Kinetics of the Topochemical Interaction of Certain Metal Bromides with Hydrogen Chloride

E. T. Labykina

As the object of investigation we took exchange reactions between bromides of a number of metals and hydrogen chloride:

\[ \mathrm{MeBr} + \mathrm{HCl} \rightarrow \mathrm{MeCl} + \mathrm{HBr}. \]

Reactions between solid halides and metal oxides, on the one hand, and halogens and hydrogen halides, on the other, “in the absence of water” were first studied by Potylitsyn [1]. As a result of his investigations he came to the conclusion that the chemical activity of solid substances is in a definite quantitative dependence on the magnitude of the atomic weight of the metal. Potylitsyn notes that it would be of interest to confirm the regularity obtained by studying the rates of similar reactions.

The literature contains indications of a connection between the physical, as well as physicochemical, properties of solid substances and their chemical activity [2, 3, 4, 5]. Nevertheless, in the chemistry of solids there is no general theory explaining the connection between the reactivity of solid substances, usually revealed in the study of kinetic regularities, and a number of physicochemical properties of solids.

Thus, the accumulation of facts in this field and their explanation are of substantial interest for the development of the theory of the chemistry of solids.

Our aim was to reveal the regularity of the connection between the reactivity of solid substances—bromides of monovalent and certain divalent metals—and the magnitude of the ionic radius of the metal, the energy of the crystal lattice, the molecular volume, and the crystal structure of the bromide, and also to identify a number of kinetic features of topochemical exchange reactions.

For the investigation we took bromides of sodium, potassium, rubidium, cesium, copper, silver, thallium, barium, and lead.

The salts of the alkali metals and thallium were ready-made preparations of “chemically pure” grade; the bromides of copper, silver, barium, and lead were prepared according to preparative manuals [6, 7].

Experimental Data

The rate of the reactions was measured from the change in weight of the reacting salt in a stream of dry hydrogen chloride. The method of spiral quartz balances was used.

The experiments were carried out in the series NaBr--KBr--RbBr--CsBr

at \(t = 250^\circ, 300, 350^\circ\mathrm{C}\), in the series CuBr--AgBr--TlBr

at \(t = 210^\circ, 250, 280, 300, 320, 340^\circ\mathrm{C}\), and in the series BaBr\(_2\)--PbBr\(_2\)

at \(t = 200, 210^\circ, 250, 300^\circ\mathrm{C}\).

From the results of the experiments, constants characterizing the reaction rate and the activation energies of the reactions were calculated (Fig. 1). To calculate the rate constants, the Kolmogorov--Erofeev equation [8,9] was used:

\[ \alpha = 1 - e^{-kt^n}, \tag{1} \]

where \(\alpha\) is the fraction of substance that has reacted by the time \(t\), and \(n\) and \(k\) are constants determined graphically. The data are given in Table 1.

Independently of the processes that complicate a chemical reaction for substances in the solid state (diffusion, adsorption, crystallization), the rate of topochemical reactions obeys a general regularity; namely, the curve of the dependence of the reaction rate on time is characterized by the presence of a maximum, and with increasing temperature the maximum shifts along the time axis toward the origin, while at higher temperatures the reaction begins at the maximum rate (Figs. 2--8).

On the basis of the kinetic study we have established a parallelism between the reactivity of solid metal bromides, the cation radius, the change in crystal-lattice energy, and the change in molecular volume in the transition MeBr \(\to\) MeCl (Table 2).

Fig. 1. Dependence of \(\lg K\) on \(\dfrac{1}{T}\).

\[ \begin{cases} \text{I--RbBr + HCl;} \quad \text{II--CsBr + HCl;}\\ \text{III--AgBr + HCl;} \quad \text{IV--CuBr + HCl;}\\ \text{V--TlBr + HCl.} \end{cases} \]

The smaller the change in crystal-lattice energy in the transition MeBr--MeCl and the smaller the relative change in molecular volume, the higher the reactivity of the solid bromides and the faster the reaction proceeds.

The microscopic picture of the crystalline transformation of the crystals of the initial bromides and of the reaction products—the chlorides of the corresponding metals—shows that in the process

\[ \mathrm{MeBr}+\mathrm{HCl}\to \mathrm{MeCl}+\mathrm{HBr} \]

there is a substantial difference for the bromides of the alkali metals and for the bromides of silver, thallium, and copper.

If the external appearance, the shape of the crystals, and their transparency changed hardly at all for salts of metals with 18-electron shells (Figs. 9 and 10), then for the salts of the alkali metals a large change was observed: before the reaction, crystals of rubidium and cesium bromides had the appearance of formations with rectangular faces, completely transparent; after the reaction the product is intergrown druses of small crystals,

Table 1

Kinetic-analysis data according to the Kolmogorov—Erofeev equation

The color of the accretions is milky white; at the boundaries of the accretions, small, regularly formed cubes of the corresponding chlorides are visible (Figs. 11 and 12).

In the case of reactions of alkali-halide salts, it may be assumed that the anionic vacancies formed on the surface of the crystal migrate over the surface and are filled by chlorine ions, but not at the places where they originally arose; otherwise the original lattice structure would have been preserved. The cause of defect migration may be not simply thermal motion, but the chemical mechanism of the reaction. In the present case, at the phase boundary there may form

Table 2

Activation energy of the reaction $\mathrm{MeBr} + \mathrm{HCl} \to \mathrm{MeCl} + \mathrm{HBr}$, and its relation to the molecular volume and crystal-lattice energy

Fig. 2. Change in the reaction rate
\(\mathrm{RbBr + HCl = RbCl + HBr}\) with time.

Fig. 3. Change in the reaction rate
\(\mathrm{CsBr + HCl = CsCl + HBr}\) with time.

Fig. 4. Change in the reaction rate
\(\mathrm{AgBr + HCl = AgCl + HBr}\) with time.

intermediate unstable compounds—polyhalides (which is characteristic precisely of cesium and rubidium), whose lattice dimensions probably differ from the lattice dimensions of the halides and, thus, the transition to the final reaction product—the chloride—must be accompanied by a change in lattice dimensions and recrystallization, as we in fact observe.

Fig. 5. Change in the reaction rate of
$\mathrm{CuBr}+\mathrm{HCl}=\mathrm{CuCl}+\mathrm{HBr}$ with time.

Fig. 6. Change in the reaction rate of
$\mathrm{TlBr}+\mathrm{HCl}=\mathrm{TlCl}+\mathrm{HBr}$ with time.

The formation of cesium polyhalides in reactions of this type has been experimentally confirmed [10]. The absence of reaction between sodium and potassium bromides (potassium bromide enters into reaction only at

\(t = 350^\circ\) to a very slight extent) and hydrogen chloride, is possibly explained by the low tendency of sodium and potassium bromides to form polyhalides.

Fig. 7. Change in the rate of the reaction
\(\mathrm{PbBr_2 + 2HCl = PbCl_2 + 2HBr}\) with time

\[ \left\{ \begin{array}{ll} \mathrm{I} & —\,210^\circ\mathrm{C},\\ \mathrm{II} & —\,250^\circ\mathrm{C},\\ \mathrm{III} & —\,300^\circ\mathrm{C}. \end{array} \right. \]

Fig. 8. Change in the rate of the reaction
\(\mathrm{BaBr_2 + 2HCl = BaCl_2 + 2HBr}\) with time

\[ \left\{ \begin{array}{ll} \mathrm{I} & —\,210^\circ\mathrm{C},\\ \mathrm{II} & —\,250^\circ\mathrm{C},\\ \mathrm{III} & —\,300^\circ\mathrm{C}. \end{array} \right. \]

As regards the halides of monovalent metals with 18-electron cations, the preservation of the appearance and shape of the crystals after the reaction probably indicates an ionic mechanism for these reactions.

We observed an increased reactivity of copper bromide, which we explain by its crystal structure being different from

Fig. 9. Crystals of thallium bromide before the reaction. ×120.

Fig. 10. Crystals of thallium chloride formed as a result of the reaction. ×120.

Fig. 11. Crystals of cesium bromide before the reaction. ×120.

Fig. 12. Crystalline formations of cesium chloride after the reaction. ×120.

Fig. 13. Tetragonal crystals of copper bromide with vicinal faces. The arrow indicates a break in the growth spiral. ×300.

of the other bromides, namely, copper bromide crystallizes in the zinc-blende type. For crystals of this type, defects are characteristic—screw dislocations, as a result of which growth spirals are formed.

Microscopic observation of copper bromide crystals confirms the presence of growth spirals. In Fig. 13 one can see vicinal faces of tetrahedral copper bromide crystals and a break in spirally proceeding growth steps. It is known that the growth of a crystal as a result of the motion of screw dislocations proceeds without activation energy [11, 12], which could not but affect the reaction rate.

Kinetic analysis of the experimental data

In the general case, a reaction proceeding between a solid substance and a gas is divided into five stages:

1. Transport of the gaseous reactant to the surface.
2. Adsorption of the gas.
3. Reaction on the surface of the solid substance.
4. Desorption of the reaction products.
5. Removal of the gaseous reaction product from the surface.

The slowest of the stages will determine the rate of the entire process.

In order to elucidate the limiting stage in the case of our reactions, we carried out a more detailed kinetic analysis of the experimental results. We used:

1) the parabolic equation

\[ K = \frac{x}{\sqrt{t}} \ldots \ldots (1), \]

first recommended by Tammann for describing the kinetics of diffusion processes [13];

2) the equation of monomolecular topochemical kinetics [14]

\[ K = \frac{2}{3t}\ln\frac{a}{a-x}; \tag{2} \]

3) the Kolmogorov—Erofeev equation [8]

\[ \alpha = 1 - e^{-kt^n}; \tag{3} \]

4) the Drozdov—Rotinyan equation

\[ M = \frac{2.3}{t}\lg\frac{a}{a-x} - \beta\frac{x}{t}, \tag{4} \]

used by them to describe the kinetics of heterogeneous processes in which there is diffusion retardation [15, 16];

5) the equation used by us on the basis of the data of A. P. Buntin [4], taking into account the magnitude of the initial surface area,

\[ K' = \frac{a^{1/3} d^{2/3}}{2}\cdot\frac{1}{t} \left[1-\sqrt[3]{\frac{a-x}{x}}\right]; \tag{5} \]

6) the transition-state equation [17, 18] for the case when, for the reaction rate, the role of the initial substances is played by molecules adsorbed on the surface

\[ \tau = C_a \frac{kT}{h} e^{-E/RT}. \tag{6} \]

Table 3 gives the results of the applicability of all these equations. Analysis of the experimental results obtained from the application of all the kinetic equations presented makes it possible to represent more clearly the kinetic features of the process and, to some extent, the mechanism of the reactions studied.

First of all, with such a comprehensive kinetic analysis one can judge the role of diffusion in the rate of a topochemical reaction.

The reactions of alkali-metal bromides with hydrogen chloride are described by a parabolic equation. But it should be noted that the constant calculated from this equation does not remain constant with time, but gradually increases, which indicates a deviation of the process from a parabolic law and, consequently, from the law of purely diffusion kinetics.

Table 3

Results of kinetic analysis of the experimental data—constants obtained from equations (1)—(6)

*) \(N\)—Avogadro’s number,
\(M\)—molecular weight.

**) A dash denotes inapplicability of the equation.

A parabolic dependence of the reaction rate on time is still not necessarily proof of a diffusion process. Recent studies carried out by Sotskov and co-workers

reactive diffusion using radioactive isotopes confirmed this [19]. We have shown experimentally that, despite the process taking place in the kinetic region, the rate of displacement of the phase boundary obeys a parabolic law, whereas the diffusive removal of atoms from the phase boundary proceeds considerably faster.

Calculation of the constants from the equation of monomolecular kinetics for these reactions shows that the constants decrease with time, which confirms the presence of diffusional retardation. At the same time, the magnitude of the diffusional retardation \(\beta\), calculated from equation (4), is either constant (\(\beta = 0.71\)) in the case of the interaction of rubidium bromide, or decreases with temperature for cesium bromide: at \(t = 250^\circ\), \(\beta = 0.69\); at \(t = 300^\circ\), \(\beta = 0.56\).

When the rates of reaction and diffusion are commensurate, the value of \(\beta\) should increase with temperature [20].

The increase in the value of \(\beta\) is explained by the fact that the temperature dependence of the diffusion rate is expressed less sharply than that of the reaction rate. Since the value of \(\beta\) decreases with temperature, i.e., the diffusional retardation decreases, it may be assumed that diffusion in the layer of the reaction product has no limiting significance in the calculated time interval. Rather, the diffusional retardation can be explained by surface diffusion, which, as the temperature is raised, decreases owing to the increased mobility of the surface particles.

In the interaction of bromides of divalent metals with hydrogen chloride, the same regularities are observed as for alkali halide salts. Equation (1) describes very well the reaction of barium bromide at lower temperatures (200–210°), and with a very rough approximation at \(t = 300^\circ\). The value of \(\beta\) according to equation (4) for barium bromide does not change with increasing temperature: \(\beta_{210^\circ} = 0.45\), \(\beta_{300^\circ} = 0.44\). For lead bromide the coefficient of diffusional retardation increases with temperature: \(\beta_{210^\circ} = 0.34\), \(\beta_{300^\circ} = 0.45\). In this case this indicates commensurate rates of diffusion and reaction [20].

With regard to the reactions involving bromides of metals with 18 electrons, namely the bromides of copper, silver, and thallium, it may be concluded that their rate obeys the law of monomolecular topokinetics.

At high temperatures the reactions are also described by equation (1).

The subordination of the processes at high temperature to equation (1) indicates the possible limiting influence of the diffusion stage: at low temperature the reaction rate is lower than the diffusion rate, but with increasing temperature the reaction rate and the diffusion rate evidently become commensurate, since the change in the diffusion rate with temperature proceeds more slowly than the change in the reaction rate.

For all systems without exception, the generalized Kolmogorov–Erofeev equation (3) proved applicable. This equation makes it possible to compare kinetic data for systems having somewhat different character, and, moreover, its applicability over a wider range of the reaction (up to 70–80% conversion) is a major advantage.

In addition to the equations listed, we used an equation that takes into account the influence of the magnitude of the initial surface of the reacting substance on the reaction rate.

As shown by A. N. Bulygin [3], the initial surface of the solid substance entering into the reaction is one of the factors affecting the magnitude of the reaction-rate constant. In fact, if

\[ \frac{dx}{dt}=KS_t \tag{7} \]

where

\[ S_t=S_0\left(\frac{a-x}{a}\right)^{2/3}, \tag{8} \]

then

\[ \frac{dx}{dt}=KS_0\left(\frac{a-x}{a}\right)^{2/3}. \tag{9} \]

Expressing the initial surface through the sum of the surfaces of crystals having specified sizes, we obtain:

\[ S_0=\frac{6a}{a_k^{1/3}d^{2/3}}, \tag{10} \]

where \(a\) is the charge of salt before the reaction,
\(a_k\) is the weight of one crystal,
\(d\) is the specific gravity of the bromide.

After integration of equation (9) and substitution of \(S_0\), we obtain

\[ K'=\frac{a_k^{1/3}d^{2/3}}{2}\cdot\frac{1}{t} \left[1-\sqrt[3]{\frac{a-x}{a}}\right], \tag{11} \]

an expression for the reaction-rate constant referred to \(1\ \mathrm{cm}^2\) of surface. The dimension of \(K'\) is expressed in \(\mathrm{g}\cdot\mathrm{cm}^{-2}\) per unit time\(^{-1}\). Calculation of \(K'\) shows the influence of such a physicochemical factor as specific gravity on the reactivity of the reacting substances and, consequently, of the values of the molecular volume and molecular weight of the substance associated with it.

In addition, from the obtained values of \(K'\) it is very easy to calculate the reaction rate expressed in molecules of the reacting substance from \(1\ \mathrm{cm}^2\) of surface per unit time.

From the standpoint of the rate of chemisorption, it was of interest to use the equation proposed by transition-state theory for zero-order reactions for the case when only adsorbed molecules play the role of the initial molecules. For this case Eyring [18] proposes the formula:

\[ v=C_a\frac{kT}{h}e^{-E/RT}, \]

where \(C_a\) is the number of sites for the activated complex on \(1\ \mathrm{cm}^2\) of surface, equal to \(10^{15}\);

\[ \frac{kT}{h} \]

is the frequency factor, or the effective rate of passage of the activated complex over the energy barrier, equal to \(10^{12}\).

\(E\) is the experimental activation energy.

The data obtained by us show that the absolute rate of che-

the adsorption rates are significantly higher than the rates of the reactions we studied (Table 3), i.e., the adsorption process should not limit the reaction rates in this case.

Conclusions

1. The rate of the reactions studied, in the interval of maximum rates, is determined by the rate of the chemical process and increases in the series: KBr—RbBr—CsBr, AgBr—TlBr—CuBr, PbBr₂—BaBr₂, which is associated with an increase in the ionic radius, with a decrease in the change in crystal-lattice energy and in molecular volume.

2. The diffusion retardation that occurs in the reactions of alkali-metal bromides and of barium and lead bromides depends on surface diffusion; as the temperature increases, the rate of surface diffusion increases and the retardation decreases.

3. The adsorption rate is several orders of magnitude higher than the reaction rate and therefore should have no influence on the process.

4. Reactions of salts with 8-electron cations and reactions of salts with 18-electron cations are accompanied by different crystal-chemical mechanisms.

5. The deviation of copper bromide from the general regularity is explained by its crystal structure, which is characterized by the presence of screw dislocations.

6. A quantitative dependence is given for the rate of the reaction of metal bromides with hydrogen chloride on the magnitude of the initial surface area and on the magnitude of the specific weight of the bromide.

LITERATURE

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