Chemistry

V. I. Posypaiko and N. S. Dombrovskaya

Decomposition of the Composition Diagram and Exchange Reactions of a Quinary Reciprocal System of Nine Salts: Chlorides, Bromides, and Sulfates of Lithium, Sodium, and Thallium

(Presented by Academician I. V. Tananaev, 16 XI 1960)

Developing the ideas of N. S. Kurnakov in the field of multicomponent equilibria, V. P. Radishchev theoretically derived five types of decomposition of quinary reciprocal systems of nine salts: A, B, C, D, and E (¹). Determination of the type of decomposition and finding the singular and nonequilibrium stars make it possible to evaluate exchange reactions and to reduce experimental studies of reciprocal systems (²). Type A has been described using as an example the systems Na, K, Ag ∥ Cl, Br, NO₃ (³). In the present work, type C has been experimentally confirmed for the first time. The composition diagram

Table 1

Indices of vertices, cutting elements, and stable cells of the composition diagram in the quinary reciprocal system of 9 salts:
Li, Na, Tl ∥ Cl, Br, SO₄

Base triangle: 4—2ᴮ—4
Cutting tetrahedra:
1) 24—2ᵃ—4; 2) 4—2ᶜ—42; 3) 24—2ᴮ—4; 4) 4—2ᵃ2ᴮ—4;
5) 4—2ᴮ2ᶜ—4; 6) 4—2ᴮ—42.

Stable cells:
1) 024—2ᵃ—4 }
2) 4—2ᶜ—420 } Sprouts

Pentatopes of the cyclic part of the star:
3) 24—2ᵃ2ᴮ—4; 4) 24—2ᴮ—2ᴮ—42; 5) 4—2ᵃ2ᴮ2ᶜ—4;
6) 4—2ᴮ2ᶜ—42

of the quinary reciprocal system of 9 salts is represented in the form of a four-dimensional nine-vertex polytope (a prism of the second kind). The determination of the cutting and stable elements of the composition diagram was carried out with the aid of a table of vertex indices* (⁴).

* The index of a vertex indicates the number of stable diagonals incident to the given vertex of the polytope.

Table 1 gives the indices of the vertices of the singular and nonequilibrium stars. In type C both stars are identical, as a result of which the sets of vertex indices are the same. The arrangement of the cations in the nonequilibrium star is the same, while the arrangement of the anions is reversed.

Fig. 1. Ternary system $\mathrm{LiBr—NaCl—\frac{1}{2}Tl_2SO_4}$

As can be seen from Table 1, the secant tetrahedra 3, 4, 5, and 6 have a common base—the basic triangle $4—2^{\mathrm{B}}—4$. For the nonequilibrium star it corresponds to the salts $\mathrm{LiBr—NaCl—\frac{Tl_2SO_4}{2}}$, and for the singular star to $\mathrm{\frac{Li_2SO_4}{2}—NaCl—TlBr}$. The ternary systems corresponding to these triangles were checked experimentally. The nonequilibrium triangle $\mathrm{LiBr—NaCl—\frac{Tl_2SO_4}{2}}$ is characterized by the presence of six crystallization fields (Fig. 1): three fields of the components $\mathrm{LiBr}$, $\mathrm{NaCl}$, $\mathrm{Tl_2SO_4}$, two fields of the exchange products $\mathrm{Li_2SO_4}$, $\mathrm{Na_2SO_4}$, and a small field of phase X. In the quinary reciprocal system $\mathrm{Li, Na, Tl \parallel Cl, Br, SO_4}$, the salt combination corresponding to the components of the nonequilibrium star is the least stable.

The basic triangle (Fig. 2) of the singular star $\mathrm{\frac{Li_2SO_4}{2}—NaCl—TlBr}$ is a simple ternary system with three fields of the initial components and a ternary eutectic point at $424^\circ$ and composition $2\%\,\mathrm{\frac{Li_2SO_4}{2}} + 7\%\,\mathrm{NaCl} + 91\%\,\mathrm{TlBr}$. Thus, the stability of the basic triangle is confirmed. Both triangles—the nonequilibrium and the stable—possess considerable regions of immiscibility. In type C, the intersection of the nonequilibrium and basic triangles is effected along the conversion line (1), which indicates that both triangles are located in one hyperplane of the four-dimensional diagram. The conversion line is determined by points of the composition diagram corresponding to

$50\%\,\mathrm{\frac{Li_2SO_4}{2}} + 50\%\,\mathrm{TlBr} \rightarrow \mathrm{NaCl}$

or

$50\%\,\mathrm{LiBr} + 50\%\,\mathrm{\frac{Tl_2SO_4}{2}} \rightarrow \mathrm{NaCl}$.

As can be seen, the component $\mathrm{NaCl}$ enters into both triangles, so that the exchange decomposition reduces to the reaction of a pair of salts:

$\mathrm{LiBr + \frac{Tl_2SO_4}{2} \rightarrow \frac{Li_2SO_4}{2} + TlBr},$

while the component $\mathrm{NaCl}$ remains unchanged.

Fig. 2. Ternary system TlBr — NaCl — \( \tfrac{1}{2}\mathrm{Li}_2\mathrm{SO}_4 \)

Thus, the exchange reactions in the quinary reciprocal system Li, Na, Tl \(\parallel\) Cl, Br, SO\(_4\) are expressed in the form of the following equations:

Nonequilibrium star:

\[ \mathrm{LiBr} + \tfrac{1}{2}\mathrm{Tl}_2\mathrm{SO}_4 \to \tfrac{1}{2}\mathrm{Li}_2\mathrm{SO}_4 + \mathrm{TlBr}, \]

\[ \mathrm{LiBr} + \mathrm{NaCl} \to \mathrm{LiCl} + \mathrm{NaBr}, \]

\[ \mathrm{NaCl} + \tfrac{1}{2}\mathrm{Tl}_2\mathrm{SO}_4 \to \tfrac{1}{2}\mathrm{Na}_2\mathrm{SO}_4 + \mathrm{TlCl}. \]

Singular star:

\[ \tfrac{1}{2}\mathrm{Tl}_2\mathrm{SO}_4 + \mathrm{LiBr} \to \mathrm{TlBr} + \tfrac{1}{2}\mathrm{Li}_2\mathrm{SO}_4, \]

\[ \tfrac{1}{2}\mathrm{Na}_2\mathrm{SO}_4 + \mathrm{LiCl} \to \tfrac{1}{2}\mathrm{Li}_2\mathrm{SO}_4 + \mathrm{NaCl}, \]

\[ \mathrm{NaBr} + \mathrm{TlCl} \to \mathrm{NaCl} + \mathrm{TlBr}. \]

Summing and canceling, we obtain:

\[ \mathrm{LiBr} + \frac{\mathrm{Tl}_2\mathrm{SO}_4}{2} \to \frac{\mathrm{Li}_2\mathrm{SO}_4}{2} + \mathrm{TlBr}. \]

All-Union Scientific Research Institute
of Chemical Machine Building

Received
14 XI 1960

REFERENCES

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