V. R. Bursian. Therefore we shall confine ourselves to presenting the results.

The energy \(U\), which must be expended in order to break up one gram-molecule of a salt (for example \([NaCl]\)) into free ions \(Na\) and \(\overline{Cl}\), according to the cited abstract by Bursian, can be calculated if the structure of the crystal is known, i.e. the spatial arrangement of the ions (which is obtained from X-ray interference patterns for the given crystal) and the coefficients of volume compression of the crystals, obtained from measurements of their elastic constants.

The quantities \(U_{MX}\) have been calculated only for a small number of crystals. We give tables of the values of \(U\) found, in large calories per gram-molecule.

TABLE 1.

TABLE 2.

It must be noted, however, that these values are associated with large errors, both as a result of errors in measuring the compressibility coefficients and because of shortcomings of the calculation itself. This applies especially to divalent compounds.

§ 3. Heats of dissociation of gases. The determination of the heats of dissociation of gas or vapor molecules is one of the most difficult thermochemical problems. Therefore I shall permit myself to dwell in somewhat greater detail on the methods for investigating this quantity. We shall be interested chiefly in the heats of dissociation of the molecules \(H_2\), \(Cl_2\), \(Br_2\), \(J_2\), etc., of simple diatomic molecules of the elements. We shall therefore confine ourselves for the present to considering the dissociation of molecules of the type \(X_2\). As is known from the theory of chemical equilibria, at any temperature, along with molecules \(X_2\), there is a certain quantity of decomposed molecules of the type \(X\). The reaction \(X_2 \rightleftarrows X + X\) always takes place in a medium of \(X_2\); some fraction of the molecules \(X_2\) is always decomposing into atoms, and these atoms are again combining. The numbers of molecules \(X_2\) and \(X\) at each instant are determined by the ratio of the rates of the forward and reverse reactions. This ratio is denoted by a quantity \(K\) constant for each reaction, which is a function of temperature (with increasing temperature the equilibrium shifts, the quantity of \(X\) increases, the quantity of \(X_2\) decreases) and of the concentration of the reacting molecules.

According to the law of mass action, the constant \(K\) is related to the concentrations \(C\) (usually expressed in gram-molecules per cubic decimeter) of the individual components taking part in the reaction. Thus, if the reaction is expressed by the formula \(n_1 A_1 + n_2 A_2 + \ldots \rightleftarrows m_1 B_1 + m_2 B_2 + \ldots\), then

\[ K=\frac{C_{B_1}^{m_1}\cdot C_{B_2}^{m_2}\ldots}{C_{A_1}^{n_1}\cdot C_{A_2}^{n_2}\ldots}. \tag{2} \]

Here \(C_{B_1}\), \(C_{B_2}\), etc. are the concentrations of the molecules \(B_1\), \(B_2\), etc.

For the case of the reaction \(X_2 \rightleftarrows 2X\), according to formula (2) we have

\[ K=\frac{C_X^2}{C_{X_2}}. \tag{3} \]

If \(a\) is the degree of dissociation of \(X_2\), i.e. the ratio of the number of dissociated molecules \(X_2\) to the undissociated ones, then from one gram-molecule of \(X_2\), in the case of dissociation, only \((1-a)\) gram-molecules are present. The number of gram-molecules of \(X\), obviously, is equal to \(2a\). If \(V\) is the volume occupied at the given temperature by one gram-molecule of vapor, then the molecular concentration is

\[ C_{X_2}=\frac{1-a}{V}\quad \text{and}\quad C_X=\frac{2a}{V}. \]

Hence, according to (2),

\[ K=\frac{4\alpha^2}{V(1-\alpha)} \tag{4}. \]

Thus, knowing the degree of dissociation \(\alpha\), one can calculate \(K\). The quantity \(K\) is connected in a very simple way with the energy \(D\) required to split the molecule \(X_2\) into atoms, i.e. with the heat of dissociation sought; namely,

\[ \frac{d\ln K}{dT}=\frac{D}{RT^2} \tag{5}, \]

where \(T\) is the absolute temperature, and \(R\) is the gas constant, equal to 1.98 calories. If one determines experimentally how \(\alpha\) changes with a change in temperature, then, by plotting \(\ln K\) against \(T\), the quantity \(\dfrac{D}{RT^2}\), and hence \(D\), can be found by graphical differentiation of this curve. Usually, however, one proceeds otherwise; denoting by \(K_1\) the value of \(K\) at temperature \(T_1\), and by \(K_2\) that at \(T_2\), we obtain, integrating (5), \(\ln K_1=-\dfrac{D}{RT_1}+B\) and \(\ln K_2=-\dfrac{D}{RT}+B\); subtracting, we have

\[ \ln K_1-\ln K_2=\ln\frac{K_1}{K_2}=\frac{D}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right), \]

whence

\[ D=\frac{RT_1T_2}{T_1-T_2}\ln\frac{K_1}{K_2} \tag{6}. \]

If the natural logarithm is replaced by the common logarithm and the value \(R=1.98\) is substituted, we obtain

\[ D=\frac{4.571\cdot T_1T_2}{T_1-T_2}\log\frac{K_1}{K_2}, \tag{7} \]

where \(D\) will then be expressed in small calories per gram-molecule \(X_2\). The quantity \(D\) changes very little with temperature. Therefore, substituting the observed \(K_1\) and \(K_2\) for various \(T_1\) and \(T_2\) into formula (7), we must always obtain one and the same value of \(D\). This is a good check on the correctness of the observations. In the first measurements, \(\alpha\) was determined from the change in the pressure of a gas or vapor with increasing temperature. The point is that in the case of the reaction \(X_2 \rightleftarrows X+X\) the number of molecules increases, since instead of one molecule \(X_2\) two appear. Therefore the pressure will increase more strongly than is implied by the equation of state of the gas \(X_2\). From these deviations one can determine \(\alpha\), and consequently \(K\). However, with the exception of \(J_2\) and \(Br_2\), all the other simple gases of interest to us possess a large value of \(D\) and correspondingly very slight dissociation at

not very high temperatures. Thus, for example, for \(H_2\) the value \(\alpha\) at \(2115^\circ\mathrm{C}\) is \(0.0035\). Experimenting at such high temperatures presents very great difficulties; therefore special methods were devised for finding \(\alpha\), of which I shall indicate only one.

As is known, a mixture of chlorine and hydrogen, under the action of a spark, combines with an explosion. The reaction proceeds almost instantaneously throughout the whole mixture. The energy liberated thereby instantaneously heats the mixture to a very high temperature, which then quickly falls because of thermal conductivity. This short time, however, is sufficient for the establishment of the equilibrium corresponding to the law of mass action. Producing an explosion in a mixture consisting of \(\frac{1}{2}\) gram-molecule of \(H_2\) and \(\frac{1}{2}+(mi)\) gram-molecules of \(Cl_2\), after the explosion we obtain 1 gram-molecule of \(HCl\) and \(mi\) gram-molecules of \(Cl_2\). The heat liberated in the reaction \(\frac{1}{2}H_2+\frac{1}{2}Cl_2=HCl\) is equal to 22000 small calories; if by \(\Delta T\) we denote the difference \(T_e-T_a\), where \(T_e\) is the maximum temperature of the mixture, and \(T_a\) is its initial temperature, then we have the calorimetric equation

\[ 22000=\Delta T\left[C_{HCl}+(mi)C_{Cl_2}\right], \tag{8} \]

where \(C_{HCl}\) and \(C_{Cl_2}\) are the molecular heat capacities of \(HCl\) and \(Cl_2\). In this way, determining \(\Delta T\) for various \(mi\,Cl_2\), one can measure the heat capacities of \(HCl\) and \(Cl_2\).

However, equation (8) is valid only up to those temperatures \(T\) at which the dissociation of \(Cl_2\) and \(HCl\) is negligible. But when dissociation becomes appreciable, part of the heat liberated is spent on splitting the molecules of \(HCl\) and \(Cl_2\) into atoms; if this heat is denoted by \(D_{HCl}\) and \(D_{Cl_2}\), and the degree of dissociation at temperature \(T\) by \(\beta\) and \(\alpha\), then instead of equation (8) we obtain

\[ 22000=\Delta T\left[C_{HCl}+(mi)C_{Cl_2}\right]+D_{HCl}\beta+(mi)D_{Cl_2}\alpha . \tag{9} \]

However, \(D_{HCl}\) is a quantity comparatively very large relative to \(D_{Cl_2}\), and therefore \(\beta\) (which, according to formula (5), depends on \(D\) as \(e^{-\frac{D}{2T}}\)) is a quantity negligibly small in comparison with \(\alpha\). Therefore the quantity \(D_{HCl}\beta\) may be neglected. Then, for determining \(D_{Cl_2}\alpha\), we have the equation

\[ D_{Cl_2}\alpha=\frac{22000-\Delta T(C_{HCl}+mi\,C_{Cl_2})}{mi}. \tag{9} \]

For different \(mi\) we shall obviously obtain different \(\Delta T\) and \(T_e\). Thus we learn the dependence of \(D_{Cl_2}\alpha\) on \(T_e\). Combining this with equations (4) and (7), we obtain one more condition connecting \(\alpha\) and \(D_{Cl_2}\) at various \(T_e\):

\[ D_{Cl_2}= \frac{4.571\,T_{e_1}\cdot T_{e_2}}{T_{e_1}-T_{e_2}}\, \lg \frac{\alpha_1^2(1-\alpha_2)\,mi_1(1+mi_2)} {\alpha_2^2(1-\alpha_1)\,mi_2(1+mi_1)} . \tag{10} \]

under the condition of constancy of the pressure of the mixture at the beginning of both experiments. Thus each pair of observations \(T_e\) gives three equations with three unknowns \(a_1\), \(a_2\), and \(D\). Since \(D\) is a quantity almost independent of temperature, the constancy of the \(D\) calculated from different pairs of experiments is a criterion of the correctness of the experiment. It remains to indicate how \(T_e\) is measured. With a membrane manometer, whose readings follow the change of pressure in \(0.02\) sec., the maximum pressure in the mixture at the moment of explosion is measured. Knowing the initial \(T_a\) and the pressure, one can determine from Clapeyron’s equation or, more precisely, from the van der Waals equation, the maximum temperature \(T_e\). Changes in pressure connected with dissociation may, for small dissociations, be neglected.

They may, however, also be taken into account. This adds to the system of equations (10) and (9) one more equation connecting the unknown \(T_e\) with \(a\), i.e., for a pair of experiments there will be not three, but five equations with five unknowns

\[ T_{e_1},\ T_{e_2},\ a_1,\ a_2\ \text{and}\ D. \]

This method was developed by Nernst and his pupils. Recently (Zs. f. Elektrochemie, vol. 30, pp. 36 and 49—1924) this method was brilliantly applied by Nernst’s pupil Fole (M. Voll) to the determination of the heats of dissociation of \(Cl_2\) and \(H_2\). It was especially difficult to work with \(H_2\), since the corresponding \(D_{H_2}\) is very large and, therefore, it is necessary to take into account the dissociation \(2HCl \rightleftarrows H_2 + Cl_2\), as well as the dissociation of the \(Cl_2\) produced in this decomposition. For this purpose Fole made explosions of mixtures: 1) \(H_2\) and \(Cl_2\) with an excess of \(H_2\), and 2) mixtures of \(H_2\), \(Cl_2\), and \(HCl\). This made it possible for him to set up the required number of equations and to determine the dissociation of \(H_2\).

By the way, the magnitude \(D_{H_2}\) can be determined as the difference between the ionization potential of \(H_2\) and \(H\) (see Uspekhi Fizicheskikh Nauk, vol. III, p. 467).

We give a table for \(D_H\) and \(D_{Cl}\) by different methods:

TABLE 3.

Apparently, the last number should be considered the most reliable. It must be noted that measurements of the heats of dissociation of durable compounds, even by the explosion method set forth above, are connected with such a number of assumptions and difficulties that the accuracy in determining these quantities is not great. For \(D_H\) we shall adopt the value \(94 \pm 10\) large calories; for \(D_{Cl_2}\), \(54 \pm 5\) large calories.

We give a table of the heats of dissociation of simple gases and vapors.

TABLE 4.

§ 4. Ionization potentials of metallic vapors.

In my article “Potentials of excitation and ionization” methods were set forth for determining the first ionization potential of metallic vapors. The work of tearing one electron away from an atom is expressed in terms of the ionization potential \(V\), as \(\frac{V_J e}{300}\), where \(V_J\) is the ionization potential expressed in volts, \(e\) is the charge of the electron, equal to \(5.77 \times 10^{-10}\) \(CGSE\). For the ionization of one gram-atom the energy will evidently be \(N\) times greater, where \(N\) is Avogadro’s number, i.e. the number of atoms in a gram-atom, equal to \(60.6 \times 10^{22}\).

Thus the ionization energy \(J_M = \frac{Ne}{300} V_J\) ergs, or \(\frac{Ne}{4.184 \times 10^7 \times 300} V_J\), small cal. Since \(Ne = 96540\) coulombs \(= 96540 \times 3 \times 10^9\) \(CGSE\), \(J_M = 23.07 \times 10^3 \times V_J\) small cal. \(= 23.07 \times V_J\) large cal. Approximately we shall consider that 1 volt corresponds to 23 large cal. \(J_M\) is the heat that must be expended on the reaction \(M = M + e\). As indicated in the cited abstract, the quantities \(V_J\) can be found with very great accuracy from optical data, namely from the value of the frequency \(\nu_0\) of the spectral limit. This frequency, very accurately determined by opticians, is related to the ionization potential \(V_J\) by the relation \(h\nu_0 = \frac{V_J e}{300}\).

The magnitude of the second ionization potential \(V'_J\), corresponding to the ejection of a second peripheral electron, when the first has already been removed, i.e. the potential determining the energy of removal of an electron from a singly ionized atom, had not been directly measured up to the present time. However, Paschen (F. Paschen) and Fowler, observing the spectrum of the alkaline-earth metals in a strong discharge, found, besides the ordinary line spectrum of the given metal, another spectrum superposed upon it, likewise correctly formed according to its own series laws. All the data, into which we shall not now enter, compelled one to think that this second line spectrum is emitted by ionized atoms of the metal. Then from the limiting frequency \(\nu'_0\) of this spectrum it was possible to calculate \(V'_J\)—the ionization potential [[unclear: end of line cut off]].

assuming that in this case as well the formula \(\dfrac{V'_J e}{300}=h\nu'_g\) is valid. \(V'_J\) proved, for all the alkaline-earth metals, to be almost exactly twice as large as \(J_M\). Below we give the values found. However, it was not possible to find this quantity for all the alkaline-earth metals. Thus, for \(\bar H_y^+\) it was not determined.

It is of considerable interest to find a method for the direct determination of the quantity \(V'_J\), in order 1) to verify the correctness of the formula \(h\nu'_g=\dfrac{eV'_J}{300}\), or, more precisely, to verify the correctness of the assumption that the spectrum found by Paschen is indeed emitted by the ion \(M\), and 2) to make it possible to measure the quantity \(V'_J\) for those metals for which it has not been found optically.

Recently such a method was developed in my laboratory at the Physico-Technical X-ray Institute (in Leningrad). This method made it possible to determine all possible ionization potentials: both the first, corresponding to the removal of the first valence electron from the atom, and the subsequent ones, corresponding to the removal of the second electron from the singly charged ion and of the third valence electron from the doubly charged ion (in the cases of trivalent metals).

TABLE 5.

In addition, \(J_{Ag}=173,\ J_{Cu}=176.7\).

§5. Electron affinity. This concept was first introduced by Franck (J. Franck) after his work on the mobilities of negative ions in various gases and on the quenching of the fluorescence of mercury vapor when it was mixed with other gases.

The velocity which ions acquire in a field with an intensity of one volt per centimeter is called the mobility \(u\). The mobility of an ion is, obviously, the smaller the greater the resistance of the gas to its motion; indeed, the law \(up=\mathrm{const}\) was established. The ratio of the mobility of the positive ion to the mobility of the negative ion is very close to unity, while the absolute values of these quantities (always of the order of 1–6 cm/sec for a field of 1 volt/cm) show that the gaseous ion is a particle of molecular dimensions. The question of whether it represents a

itself an ion of a single molecule, charged with a positive or negative charge, or else an entire conglomerate of molecules, has not yet been settled definitively, although all recent experiments seem to incline one toward the first point of view. At very low pressures the appearance of two groups of negative ions was discovered: some—with a normal value of the mobility, corresponding to the law \(up=\mathrm{const}\), others—with a mobility many hundreds of times greater than the normal value. The lower the pressure, the greater the number of ions of the second group and the fewer ions of the first. For different gases the pressure at which the second group of ions begins to predominate is different. The magnitude of the mobility of the anomalous ions proved to be very close to the calculated value of the mobility of free electrons. All the data argue for the following picture of the phenomenon. The initial stage of the negative ion is the electronic state: always, in any ionization (with the exception of rare cases of ionization of an electrolytic character, which will be discussed below), the negative charge appears in the form of an electron. Being in a medium of molecules, the electron, after a series of collisions, combines with a gas molecule, forming a normal negative ion. The lower the pressure, i.e. the smaller the number of collisions of the electron with molecules, the more slowly the reaction of combination of the electron with a molecule proceeds. Thus, at low pressures the electron may traverse the entire path in the measuring apparatus in the electronic state, and at these pressures we shall evidently obtain the abnormally large mobilities that are in fact observed for negative ions. In the case of positive ions, which, as is known, always at the first moment of their formation appear in the form of atoms deprived of one or several electrons, phenomena of this sort—abnormally large mobilities—should not be observed, which is in agreement with the experimental data. As we have indicated, in different gases the pressures at which free electrons appear in large numbers are different. This means that the rate of combination of electrons with a molecule, the rate of the reaction \(M + e = M\), is different for different substances under identical conditions of pressure and temperature. In Table 6 are given Loeb’s (L. Loeb) data on the average number of collisions \(n\) of an electron with a molecule required for the formation of a negative ion.

TABLE 5.

It is quite obvious that the number of collisions necessary for combination decreases with increasing electronegative or acidic properties of the molecule. In the noble gases \(n=\infty\)—the electron does not combine with the molecule at all; hydrogen and nitrogen have a very large \(n\), but not an infinite one: we know that hydrogen, being an electropositive element, nevertheless enters into a definite compound with metals; nitrogen, as is known, is a neutral element, occupying a middle position in the table. Oxygen is already an electronegative element, readily combining with metals; \(NO_2\), \(CO_2\)—these are compounds with acidic properties, which are still smaller for them. Finally, the halogens have the smallest value, in accordance with their sharply expressed electronegative properties. Halogen salts, when dissolved in water, always dissociate into a positive metal ion and a negative halogen ion.

This ability of a molecule to enter into combination with an electron was called by Franck electron affinity, while assuming that the measure of affinity may be the rate of the reaction \(M+e=\bar M\). He was also the first to draw attention to the circumstance that the electron affinity so defined increases with increasing electronegative properties of the molecule. However, already in the very name “affinity” there sounded the desire to determine this quantity quantitatively as the magnitude of the thermal effect of the combination of a molecule with an electron. We saw in the paragraph on dissociation that the magnitude of this energy indeed determines the equilibrium state between \(\bar M\) and \(e\) in the case of the reaction \(M+e=\bar M\), but from this one can by no means say anything about the magnitude of the rate of reaction in stages far from equilibrium, when the reaction practically proceeds in one direction. What determines the rate of reaction, the activity, what the role of catalysts is—these are questions not resolved by chemistry. It was only possible to suppose, taking into account the parallelism between the rate of the reaction \(M+e=\bar M\) and the electronegative properties of \(M\), that for this given reaction the greater its thermal effect \(E\), the greater the rate. This point of view was confirmed by measurements of mobility in a flame.

One could think that inside the flame there actually exist conditions of equilibrium between molecular ions and electrons, i.e. that a reversible reaction \(M+e\rightleftarrows \bar M\) takes place; electrons either combine with \(M\), or under the action of temperature the ion decomposes into a molecule plus a free electron. According to the law of mass action, \(\dfrac{C_e C_M}{C_{\bar M}}\) is proportional to \(e^{-\frac{E}{kT}}\), i.e. the number of free electrons \(C_e\) is proportional to \(e^{-\frac{E}{kT}}\), where \(E\) is the thermal effect of the reaction. We see that the larger \(T\), the larger \(C_e\). Indeed, measurement of mobility in a flame showed,

that at the temperatures existing there the majority of the negative carriers of electricity are in the electronic state (mobility of the order of \(10^4 \frac{\mathrm{cm}}{\mathrm{sec}}\)). By mixing a small amount of halide vapors into the flame, Frank showed that the mobility of the negative ions assumes a normal value, many hundreds of times smaller. The concentration of free electrons falls almost to 0. Since \(T\) remains the same, this phenomenon means that the value \(E'\) for the halides many times exceeds \(E\) for other gases, which is in agreement with the data set forth below.

Frank cited a whole series of physical phenomena which indicated the tendency of certain atoms and molecules to capture an electron. It turned out thereby that the classification of molecules according to the magnitude of this tendency to capture an electron always coincided with the above-indicated series of increasing electronegative properties. But all these phenomena, while qualitatively confirming Frank’s basic idea, did not give him the possibility of determining quantitatively the value \(E\), even by some indirect route. Moreover, all these phenomena concern the absorption of an electron by a molecule. It was desirable, however, to find the value \(E\) for an atom.

§ 6. Optical method for determining the affinity for electrons. The following considerations formed the basis for the determination of the value \(E\). Combining with a neutral atom, the electron enters organically into the atomic system, moving, like other electrons, in some stable orbit. Its energy\(^1\) is then expressed by the quantity \(-W_1\). If its energy before combination was equal to 0, then in the process of combination the energy

\[ 0 - (-W_1) = W_1 \]

is released. In Frank’s opinion such a process is in no way essentially different from the process of combination with an atomic ion, where, as we have seen,\(^2\) this energy passes into radiant energy, whose frequency \(\nu_0\) is connected with the energy \(W_1\) by the relation

\[ h\nu_0 = W_1 = \frac{eV_j}{300}, \]

where \(V_j\) is the ionization potential of the atom, and \(\nu_0\) is the frequency corresponding to the boundary of the spectrum of the element. Frank sees only one difference in these two processes. As is known, when an electron combines with an atomic ion, the entire spectrum of the element is emitted, and not only the single limiting line of the spectrum. This is connected with the circumstance that, besides the stable orbit with energy \(W_1\), there is also a whole series of orbits with energies \(W_2\), \(W_3\), etc., and the electron, in passing from infinity to the first orbit, can also stop at a number of intermediate ones.

In the case of the combination of an electron with a neutral atom, whose field decreases with distance much more rapidly than inversely propor—

\(^1\) See my cited article: “Ionization potentials and potentials of coupling of gases and vapors.”

\(^2\) See ibid.

proportional to the second power of the distance. Frank assumes that these orbits are so closely spaced that the electron always passes directly to the first normal orbit and does not reach a center situated only beyond one limiting line, determined by the relation

\[ h\nu_0 = W_1 = \frac{eE}{300}, \]

where \(E\) is the electron affinity, expressed in volts.

Further, Frank assumes that if the energy of the electron before its union with the atom was \(\frac{1}{2}mv^2\), i.e., if it was moving with velocity \(v\), then upon its union with the atom all the lost energy

\[ = \frac{1}{2}mv^2 + W_1 = \frac{1}{2}mv^2 + \frac{eE}{300} \]

will be emitted in the form of monochromatic radiation, whose frequency is determined by the relation

\[ \frac{1}{2}mv^2 + \frac{eE}{300} = h\nu. \]

This would mean that beyond the boundary of the element spectrum

\[ \nu_0 = \frac{eV_a}{300h} \]

one could observe a continuous spectrum corresponding to the various initial velocities of the electrons before their recombination with atoms. Thus, in a Geissler tube and in an arc, where spectra are usually observed, electrons under the action of the electric field may possess appreciable velocities, and such a phenomenon ought to occur. However, so far as I know, up to the present time no experiments have been carried out with the aim of elucidating this circumstance. On the other hand, another phenomenon has been observed, apparently confirming the point of view set forth. When vapor is illuminated by light of frequency \(\nu_0\), ionization of it is observed, as was to be expected, i.e., the absorption of a quantum \(h\nu_0\) corresponds to the acquisition by the electron of an energy \(V_a\) volts, precisely that which is necessary for ionization. It turned out that illuminating the vapor with light of frequency \(\nu > \nu_0\) also produces an equally effective ionization, indicating that the quantum \(h\nu\) can also be entirely absorbed by the electron, the energy of the detached electron

\[ \frac{1}{2}mv^2 \]

being

\[ = h\nu - h\nu_0. \]

If a quantum can be entirely absorbed by an electron and converted into its kinetic energy, then, probably, the reverse process is also possible: the transformation of the electron’s kinetic energy

\[ \frac{1}{2}mv^2 + \frac{eV_a}{300} \]

into the energy of one light quantum.

Thus, when electrons possessing different velocities combine with neutral atoms possessing an affinity for the electron, a continuous spectrum with a sharp boundary

\[ \nu_0 = \frac{eE}{300h} \]

on the side of long wavelengths should be emitted. From this boundary toward the short-wave side there extends a continuous spectrum, and the distribution of intensity in it should correspond to the distribution of the energy \(\frac{1}{2}mv^2\) among the electrons entering into combination with the atoms.

Analyzing Steubing’s data on the spectrum of iodine, Franck observed that there is there a region of continuous spectrum having a sharp boundary on the side of the lower frequencies at \(\lambda = 4400\ \text{\AA}\). It must be said that the molecular spectrum of iodine is so complex—the individual lines composing the bands are so closely spaced—that, in the case of insufficient resolving power of the spectrograph, all the bands appear as portions of a continuous spectrum. However, Steubing used very good optical instruments, which compels one to think that the portion of continuous spectrum he found really does not consist of lines lying close to one another. Steubing made his observations in a Geissler tube filled with iodine vapor. He drew attention to the fact that the continuous portion of the spectrum becomes brighter when the temperature of the tube is raised.

In the tube, under an intense discharge, part of the iodine is always dissociated into atoms; therefore one might have attributed this continuous spectrum to atoms and not to iodine molecules, which was confirmed chiefly by the increase in brightness of this spectrum with increasing temperature and, consequently, with the increase in the number of iodine atoms due to its dissociation (at \(500^\circ\), approximately half of the iodine molecules are in the atomic state).

This latter circumstance, together with the sharpness of the boundary on the side of the low frequencies, led Franck to the idea that this continuous spectrum is a spectrum characteristic of the electron. He found, from the formula

\[ h\nu = \frac{hc}{300} = E = 9.6\ \text{volts or }59\ \text{calories}. \]

However, Gerlach and Gromann (W. Gerlach und Frl. Gromann), in carrying out in 1923 a detailed investigation of the spectrum of iodine, found:

1) At reduced iodine pressures of the order of \(10^{-3}\) mm, the intensity of the continuous region at \(4800\ \text{\AA}\) decreases together with the decrease in brightness of the whole banded molecular spectrum, although the brightness of the line spectrum of atomic iodine increases. This indicates a connection between the continuous spectrum and the molecular band spectrum and the absence of a connection with the atomic spectrum.

2) Raising the temperature to \(800^\circ\) lowers the intensity of the banded spectrum in the green and red regions, but at the same time increases the intensity of the ultraviolet bands, also corresponding to molecules, so that the increase in brightness of the continuous region at \(4800\ \text{\AA}\) may be due simply to a redistribution of energy in the spectrum of the molecule in the sense of an increase in the energy falling in the higher frequencies, and cannot be regarded as proof that this continuous region is emitted by atomic iodine. At temperatures above \(1000^\circ\), the intensity of the continuous region at \(4800\ \text{\AA}\) decreases.

3) The sharpness of the boundary at 4800 Å turned out to be an illusion connected with the special character of the absorption of light by the photographic plates used by Steubing. The boundary proved not at all so sharp upon a more careful consideration of the question. To a considerable degree this sharpness was also due to the fact that just here begins one of the bands superposed on this continuous part of the spectrum. These results made Frank’s assumption and the value of \(E\) found by him very improbable.

However, Gerlach and Grotrian, somewhat farther in the ultraviolet region of the spectrum, found a short section of continuous spectrum with a sharp boundary at \(\lambda = 3460\) Å. This section of the spectrum possessed properties entirely different from the properties of the entire band spectrum and, apparently, was actually caused by the emission of iodine atoms.

The grounds for such a conclusion are the following:

1) This section at \(\lambda = 3460\) Å remains relatively bright at the lowest pressures, when the whole band spectrum and the continuous section at \(\lambda = 4800\) Å almost disappear, and all the energy passes into the line spectrum of atomic iodine.

2) When the temperature is raised to \(1300^\circ\) C, the intensity of this section continuously increases, revealing an obvious connection with the dissociation of iodine into atoms.

3) The boundary of this section on the side of small frequencies (at 3460 Å) shows extreme sharpness under the most careful investigation. All these circumstances forced Gerlach and Grotrian to come to the conclusion that it is precisely this section of the continuous spectrum that is caused by affinity for the electron. For the value \(E\) they find 3.55 volts, or \(81.82 \pm 0.2\) cal. per gram-atom.

Angerer, investigating the spectrum of chlorine, also discovered there a section of continuous spectrum with a sharp boundary and found that \(E = 89\) cal.

It must, however, be noted that until it proves possible to observe the spectra of electron affinity under pure conditions, in the absence of ionization and emission of the band and line spectrum, one cannot be certain that the sections of the spectrum found are actually caused by the phenomenon of combination of an electron with an atom, and do not belong to emissions of ionized atoms and molecules of iodine. For it is known that even vapors of metals under certain temperature conditions emit continuous spectra.

§ 7. Calculation of electron affinity from the ionization potentials of \(HCl\), \(HBr\), and \(HJ\). In my preceding article (in Uspekhi Fizicheskikh Nauk) I gave data for the ionization potentials of \(HCl\), \(HBr\), and \(HJ\), obtained by Knipping. The values of these potentials must be decreased by 0.7 volt for the reason that

that measurements, made in the same apparatus, gave for helium an ionization potential 0.7 volt greater than that calculated from the limit of the helium spectrum \( \Gamma_\varphi \), found by Lyman.

Introducing this correction and converting into large calories, we obtain \(J_{HCl}=316\) large calories, \(J_{HBr}=302\) large cal., \(J_{HJ}=293\) large cal.

As was indicated in the preceding article, Knipping supposed that in the ionization of heteropolar compounds of the type of salts and acids the molecule decomposes electrolytically according to the formula \(HCl = \overset{+}{H}+\overline{Cl}\). It should be noted, however, that until very recently it had been observed that gas ionization always consists in the detachment from the molecule of a free electron, and not of a negatively charged atom.

We shall note, however, that most investigations were always carried out in gases of the homeopolar type, where one could not expect electrolytic dissociation of the molecule upon ionization.

In positive rays (though under extremely strong voltages) Thomson observed negatively charged fragments of molecules. Thus there is nothing in experiment that contradicts Knipping’s supposition. Quite recently I and my collaborators carried out a series of experiments proving the possibility of electrolytic decomposition of a molecule when it is bombarded by slow electrons.

We investigated the ionization potentials of the vapors \(HgJ_2\). We found for \(HgJ_2\) an ionization potential \(V_J\) of 10.5 volts, and a second \(V'_J\) of 25.5 volts. Then, in a special apparatus, we investigated what sort of negative ions appear under such ionization. We learned this by determining the mass of the ions from their deflection in a magnetic field. It turned out that these ions are iodine atoms carrying one negative charge. These ions appeared at an energy of the bombarding electrons of 11 volts, which was in agreement with the ionization potential \(V_J = 10.5\) volts found by another method.

In \(HgCl_2\) vapors we found that the negative ions are chlorine atoms carrying one charge. The number of \(\overline{Cl}\) strongly increased at an energy of the bombarding electrons equal to 25 volts, which evidently indicates the existence of two types of ionization associated with the appearance of \(J\). This second number closely coincides with the second ionization potential found by us in \(HgJ_2\) vapors, \(=25.5\) volts. Evidently two types of decomposition take place here:

\[ 1)\ HgJ_2=\overset{+}{Hg}+\overline{J}+J \quad \text{and} \quad 2)\ HgJ_2=\overset{++}{Hg}+\overline{J}+\overline{J} \]

Thus it was directly proved that in a heteropolar compound of the type \(HgJ_2\) ionization has an electrolytic character.

All that has been said makes Knipping’s supposition about the character of the ionization of \(HCl\), \(HBr\), and \(HJ\) very probable. If this is so,

it, composing Born’s cyclic process and using formula (1), we obtain

\[ J_{HJ}=Q_{HJ}+\frac{1}{2}D_{H_2}+\frac{1}{2}D_{J_2}+J_H-E_J,\quad \text{whence } E_J=\left(J_{HJ}-Q_{HJ}\right. \]

\[ \left.-\frac{1}{2}D_{H_2}-\frac{1}{2}D_{J_2}-J_H\right)=86\ \text{large cal.}, \]

i.e., a number very close to that which was obtained from the electron affinity. Writing correspondingly the equation for \(HCl\) and \(HBr\), we obtain \(E_{Br}=93\), \(E_{Cl}=94.5\); since in the quantities \(D_{H_2}\), \(D_X\), and \(J_{HX}\) the error may quite well reach several calories, the agreement of the optical data should be regarded as excellent.

Therefore, in what follows we shall use the optical data for \(E\), setting \(E_{Cl}=89\), \(E_J=82\); for bromine, however, the number is taken approximately 1 less than for chlorine, i.e. 88.

§ 8. Verification of the fundamental equation and calculation from chemical and ionization data. We now have all the data for checking the fundamental equations of the Born cyclic process (eqs. I and II) for salts of the type \(MX\) and \(MX_2\), where \(M\) is one of the metals of the first or second group, and \(X\) is one of the halogens, excluding \(F\), for which the affinity is unknown.

For compounds \(MX\) we have:

\[ U_{MX}=Q_{MX}+D_M+\frac{1}{2}D_X+J_M-E_X \quad \text{and} \quad U_{MX_2}=Q_{MX_2}+D_M+D_X+J'_M+ \]

\[ +J''_M-2E'_X \]

We give the \(U_{MX}\) and \(U_{MX_2}\) calculated from these formulae, as well as the differences \(\Delta\) between these numbers and the values of \(U\) calculated by Born from compressibility, presented in Tables 8 and 9.

TABLE 7.

As is seen from the tables, a systematic discrepancy occurs only for the lithium salts and the divalent calcium salt. The constancy of the quantities \(\Delta\) for all salts of \(Li\) and \(Ca\) indicates that an error has crept into Born’s calculations.

systematic error. And this is not surprising. The lithium ion, unlike the other ions, is surrounded by only two electrons. Therefore its field is far from spherical symmetry. In all the other ions there are eight outer electrons; they fill the spherical volume rather uniformly, which gives grounds for assuming that the field of these ions is very close to a field of central forces. Therefore Born’s calculations for \(Li\) are very likely associated with a larger error. As regards the divalent salts \(Cu\), their double charge also makes all calculations more complicated. For the \(Rb\) salts the discrepancy reaches \(10\%\).

As is seen, the quantity \(\Delta\) reaches \(15\%\) for the \(Li\) salts, \(10\%\) for \(RbCl\) and \(RbBr\), \(6\%\) for the \(Cu\) salts, \(4\%\) for the \(Cs\) salts, and \(1\%\) for the \(K\) and \(Na\) salts. Since it is precisely for the \(K\) and \(Na\) salts that Born’s calculations and the initial values of the elastic coefficients are the most accurate, the agreement to within \(1\%\) for the salts of these metals is especially valuable and proves the correctness of the theoretical ideas underlying Born’s circular process and of the numerical values of the quantities entering into it.

§ 9. Calculation of the electron affinity of the atoms \(S\) and oxygen for oxides of the type \(M_{2}O\), \(MO\), \(MS\), \(M_{2}S\), \(MF\) and \(MF_{2}\). Taking into account that the energy \(U\) of the \(Na\) salts proved to satisfy Born’s circular process with an accuracy up to \(1\%\), one might think that Born’s energy for \(NaF\) and \(KF\) has been calculated with the same accuracy. Then from equation (1), substituting there the value \(U\) from Table 7, we obtain for the difference

\[ E_{F}-\frac{1}{2}D_{F}=35{,}4 \]

from \(U_{NaF}\), and

\[ E_{F}-\frac{1}{2}D_{F}=21{,}4. \]

In view of the fact that the data for \(NaF\) are more reliable, we shall retain, as Grimm does, the value \(35{,}4\), but take as the limit of error \(\pm 15\) calories; thus

\[ E_{F}-\frac{1}{2}D_{F}=35{,}4 \pm 15\ \mathrm{Cal}. \]

In exactly the same way the quantities \(E_{O}-\frac{1}{2}D_{O}\) are calculated for oxygen. Here, however, it must be borne in mind that, because of the divalency of oxygen, in the circular process not one but two electrons are joined to it, so that \(E_{O}\) is the energy liberated when two electrons are joined to an oxygen atom.

The starting point of the calculation is the lattice energy of magnesium oxide, calculated by Born and Borman: \(U_{MgO}=828\) large calories, whence from the equation of the circular process:

\[ U_{MgO}=Q_{MgO}+D_{Mg}-\frac{1}{2}D_{O}+J_{Mg}+J'_{Mg}-E_{O}, \]

we find

\[ E_{O}-\frac{1}{2}D_{O}=-118 \pm 31\ \mathrm{Cal}. \]

The quantity \(E-\frac{1}{2}D_{O}\) is negative. This means that the heat of dissociation of oxygen \(D_{O}\) exceeds by 118 calories the magnitude of the doubled affinity of the atom \(O\) for two electrons.

The same could have been done for sulfur, since Born and Borman gave the value \(U\) for zinc blende \(ZnS = 753\). Here the quantity \(E_s - \dfrac{1}{2}D_s = 4 \pm 15\) large cal.; however, taking into account that the quantity \(D_s\) for sulfur vapor is known \((=104\) large cal.), one can here go further and compute the quantity \(E_s\), which \(=56 \pm 15\) large cal. Such energy is liberated when two electrons combine with a sulfur atom.

Knowing the value \(E - \dfrac{1}{2}D\) for \(S\) and \(O\), one can calculate the energies of lattices of the types \(MO\) and \(MS\), where \(M\) is a metal of the second group, and of the types \(M_2O\) and \(M_2S\), where \(M\) is a metal of the first group. For this last case the equation of the cyclic process will be written as follows: \(U_{M_2O}=Q_{M_2O}+2D_M+\dfrac{1}{2}D_O+2J_M-E_i\), and analogously for \(S\).

Thus Grimm calculates the energy \(U\) for the compounds \(MF\), \(MF_2\), \(M_2O\), \(MO\), \(M_2S\) and \(MS\).

TABLE 8.

§ 10. Ionization of salt vapors. The ionization potentials of salt vapors had not previously been measured. Meanwhile, as will be shown below, these quantities are of very great significance for the question under consideration.

At the Physico-Technical X-ray Institute, under my direction, experiments were undertaken for the first time to determine the ionization potentials of vapors of salts of the type \(MX_2\) \((HgCl_2;\ HgJ_2;\ ZnCl_2;\ CdCl_2)\). Two ionization potentials were found for each salt, of which the first was approximately 2.5 times smaller than the second; this indicated two substantially different types of ionization—one connected, probably, with the appearance of single charges, the second with double charges. This second type of ionization was most naturally to be connected with the complete electrolytic dissociation of the molecule \(MX_2\) into \(M^{++}+\overline{X}+\overline{X}\). The energy \(J_{MX_2}\) required for such decomposition will be \(U_{MX_2}-D_{\mathrm{мх}}\), ...

where \(D_{MX_2}\) is the heat of sublimation of the salt \(MX_2\), i.e., that energy which must be expended in order to convert 1 gram-molecule of the salt from the solid state into the gaseous state.

Indeed, we can decompose 1 gram-molecule of the solid salt \(MX_2\) into the free ions \(M^{+} + X^{-} + X\) in two ways. First, we can carry out the direct destruction of the lattice into its constituent ions. For this, by definition, an expenditure of energy \(U_{MX_2}\) will be required (the lattice energy). Second, we can convert the solid salt into vapor, which will require an expenditure of energy \(D_{MX_2}\), and then, already in the vapor state, decompose it into the same ions \(M^{+} + X^{-} + X\) with an expenditure of energy \(J_{MX_2}\). Since the initial and final states are the same, the energy \(U_{MX_2} = D_{MX_2} + J_{MX_2}\).

If the assumption is correct that the ionization potential of the salts \(MX_2\) observed by us indeed corresponds to the decomposition

\[ MX_2 = M + X^{-} + X, \]

and this is quite probable, then we can verify the correctness of the relation

\[ J_{MX_2}=U_{MX_2}-D_{MX}=Q_{MX}+D_M+D_{X_2}+J_M-T_M-2E_X-D_{MX}. \tag{a} \]

We shall make this comparison below.

For the present let us turn to the first ionization potential observed by us. Here a number of decompositions is possible, connected with the appearance of singly charged ions. The most natural are

\[ \text{1) } MX_2=M+X^{-}+X,\quad \text{2) } MX_2=MX+X^{-}\ \text{and 3), } MX_2=MX_2^{+}+I . \]

We can directly calculate only the energy necessary for decomposition (1). Therefore we shall suppose that the first ionization potential in fact corresponds to this type of decomposition.

Let us construct a cyclic process of the Born-process type.

\[ \begin{array}{ccc} (M)+X+X & \xrightarrow{\; +D_M \atop +D_{X_2}\;} & |M|+X_2 \\[6pt] \Big\uparrow\scriptstyle{+J_M-E_X} & & \Big\downarrow\scriptstyle{Q_{MX}} \\[6pt] M^{+}+X^{-}+X & \xleftarrow{\;-J_{MX}\;} & \begin{array}{c} |MX_2|\\ \scriptstyle{-D_{MX}}\\ (MX_2) \end{array} \end{array} \]

whence

\[ J_{MX_2}=J_M-E_X+D_M-D_{X_2}+Q_{MX}-D_{MX}. \tag{b} \]

For calculating the right-hand sides of the equality it is necessary to know the quantities \(D_{MX}\), which are not directly known. However, from the boiling temperatures of the salts under investigation one can, using the formulae of physical chemistry, calculate the quantity \(D_{MX}\). The boiling temperatures of the salts \(ZnCl_2\), \(CdCl_2\), \(HgCl_2\), \(HgJ_2\) are given in the new Landolt tables and are respectively \(730^\circ C\), \(900^\circ C\), \(307^\circ C\), and \(358^\circ C\). Calculating the heats of sublimation corresponding to these boiling temperatures, we obtain: \(D_{ZnCl_2}=23\) large cal. per gram-molecule, \(D_{CdCl_2}=26\) l. cal., \(D_{HgCl_2}=13\) l. cal., \(D_{HgJ_2}=16\) large cal.

Substituting these numbers in equations (a) and (b), we obtain the values of \(J^{b}_{MX_2}\) and \(J'^{(b)}_{MX_2}\) (calculated). The quantities \(J^{(H)}_{MX_2}\) and \(J'^{(H)}_{MX_2}\) are the ionization potentials, expressed in large calories, observed by us directly. The comparison of \(J^{(H)}\) and \(J^{(b)}\) is made in Table 9 (\(\Delta\) is the difference between \(J^{(H)}\) and \(J^{(b)}\)).

TABLE 9.

Since the quantities \(D_M\), \(D_{MX_2}\), \(D_X\) are determined with not very great accuracy and fluctuations in the values of each of these quantities of \(\pm 5\) l. cal. are quite possible, the accuracy in determining \(J^b\) does not exceed \(\pm 15\) large cal. In determining the ionization potential an error of \(\pm 0.3\) volt \(=\pm 8\) large cal. is also possible. Comparing these fluctuations with the quantities \(\Delta\) and \(\Delta'\), we see that the discrepancies between \(J^{(H)}\) and \(J^{(b)}\) in all cases lie within the limits of possible errors. The sole exception is the value \(J_{HgJ_2}\). Here \(\Delta=30\) large cal., which goes beyond the limits of possible errors and shows that in this case the first ionization potential of \(HgJ_2\) corresponds not to the decomposition

\(HgJ_2=\overset{+}{Hg}+\overset{-}{J}+J\), but to one of the other two.

We can use our experimental data in another way as well. Namely, postulating that the first ionization potentials observed by us correspond to the decomposition \(MX_2=\overset{+}{M}+\overset{-}{X}+X\) and the second \(MX_2=\overset{+}{M}+\overset{-}{X}+\overset{-}{X}\), we (similarly to what Grimm did with respect to the ionization potentials \(HCl\), \(HBr\), \(HJ\) found by Knipping) can find the quantities \(E_{Cl}\) and \(E_J\) from formulae (a) and (b). For \(E_{Cl}\) we can obtain 6 values (2 from each salt). For \(E_J\) there is only one in all, since \(J_{HgJ}\) does not correspond to decomposition (1).

We give the table.

TABLE 10.

As can be seen, the difference between the mean value \(E_{ct}\) obtained by us and the optical value \(E'_{ct}\) is only 2 large calories, i.e. 2.4%. There is only one value for \(E_l\), but it agrees with the optical value to within 1.2%.