THE SIMPLEST CHEMICAL REACTIONS

N. Semenov, Leningrad

I. THEORY AND EXPERIMENTAL RESULTS

Already from very early times chemists had the feeling that free atoms are especially active and that, not infrequently, the active properties of gases in statu nascendi were explained by the atomic state of freshly obtained gases. However, this point of view, apparently, was first made the basis of rigorous theoretical considerations only 10 years ago, by Herzfeld and Polanyi in applying the theory to the reaction of combination \( \mathrm{H}_2 + \mathrm{Br}_2 \), and by Nernst to the theory of the photochemical formation of HCl.

The basic idea of Polanyi was the assertion that the reaction between a free atom \(A\) and a molecule \(B_2\) proceeds according to the scheme \(A + B_2 = AB + B\). In the case when the thermal effect of this reaction is positive, it proceeds at almost every collision and requires no activation energy; in the case, however, when the effect of the reaction is negative and equal to \(q\) (the reaction is endothermic), the reaction takes place only if the relative kinetic energy of \(A\) and \(B_2\) is equal to or greater than \(q\).^1

In application to the reaction \(\mathrm{H}_2 + \mathrm{Br}_2 = 2\mathrm{HBr}\), this idea leads to the following results:

^1 Polanyi’s conceptions may at first glance seem far more trivial than they actually are. The point is that, in almost all reactions studied up to now, regardless of whether they are endothermic or exothermic, by no means every collision

By virtue of thermal motion, \(\mathrm{Br}_2\) partially dissociates into atoms:

\[ \mathrm{Br}_2 \rightleftarrows 2\mathrm{Br} - 46000\ \text{cal.} \tag{1} \]

The Br atom reacts with \(\mathrm{H}_2\) according to the scheme:

\[ \mathrm{Br} + \mathrm{H}_2 = \mathrm{HBr} + \mathrm{H} - 15000\ \text{cal.} \tag{2} \]

This reaction (2) is endothermic and occurs only in the case when the relative kinetic energy of the components is \(15000\ \text{cal}\) per mole, or \(\dfrac{15000}{N}\ \text{cal}\) for each pair of reacting particles (\(N\) is Avogadro’s number).

The resulting H atom reacts with \(\mathrm{Br}_2\) according to the scheme:

\[ \mathrm{H} + \mathrm{Br}_2 = \mathrm{HBr} + \mathrm{Br} + 40000\ \text{cal,} \tag{3} \]

and this reaction is exothermic and proceeds at every collision. The Br atom obtained can again produce reaction (2), unless the reverse of the first reaction, the recombination of atoms \(\mathrm{Br} + \mathrm{Br} = \mathrm{Br}_2\), leads to the useless (in the sense of the reaction of HBr formation) disappearance of the Br atom.

The rate of the reaction of HBr formation under the stated assumptions will be determined by the number of favorable collisions of Br atoms and \(\mathrm{H}_2\) molecules. The number of such collisions will be proportional to the product of the concentrations \((\mathrm{H}_2)\) and \((\mathrm{Br})\) and is equal to \(n = k(\mathrm{H}_2)(\mathrm{Br})\), where \(k\) is a certain constant determined by the number of collisions of \(\mathrm{H}_2\) and Br at unit concentrations.

Not all of these collisions will lead to reaction, but only those which occur at a relative kinetic energy \(> 15000\ \text{cal}\) per mole.

leads to reaction, but only those which occur with sufficient kinetic energy. Thus, for example, despite the fact that the decomposition

\[ \mathrm{Cl}_2\mathrm{O} + \mathrm{Cl}_2\mathrm{O} = 2\mathrm{Cl}_2 + \mathrm{O}_2 \]

is accompanied by the liberation of \(30000\ \text{cal}\), the reaction occurs only if the colliding molecules possess an excess kinetic energy of \(22000\ \text{cal}\) per mole. Thus, Polanyi’s reactions are not an exception showing that the reaction of an atom with a molecule proceeds freely, without those harmful resistances which take place in the case of a reaction between two molecules.

According to the Maxwell–Boltzmann law, the probability of such a collision is determined by the value \(e^{-\frac{15000}{RT}}\), where \(R\) is the gas constant (about \(2\) cal) and \(T\) is the absolute temperature. Hence the number of reactions (2) per unit time will be:

\[ w' = k\,(\mathrm{H}_2)(\mathrm{Br})\,e^{-\frac{15000}{RT}}. \]

Since each reaction (2) entails reaction (3), the number of HBr molecules appearing per unit time and equal to the rate \(w\) of the reaction will be:

\[ w = 2k\,(\mathrm{H}_2)(\mathrm{Br})\,e^{-\frac{15000}{RT}}. \]

It remains to determine the concentration of the atoms \((\mathrm{Br})\). In the equilibrium state the dissociation constant of \(\mathrm{Br}_2\), equal to the ratio \(\frac{(\mathrm{Br})^2}{\mathrm{Br}_2}\), is well known and, in the first approximation, is determined by the formula:

\[ C = \frac{(\mathrm{Br})^2}{\mathrm{Br}_2} = A e^{-\frac{46000}{RT}}. \]

Here \(A\) is a certain constant, and \(46000\) cal is the energy of dissociation of \(\mathrm{Br}_2\).

Hence

\[ w = D\sqrt{(\mathrm{Br}_2)(\mathrm{H}_2)}\,e^{-\frac{38000}{RT}}, \tag{1} \]

where \(D = 2k\sqrt{A}\). The expression obtained is valid only for the first stages of the reaction, when the concentration of the reaction product \((\mathrm{HBr})\) is negligible. When the concentration becomes appreciable, then at the output one must take into account the harmful reactions

\[ \mathrm{H} + \mathrm{HBr} = \mathrm{H}_2 + \mathrm{Br} \quad\text{and}\quad \mathrm{Br} + \mathrm{H}_2 = \mathrm{HBr} + \mathrm{H}. \]

As a result, instead of formula (1) a more complicated one is obtained:

\[ w = \frac{ D(\mathrm{H}_2)\sqrt{(\mathrm{Br}_2)}\,e^{-\frac{38000}{RT}} }{ m + \dfrac{(\mathrm{HBr})}{(\mathrm{Br}_2)} }, \tag{2} \]

where \(m\) is a certain number of the order of unity.

This formula describes the experimental results very accurately, which confirms the correctness of Polanyi’s basic idea concerning reactions of the type \(A + B_2 = AB + B\).

The same applies also to the reaction of combination \( \mathrm{H_2 + Cl_2}\). True, the thermal reaction of formation of \(\mathrm{HCl}\) has so far been studied only very little; but the photochemical reaction has been studied well. Frank’s student, Kuhn, showed that a \(\mathrm{Cl_2}\) molecule, on absorbing a quantum of light, breaks up into two atoms according to the scheme:

\[ \mathrm{Cl_2} + h\nu = \mathrm{Cl} + \mathrm{Cl}. \tag{1} \]

The subsequent reaction proceeds according to the scheme:

\[ \mathrm{Cl} + \mathrm{H_2} = \mathrm{HCl} + \mathrm{H} + 0\ \text{cal} \tag{2} \]

\[ \mathrm{H} + \mathrm{Cl_2} = \mathrm{HCl} + \mathrm{Cl} + 45000\ \text{and so on}. \tag{3} \]

Since here both reactions (2) and (3) require no expenditure of energy, they proceed without any additional activation at every collision.1 Thus, once begun, the reaction proceeds as a chain, causing a whole series of subsequent reactions, until a collision of \(\mathrm{Cl}\) or \(\mathrm{H}\) with the wall or with a molecule of some impurity reacting with them breaks the chain.2 As is known, the chain character of this reaction explains its abnormally large quantum yield: under favorable conditions, for each absorbed quantum of light there are \(10^5\) molecules that have reacted.

Several years ago Polanyi set himself the aim of studying reactions of the type \(A + B_2\) in the simplest

and visual conditions. These works were completed in 1928 and led to a complete and brilliant confirmation of his ideas.

He chose, for this purpose, reactions between vapors of halogens and vapors of alkali metals (which, as is known, in the vapor state consist predominantly of atoms).

We shall examine below the interesting methodology of these experiments. For the moment we shall briefly present the results of his investigations.

In full agreement with his scheme, each collision of a Na atom with a Cl₂ molecule leads to a reaction according to the scheme:

\[ \mathrm{Na}+\mathrm{Cl}_{2}=\mathrm{NaCl}+\mathrm{Cl}+35000\ \text{cal.} \tag{1} \]

The Cl atom formed, as it turns out, practically does not combine at all with Na in the volume (which has a good theoretical explanation),¹ but reacts with it only on the walls of the apparatus.

The same applies also to the recombination reaction \(\mathrm{Cl}+\mathrm{Cl}=\mathrm{Cl}_{2}\). But in the volume another reaction takes place:

\[ \mathrm{Cl}+\mathrm{Na}_{2}=\mathrm{NaCl}+\mathrm{Na}+75000\ \text{cal.}, \tag{2} \]

i.e. it also satisfies the scheme \(A+B_{2}=AB+B\). As is known from other experiments, \(\mathrm{Na}_{2}\) molecules are always present in some quantity in Na vapors.

The dissociation energy of \(\mathrm{Na}_{2}\) molecules is not so small and is equal to \(16000\ \text{cal.}\) As Polanyi showed, reaction (2) also takes place at every collision.

¹ At first glance it seems strange why atoms, being active with respect to a molecule, do not wish to react directly with one another. Meanwhile this fact follows not only from Polanyi’s data, but also from direct observations by Bonhoeffer and others on the rate of recombination \(\mathrm{H}+\mathrm{H}=\mathrm{H}_{2}\) of hydrogen, and from Jost’s observations on the recombination of Br atoms. It turned out that the reaction \(\mathrm{H}+\mathrm{H}=\mathrm{H}_{2}\) practically does not proceed at all. Recombination occurs only on the wall, while in the volume it occurs only in a triple collision \(\mathrm{H}+\mathrm{H}+N=\mathrm{H}_{2}+N\), where \(N\) is any molecule. Theoretically such a result is also understandable, for in order for two atoms to combine, their collision is not enough: however great their tendency to combine may be, for this they must transfer somewhere the energy that is released in the process. The third particle is therefore necessary as a body to which they can give this energy.

The reaction of the compound Na with Cl is associated with an intense emission of light in the form of the yellow sodium line. This phenomenon is not thermal, since under Polanyi’s experimental conditions (very low pressures) the temperature of the reaction zone exceeded the ambient temperature (in his experiments, \(600^\circ\) abs.) by only a few degrees. This luminescence is typical chemiluminescence. The origin of this chemiluminescence is as follows: in reaction (2), \(75\,000\) cal per mole is liberated, or

\[ \frac{75000}{N}\ \text{cal} = \frac{75000}{23.10^{19}}\times 4.1\times 10^7\ \text{erg} = 5\times 10^{-12}\ \text{erg} \]

for each elementary act.

A tremendous part of this energy, immediately after the reaction, appears in the form of vibrational energy of the Na and Cl atoms in the NaCl molecule.

Thus, at the first instant after the reaction we obtain an excited molecule \(\mathrm{NaCl}'\) with an excess energy of \(5\times 10^{-12}\) erg. If we recall that, in thermal equilibrium, the vibrational energy of a molecule is

\[ \frac{1}{2}kT = \frac{1}{2}\times 1.4\times T\times 10^{-16} = 7\times 10^{-17}T\ \text{ergs}, \]

then the excited molecules, in their vibrational state, correspond to a temperature \(T\) of \(70\,000^\circ\); and this is despite the low temperature surrounding them. It goes without saying that such an enormous portion of energy cannot remain in them for long, and during collisions it is dissipated and gradually passes into the general heating of the gas. However, immediately after the act of reaction this entire portion is contained in the molecule \(\mathrm{NaCl}'\), and when it collides with a Na atom this energy can make it begin to glow, just as it glows at high temperatures.^1

^1 If, between the formation of \(\mathrm{NaCl}'\) and its nearest collision with Na, a collision of \(\mathrm{NaCl}'\) with any other molecules occurs, then the energy of Cl is gradually dissipated and the probability of its transfer to Na decreases. This theoretical conclusion was confirmed by Polanyi’s experiments, in which he diluted sodium vapor with nitrogen. The more nitrogen there was, the lower the intensity of the chemiluminescence.

In order for Na to glow, its peripheral electron must be raised to the second Bohr orbit.

For this, an energy of \(3.3 \times 10^{-12}\) erg is needed. Since the molecule \(\mathrm{NaCl}'\) possesses an energy greater than this latter amount, it is natural that upon collision of \(\mathrm{NaCl}'\) with \(\mathrm{Na}\), the latter radiates the energy imparted to it according to the scheme:

\[ \mathrm{NaCl}' + \mathrm{Na} = \mathrm{NaCl} + \mathrm{Na}'; \qquad \mathrm{Na}' = \mathrm{Na} + h\nu. \]

Polanyi’s experiments showed that almost every collision of \(\mathrm{NaCl}'\) with \(\mathrm{Na}\) leads to the emission of a quantum of light.

Polanyi obtained the same results for the reaction \(\mathrm{Na} + \mathrm{I}_2\). He then studied a series of reactions between \(\mathrm{K}\) and \(\mathrm{Na}\), on the one hand, and \(\mathrm{HgCl}_2\), \(\mathrm{HgBr}_2\), etc., on the other.

In all these cases the reaction proceeds according to the scheme:

\[ \mathrm{Na} + \mathrm{HgCl}_2 = \mathrm{NaCl} + \mathrm{HgCl} + 25000; \tag{1} \]

\[ \mathrm{HgCl} + \mathrm{Na} = \mathrm{NaCl}' + \mathrm{Hg} + 53000. \tag{2} \]

The \(\mathrm{NaCl}'\) molecules produced in reaction (2), when excited, possess energy sufficient for the optical excitation of \(\mathrm{Na}\). This explains the emission of the \(D\) line.

Both reactions (1) and (2) are exothermic, and in accordance with this the experiment leads to the result that almost every collision of \(\mathrm{Na}\) with \(\mathrm{HgCl}_2\) and of \(\mathrm{HgCl}\) with \(\mathrm{Na}\) leads to reaction.

A very interesting experiment was carried out by Polanyi with the reaction of formation of \(\mathrm{HCl}\) induced by traces of \(\mathrm{Na}\).

A stream of hydrogen at a pressure of \(5\)—\(15\) mm passes over heated metallic sodium and carries with it a certain very small quantity of vapor of the latter (the partial vapor pressure of \(\mathrm{Na}\) is \(0.0005\) mm). Then the hydrogen stream enters, in the dark, a vessel with chlorine. Although at the temperatures of the experiment the reaction of formation of \(\mathrm{HCl}\) under ordinary conditions does not proceed at all, an insignificant admixture of sodium vapor changes the situation and catalyzes the rapid combination reaction

\[ \mathrm{H}_2 + \mathrm{Cl}_2. \]

This phenomenon should in fact be classified among cases of induced reactions. Its explanation follows from Polanyi’s conceptions.

Indeed, we have seen that the chemical action of light on a mixture of \(Cl_2\) is determined by the fact that light decomposes \(Cl_2\) into atoms. But the very same thing can be done in the dark by sodium: according to what was said above, the primary reaction between Na and \(Cl_2\) proceeds according to the scheme \(Na + Cl_2 = NaCl + Cl\).

Thus, here too a free chlorine atom arises, which, according to what was said above, brings about a long chain of reactions \(Cl + H_2 = HCl + H;\ H + Cl_2 = HCl + Cl\), etc. Just as in the photochemical reaction there are very many reacted molecules for each absorbed quantum of light, so here for each reacted Na atom there are very many molecules of HCl formed, as was in fact shown by Polanyi.

Polanyi also carried out an analogous experiment with the reaction of the combination of chlorine with methane, induced by sodium. Here the chain develops according to the scheme:

\[ Na + Cl_2 = NaCl + Cl; \]

\[ Cl + CH_4 = HCl + CH_3; \]

\[ CH_3 + Cl_2 = CH_3Cl + Cl \]

etc.

Up to now we have been dealing with such reactions

\[ A + B_2 = AB + B, \]

where the heat effect is positive. In these cases, as we have seen, the reaction occurs at every collision and is practically independent of temperature (it depends only insofar as the temperature increases the number of collisions, i.e. proportionally to \(\sqrt{T}\)).

An exception was the hypothetical reaction

\[ Br + H_2 = HBr + H - 15000, \]

discussed at the very beginning. In these cases Polanyi’s theory leads, as we have seen, to the conclusion that the reaction will occur not at every collision, but only in the case when the energy of the colliding molecules, calculated per mole, exceeds the absolute value \(q\) of the heat effect of the reaction. We have seen that, according to the Maxwell–Boltzmann law, in this case the reaction rate will depend on

the temperature in a very appreciable way, namely according to the law \(e^{\frac{q}{RT}}\). The larger \(q\) is, i.e., the more endothermic the reaction, the more rapidly its rate will decrease with a lowering of the temperature.

And indeed, observing the rate of the reaction between Na and HCl vapors, Polanyi confirmed this result. In this case the first act of the reaction

\[ \mathrm{Na} + \mathrm{HCl} = \mathrm{NaCl} + \mathrm{H} \]

is associated with an expenditure of 4000 calories. Consequently, here not every collision of Na and HCl will lead to reaction, but only a fraction \(e^{-\frac{4000}{RT}}\) of the collisions. At a temperature of about \(600^\circ\) abs. the value

\[ e^{-\frac{4000}{RT}} \approx \frac{1}{300}, \]

i.e., out of 300 collisions only one will lead to reaction. This result was quantitatively confirmed by Polanyi experimentally. Analogous results were obtained by Polanyi for the reactions of Cd and Zn vapors with \(\mathrm{Cl}_2\), where, as it turned out, the primary stage of the reaction leads to the formation of monochlorides according to the scheme:

\[ \mathrm{Cd} + \mathrm{Cl}_2 = \mathrm{CdCl} + \mathrm{Cl} - 12500 \quad\text{and}\quad \mathrm{Zn} + \mathrm{Cl}_2 = \mathrm{ZnCl} + \mathrm{Cl} - 8000. \]

Both reactions are endothermic, and their rate accordingly depends strongly on the temperature, decreasing with decreasing \(T\) according to the law \(e^{-\frac{q}{RT}}\). In view of the slowness of these reactions Polanyi employed for their investigation a very ingenious method. For “revealing the basic reaction” he made use of the study of the reaction of HCl formation induced by it (as we saw in the example of sodium, each act of reaction of a metal atom with \(\mathrm{Cl}_2\) calls forth a long chain of reactions of HCl formation1).

What has been said essentially exhausts the results obtained by Polanyi.

Another group of works concerns the reactions of atomic hydrogen, atomic nitrogen, and atomic oxygen. All these gases in the atomic state are extraordinarily active, and the reason for this activity apparently also lies in the remarkable property of reactions of the type $A+B_2=AB+B$ to proceed at every collision. However, we shall set aside the description of these results until one of the following issues of the journal, and for the time being shall try to draw conclusions from Polanyi’s theory for the case of surface reactions.

If a free Na atom reacts with Cl$_2$ with the formation of NaCl and a free chlorine atom, then we may suppose that in the reaction of Cl$_2$ with solid Na the reaction can proceed according to the same scheme.

The Cl atom produced in this way can, of course, at once combine with the nearest neighboring Na atom; for, as is known from Polanyi’s experiments, on the wall the reaction $\mathrm{Na}+\mathrm{Cl}=\mathrm{NaCl}$ proceeds readily. However, another result is also possible. The second Cl atom will hardly enter into the reaction simultaneously with the first. If there is even a slight delay, then the kinetic energy which this atom receives at the moment of the primary reaction will cause it to fly off rapidly from the surface into the volume; that is, as a result of the reaction of one chlorine atom of the Cl$_2$ molecule with the Na surface, the second chlorine atom, in the atomic state, will find itself in the gaseous medium. Such a conclusion has not been verified experimentally, but if it were indeed the case, we could obtain a number of very interesting results.

Indeed, this would give us a method for obtaining atoms and free radicals in the gaseous medium. Let us suppose, for example, that nitric oxide NO, at reduced pressure, is passed in a rapid stream over heated magnesium. Then, through the reaction $\mathrm{Mg}+\mathrm{NO}=\mathrm{MgO}+\mathrm{N}$, we can obtain free atomic nitrogen in the stream. Two experiments, unfortunately insufficiently verified, support this point of view.

Two years ago, in our laboratory at the Leningrad Physico-Technical Institute, Polyakov blew a rapid stream of very pure hydrogen over palladium, heated-

heated to 400° C (and previously well degassed), obtaining along the path of the jet, at a distance of 20 cm from the palladium in the cold part of the apparatus, a glow of the quartz tube, associated with a noticeable heating of it. The phenomenon ceased after the palladium became saturated with hydrogen. The phenomenon could not be explained otherwise than by a partial decomposition of hydrogen into atoms when the jet passed over the palladium. Such a result would contradict thermodynamics, if one did not adopt the viewpoint expressed above on the applicability of the Polanyi reaction to the case when one of the components is a solid. Indeed, when H₂ strikes palladium, a reaction can occur according to the scheme H₂ + wall = (H wall) + H, i.e., at the expense of the adsorption energy of one hydrogen atom, the other flies off into space. True, this reaction is endothermic, since the rupture of H₂ into atoms requires an expenditure of 100,000 cal, whereas the energy of adsorption of an H atom by palladium hardly exceeds 60,000 cal. Thus it is necessary for the hydrogen molecule to strike the palladium surface with an energy of 40,000 cal per mole; in other words, of \(10^{12}\) collisions only one will lead to the formation of an H atom in the volume. However, even under these assumptions, \(10^{14}\) hydrogen atoms will appear per second. Thus, as a result of this process the quantity of atomic hydrogen may prove immeasurably greater than that which can exist in the equilibrium state at 400° C.

It goes without saying that the phenomenon will take place only so long as the palladium is not saturated with hydrogen, since the calculation will be valid while the palladium surface is not filled with hydrogen. As soon as atomic hydrogen saturates the palladium and covers its surface, every impact of atomic hydrogen on the wall will lead to its disappearance, owing to recombination of two H atoms into an H₂ molecule, and the resulting concentration of H atoms in the volume will not exceed the equilibrium thermodynamic value corresponding to 400° C.

The second consideration in favor of the viewpoint we have expressed follows from Christiansen’s work on thermal—

for the formation of HCl. Without going into details, I shall note that he could interpret his results only by assuming that the primary formation of Cl atoms occurs as a result of the reaction

\[ \mathrm{Cl_2}+\text{wall}=(\mathrm{Cl}\ \text{wall})+\mathrm{Cl}. \]

Somewhat earlier I had expressed the same point of view with regard to the reaction of combination of \(\mathrm{H_2}+\mathrm{O_2}\).

Still more interesting conclusions may be drawn from an analysis of Polanyi’s results with the reaction of formation of HCl induced by Na.

Let us suppose, for example, that the first act of the slow oxidation of coal proceeds according to the scheme:

\[ \text{coal}+\mathrm{O_2}=\mathrm{CO}+\mathrm{O}. \]

Let us further suppose that in the oxygen there is an excess of nitrogen, which is partially adsorbed by the coal. Then the O atom formed could react on the surface of the coal with \(\mathrm{N_2}\), with formation of \(\mathrm{N_2O}\) according to the scheme

\[ \mathrm{N_2}+\mathrm{O}+\text{wall}=\mathrm{N_2O}+\text{wall}. \]

Thus, at the expense of the energy of combustion of the coal, we could obtain nitrogen oxides directly. At the same time as this thought occurred to me, I heard it from A. N. Bach, and then from A. N. Frumkin. The first of them maintained that chemical processes occurring in the organism can be understood only from the standpoint of the direct induction of their oxidative reactions. Such an inducing action need not necessarily be connected with the appearance of a substance in the atomic state. As we have seen, Polanyi showed that immediately after the reaction the energy of the NaCl′ molecule corresponds to \(70\,000^\circ\). On collision of such NaCl′ molecules with Na they transfer their energy to the latter and cause it to glow. Thus, the energy of the reaction products can be transferred to other molecules, and in this way the latter can be activated.

II. Method for Measuring Fast Reactions

Since almost every collision of reacting molecules leads to a reaction, the usual methods for measuring the rate of reactions become inapplicable, since it is impossible even to manage to mix the reacting gases. Therefore Polanyi,

Trenin, Kondrat’ev, and others, working with such reactions, applied the method of opposing jets of vapors at low pressures. An evacuated tube is taken; sodium is placed at one end, and a large part of the tube is put into a furnace heated to a temperature of about \(300^\circ\mathrm{C}\). In this case Na begins to evaporate, distilling into the cold end \(B\) of the tube (Fig. 1). In the branch \(D\) there is Br

Fig. 1

or liquefied \(Cl_2\) at such a low temperature that the vapor pressure of the halide is on the order of several thousandths of a mm. In this case, a stream of \(Cl_2\) goes toward the vapor stream. At the place where they meet, solid NaCl will form, depositing on the walls. The pressure of Na and \(Cl_2\) will fall to 0, and, under the action of the pressure difference, new and new portions of Na and \(Cl_2\) will be supplied to the reaction zone. Thus we can obtain a stationary reaction zone. The place in the tube where the reaction zone is created is determined by the pressure \(p_1\) of Na vapors at end \(A\) and the pressure \(p_2\) of \(Cl_2\) vapors in \(D\), or, in other words, by the temperature of the furnace and of the branch \(D\). The greater \(p_1\), the closer to end \(B\), and the greater \(p_2\), the closer to end \(A\), the reaction zone will be established. Along the tube from end \(A\) to the reaction zone the pressure \(p_{\mathrm{Na}}\) will fall from \(p_1\) to 0. Similarly, the chlorine pressure \(p_{\mathrm{Cl_2}}\) will fall from \(p_2\) to 0. The position of the zone will be determined by the condition that the number of Na atoms diffusing to the reaction zone

tion (under the action of the pressure gradient of sodium vapor \(p_{\mathrm{Na}}^{*}\)) must be equal to twice the number of chlorine molecules diffusing there under the action of the chlorine pressure gradient \((\mathrm{Na}+\frac12\mathrm{Cl}_2=\mathrm{NaCl})\), since only under these conditions will Na and \(\mathrm{Cl}_2\) be completely converted into solid NaCl and the state will be stable. If the reaction zone were practically infinitely narrow, then the picture of the pressure distribution of \(p_{\mathrm{Na}}\) and \(p_{\mathrm{Cl}}\) along the tube would be determined by the curve in Fig. 2.

Fig. 2

It is not difficult to calculate at what distance \(l_1\) from end \(A\) of the tube the reaction zone must be, if the total length of the tube is \(l\). Suppose that the gases are taken at a pressure of \(0.01\)—\(0.001\) mm, when collisions of molecules with one another play a smaller role than their collisions with the walls of the tube. In this case gas diffusion is determined by the formula:

\[ Q=\frac{1}{k}\frac{dp}{dl}, \]

where \(Q\) is the total amount of substance that has diffused, and \(k\), the so-called resistance of the tube, is, according to Knudsen,

\[ k=\frac{6}{d^3}\sqrt{\frac{MRT}{2\pi}}, \]

where \(d\) is the diameter of the tube, \(M\) is the molecular weight of the gas, and \(R\) is the gas constant.

According to what was said above, the stationarity condition of the zone will be determined by the equation \(Q_{\mathrm{Na}}=\frac12 Q_{\mathrm{Cl}_2}\). And since

\[ \frac{dp_{\mathrm{Na}}}{dl}=\frac{p_1-0}{l_1}=\frac{p_1}{l_1} \quad\text{and}\quad \frac{d_{\mathrm{Cl}_2}}{dl}=\frac{p_2}{l_2}=\frac{p_2}{l-l_1}, \]

then

\[ \frac{1}{k_{\mathrm{Na}}}\frac{p_1}{l_1} = \frac12\cdot\frac{1}{k_{\mathrm{Cl}_2}}\cdot\frac{p_2}{l-l_1} \quad\text{or}\quad \frac{l}{l_1}-1=\frac{k_{\mathrm{Na}}}{2k_{\mathrm{Cl}_2}}\frac{p_2}{p_1}, \]

This equation determines the position of the zone, if the pressure of Na above liquid Na and the pressure of Cl₂ above liquid Cl₂ are respectively equal to \(p_1\) and \(p_2\).

However, in reality the reaction zone is not infinitely narrow. It is precisely the width of the zone that is of interest, since it gives us a basis for determining the reaction rate.

Experimentally, the question of the distribution of the amount of substance that has reacted is investigated as follows. At the place of the reaction zone, a precipitate of NaCl appears on the walls of the tube. By cutting the tube after the experiment into a series of narrow rings, washing the precipitate from them, and determining the amount of NaCl by titration, one can find how the precipitate is distributed along the zone, and consequently what amount of Na and Cl₂ molecules has reacted in the various cross sections of the tube.

Fig. 3

In Fig. 3 the curve of the distribution of the NaCl precipitate along the tube is given (the abscissas are given in cm).

To determine the rate constant of the reaction we must know the distribution of the pressures \(p_{\mathrm{Na}}\) and \(p_{\mathrm{Cl_2}}\) in the reaction zone.

This is not difficult to do by the following procedure.

Let curve 1 (Fig. 4) give the distribution of the precipitate obtained in the experiment (here on the ordinate axis are plotted the quantities \(U\)—the density of the precipitate, referred to unit length).

Let us now consider an element of a section of the tube of length \(dl\). If there were no reaction, then the amount of Na introduced from one side into the cut-out cylindrical element would be equal to the amount of Na carried out of the element from the other side. In other words, the stationary state would be determined by the ordinary diffusion equation \(\frac{1}{k}\frac{d^{2}p}{dl^{2}}\,dl=0\). However, since in the element there occurs the disappearance of \(Udl\) of substance as a result of the reaction, the stationarity equation will take the form:

\[ \frac{1}{k}\frac{d^{2}p}{dl^{2}}-U=0. \]

Integrating this equation, we obtain \(p_{\mathrm{Na}}\) as a function of \(l\) in the following form:

\[ p_{\mathrm{Na}}=k_{\mathrm{Na}}\iint U\,dl\,dl. \]

This double integral is not difficult to obtain by double graphical integration of curve 1 (Fig. 4).

Curve 3 (Fig. 4) shows the results of such integration.

In an analogous way we obtain the graph of the distribution of chlorine pressure in the reaction zone—curves 3, (Fig. 4).

Knowing the distribution of pressure in the different regions, we can easily find the reaction-rate constant.

Indeed, assuming that the reaction rate is proportional to the number of collisions of Na and Cl molecules, we obtain:

\[ kq p_{\mathrm{Na}} p_{\mathrm{Cl}_{2}}=U, \]

where \(k\) is the reaction-rate constant, and \(q\) is the cross-section of the tube.

From this formula we find without difficulty the reaction-rate constant in the various parts of the tube. From its numerical value we conclude that every collision of Na molecules with \(\mathrm{Cl}_{2}\) atoms leads to reaction.

It must be said, however, that upon collision of Na and \(\mathrm{Cl}_{2}\) the reaction of formation of NaCl must proceed with the liberation of a free Cl atom, which already by a secondary reaction

can give a second molecule of NaCl. Polanyi’s experiment very clearly confirms the existence of two types of reactions.

The point is that the reactions of haloids with metal vapors are associated, as was indicated, with intense chemiluminescence. In studying this chemiluminescence it turned out that the maximum of its brightness by no means coincides with the maximum of the reaction, but is displaced considerably (up to 7 cm) toward

Fig. 4

the Na side. Fig. 5 gives Polanyi’s results for the reaction \(Na + J_2\). Curve 1 gives the distribution, along the length of the tube, of the precipitate, and curve 2 the intensity of the light of the chemiluminescence. This indicates that, in addition to the main reaction associated with the most rapid course of the transformation of the substance, there is some secondary reaction associated with the emission of light. The presence of such a second reaction is also indicated by the distribution of the precipitate. We see from Fig. 5 that the curve of the precipitate distribution is not symmetrical, but is strongly elongated toward Na.

Since there are no grounds for such an asymmetry other than the existence of two reactions, we may divide curve 1 into two symmetrical curves; each of these curves

has the same area and corresponds to the same amount of NaCl formed. But if the zone of the first of them has a length of about 5 cm, then the second has a length of 10 cm. It is precisely this second reaction that is connected with the emission of light. In this way Polanyi came to the conclusion that the reaction \(Na + Cl_2\) proceeds in two phases: 1) \(Na + Cl_2 = NaCl + Cl\) and 2) when Cl atoms react with Na and give NaCl.

Fig. 5

We cannot dwell here in detail on the ingenious experiments that enabled Polanyi to decipher the mechanism of the second phase of the reaction. He showed, first of all, that this secondary reaction takes place chiefly on the wall, where the adsorbed Cl and Na atoms recombine. He then showed that the part of the reaction which takes place in the volume proceeds very slowly. Thus, by no means every collision of Na and Cl atoms in the volume leads to the formation of NaCl. He further showed that even in these few cases the reaction proceeds by collision of Cl atoms with \(Na_2\) molecules. The latter was proved in the following way. He overheated the reaction zone and obtained a considerable weakening of the chemiluminescence. Intense chemiluminescence must be proportional to the rate of the secondary reaction in the volume. The experiments showed that the intensity of the glow, and hence also the rate of the secondary reaction, falls with increasing overheating of the zone according to the law \(e^{-\frac{q}{RT}}\)

where \(q = 18{,}000\) cal. This quantity is precisely equal to the dissociation energy of the \(Na_2\) molecules and, consequently, the decrease in the reaction rate must be associated with the dissociation of \(Na_2\), which increases with rising temperature. It follows from this that it is specifically the collisions of \(Cl\) with \(Na_2\), and not with \(Na\), that lead to the secondary reaction in the volume.

Further, carrying out experiments in a somewhat modified apparatus (chlorine was admitted through a narrow opening into a space filled with sodium vapor), Polanyi was able to create, in the reaction zone, an excess pressure of \(Na\) of any magnitude. In this apparatus he succeeded in determining the dependence of the glow, and hence also of the rate of the secondary reaction, on the pressure of \(Na\). It turned out that the latter increases in proportion to the square of the pressure of \(Na\), and not to its first power. If the secondary reaction occurred as a result of collisions of \(Na\) and \(Cl\), then its rate would be proportional to the first power of the pressure of \(Na\). But if the secondary reaction is connected with collisions of \(Cl\) and \(Na_2\), then it will be proportional to the pressure of \(Na_2\). The concentration of \(N_2\) molecules, by the laws of thermochemistry, will be proportional to the square of the pressure of \(Na\).

The experiments described are, it seems to me, the fundamental ones; but in addition to them Polanyi and his students have provided a whole series of supplementary experiments and considerations confirming the scheme.

1. The reaction \(\mathrm{Hg} + \mathrm{O}_2 = \mathrm{HgO} + \mathrm{O}\) requires an expenditure of about 50,000 calories and therefore normally does not proceed. However, as Zagulin showed, it is sufficient to form an excited Hg atom for the reaction to proceed very rapidly. The excitation energy of \(\mathrm{Hg}'\) is 112,000 cal., and thus the reaction \(\mathrm{Hg}' + \mathrm{O}_2 = \mathrm{HgO} + \mathrm{O}\) will be exothermic, which explains the possibility of this reaction. The formation of \(\mathrm{Hg}'\) is produced by irradiating mercury vapor with the line \(2536\,\text{\AA}\). ↩↩

2. Experimentally and theoretically, the disappearance of \(\mathrm{Cl}\) as a result of the reaction \(\mathrm{Cl + Cl = Cl_2}\) here (in contrast to the case of the reaction of \(\mathrm{HBr}\) formation considered by us) cannot play any significant role, since, owing to the large dissociation energy of \(\mathrm{Cl_2}\) (\(56000\ \text{cal}\)), the equilibrium amount of \(\mathrm{Cl}\) atoms at room temperature (and even at \(200^\circ\mathrm{C}\)) is negligibly small. ↩