THE ENERGY DIAGRAM OF SODIUM CHLORIDE BY PIERRE J. VAN RYSSELBERGE
Introduction In recent times, under the influence of various theories and experimental facts, such as the Lewis theory of valence, the results of the X-ray analysis of crystals, the properties of electrolytes, etc., it has been customary to consider salts of the type of sodium chloride as polar compounds. In such compounds the bond existing between the two constituents consists mainly of the electrical attraction of two oppositely charged ions. A crystal of sodium chloride is considered as a purely ionic lattice, in which the various ions are held together at definite distances from one another in a certain geometrical pattern because of the interplay of two kinds of forces: the Coulomb electrical forces and the Born repulsive forces of which the wave mechanics of Schrodinger has recently given an interpretation.’ I n solution, such a crystal dissociates into free ions which in dilute solutions obey, with a fairly good approximation, the laws of the Debye-Huckel theory of electrolytes. Departure from these laws has been explained by Bjerrum2 as due to partial physical association. Using Bjerrum’s termin~logy,~ we say that a crystal of sodium chloride is completely ionized but also completely “associated” and that aqueous solutions of sodium chloride are completely ionized but partially “associated,” or clustered. Nernst and his co-workers,4 on the basis of measurements of heats of dilution of strong electrolytes, were able to determine directly the degrees of association and the heat involved in the dissociation into single ions of those associated groups (Ka-C1, for instance) which if we choose to we may call neutral molecules. In order to explain these results it was found necessary to modify the Debye-Huckel theory in a fundamental way. The fact that the degrees of association found by Sernst and the resulting dissociation constants explain rather well the properties of mixtures of potassium and sodium chlorides5 makes it plausible to suppose that in such solutions we are dealing with actual neutral molecules in which a pair of electrons is shared between the two atoms. The existence of individual molecules of the alkali halides in the vapor state is obvious as shown for instance by the discussion of the photochemical decomposition of these molecules by Kistiakowsky.6 L. Pauling: J. Am. Chem. Soc., 49, 765 (1927); A. Sommerfeld: “Atombau und Spektrallinien. Wellenmechanischer Erghnzungsband,” p. I I6 (1929). * N. Bjerrum: Det. Kgl. danske Vidensk. selskab. Math-fys. Medd., VII, No. 9 (1926). a N. Bjerrum: Ber., 62B,1091 (1929). W. Nernst: 2. physik. Chcm., 135, 237 (1928). J. W. McBain and P. J. Van Rysselberge: J. Am. Chem. SOC.,5 2 , 2336 (1930). G. B. Kistiakowsky: “Photochemical Processes,” p. 3 1 (1928).
‘
T H E ENERGY DIAGRAM O F SODIUM CHLORIDE
1055
London1 gives a method of deciding mhether a compound is polar or homopolar. The expression z z e2 @ . = E -+(1) r represents the potential energy of the system of two ions (?;a+ and C1- for instance) for large values of r. E, is the sum of the ionization energy of the cation and of the electroaffinity of the anion. z, and z- are the valences of
FIG.I
the two ions, e the elementary charge, r the distance between the centers of the ions. For 9 = o we have:
If we express E, in volt electrons we obtain:
The potential energy for the system of neutral atoms passes through a minimum, then coincides very rapidly with the horizontal axis. This is a generalization of the consequences of the theory of Heitler and London2 explaining the formation of a molecule of hydrogen from two neutral atoms, on the basis of the perturbation theory of wave mechanics. At the distance R given by equation (3) the curves corresponding to the ions (polar curve), I, and the one corresponding to the neutral atoms, 11, intersect each other as shown on Fig. I . According to London, we have the following criterion: if the distance R is much larger than the known distance between two oppositely charged ions in the crystal, the compound is polar; if R is of the order of magnitude of the distance between the atoms in the molecule, the compound is homopolar.
' F. London: Z. Physik, 46, 455 ( 1 9 2 7 ) . W.Heitler and F. London: Z. Physik, 44,455 (1927).
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P I E R R E J. V A S RTSSELBERGE
London found, for instance, that hydrogen halides are probably homopolar, a conclusion already drawn by Franck,’ and that alkali halides are decidedly polar. Another test to determine whether a compound is polar or non-polar is given by Pauling2: “if the internuclear equilibrium distance calculated for a polar structure wibh the aid of the known properties of ions agrees with the value found from experiment, the molecule is polar; the equilibrium distance for a shared electron bond would, on the other hand, be smaller than that calculated.” Williambs suggests that a compound like sodium chloride exists under two forms: a purely polar one and a homopolar one having a structure analogous to that of a hydrogen molecule, in which a pair of electrons with opposite spins is shared between the two atoms. According to the d a t e (vapor, crystal or solution) of sodium chloride, variable amounts of both types of molecules are present. Such a picture would replace the idea of continuous transition from the homopolar to the polar bond, often proposed by chemists. I n the presence of these new ideas and of the rather uncertain views about the nature of chemical bonds, it seemed useful and important to us to determine a complete interaction energy diagram for sodium chloride, using trustworthy data on ionization potential, electroaffinity, heat of dissociation in the vapor state and in solution, crystal structure, etc. Such a diagram, besides being a novelty, brings into light a few interesting facts, as we proceed to show. 11. Gaseous Ions, Dissolved Ions. Ionization Potential, Electroaffinity The difference between gaseous ions and dissolved ions has been clearly explained by Fredenhagen.‘ If we call dissolution energy the one corresponding to the transformation of a dissolved ion into a gaseous atom, ionization energy the one corresponding to the transformation of a gaseous atom into a gaseous ion, and solvation energy the one corresponding to the transformation of a dissolved ion into a gaseous ion, the following relation must hold5: ionization energy = solvation energy dissolution energy gaseous atom dissolved ion dissolved ion -+gaseous atom -+gaseous ion +gaseous ion The dissolution energies should not be confused with the normal electrode potentials. The dissolution energy corresponds to the transformation of one gas atom into a dissolved ion, when the concentrations of the atoms in the gas phase and of the ions in the solution are equal.
+
1 J. Franck, H. Kuhn, and G. Rollefson: Z. Physik, 43, 155; J. Franck and H. Kuhn: 169 (1927). 2 L. Pauling: Proc. Nat. Acad. Sci., 14, 359 (1928). a A. T. Williams: Physik. Z., 31, 367 (1930). ‘K. Fredenhagen: Z. physik. Chem., 128, I , 239 (1927); 134, 33 (1928); 140, 65; 140. 435; 141, I95 (1929). 5 See specially: K. Fredenhagen: Z. physik. Chem., 140, 69 and seq. (1929).
T H E ENERGY DlAGR.451 O F SODIUM CHLORIDE
I057
In the case of S a and C1, we have the energy relationships given by Fig. 2 . j.13 I-.is the ionization potential of sodium, 3.7 V. is the electroaffinity of chlorine. If me consider as a reference energy that corresponding t o a system composed of neutral sodium and chlorine atoms in the gaseous state, the system gaseous S a + + gaeous C1- will have an energy content of: j.13 - 3 . ; 0 = +1.43 T. e. The system dissolved S a +
+ dissolved
- (3.49 + 2.46)
CY- will have an energy content of: = -5.94
uccorciing to the dissolution energies given by Fredenhagen.'
FIG.2
O n Fig. 3 where the interaction potential energy is plotted against the distance between the sodium and chlorine nuclei, the horizontal line at + I ,43 I-,from the level o is aqmptotic to the interaction curvc of the gaseous ionic system, I . I n the same way the horizontal line at 5.9; T.e. below the lcvel o is nsymptotic to the interaction curve of the dissolved ionic system. 111. Interaction Curve for the Gaseous Ionic System The interaction energy between the two gaseous ions is giten by
@ = E
a
B - -e?r+ - rl'
(4)
in which E, is the suin of the ionization energy of sodium and of the electroaffinity of chlorine, -ee?/r is the potential energy due to the Coulomb forces I< Fredenhagen: Z. phyrik. Chern., 140,
71
(1929).
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PIERRE J. VAN RYSSELBERGE
and B/rn is the potential energy due to the Born repulsive forces. At large distances 9 = E,; at moderate distances the term B/r" is negligible; at very small distances CP passes through a minimum corresponding to the equilibrium distance between the Na+ and C1- ions. Taking the derivative of 9 with regard to r and equating it to 0,we find:
R being the equilibrium distance. (4)becomes, for r =
R:
For sodium chloride, we have as shown in the preceding section E, = 1.43 V.e. Taking foroR and n the values given by Pauling' for the NaC1 crystal, i.e. R = 2.81 A and n = 8, we obtain: @'mi".
= 1.43 - 143
2.81
(I
-
i)
=
- 3.02
+
V.e.
(7)
The complete curve for the system (gaseous Na+ gaseous Cl-)J I, can then be drawn easily (Fig. 3). It cuts the horizontal axis a t r = I O A. Fredenhagenz on the basis of numerical data given in the Landolt-Bornstein tables and of computations of von Wartenberg gives for the dissociation energy of gaseous iYaC1 into gaseous Na and C1: 78,500 calories which cor'L. Pauling: J. Am. Chem. SOC.,49, 76j ( 1 9 2 7 ) . 2K. Fredenhagen: 2. phgsik. Chem., 134,38 (1928). 3 H.von Wartenberg: Z. anorg. Chem., 151, 328 (1926).
THE ENERGY DIAGRAM OF SODIUM CHLORIDE
I059
responds to -3.40 V.e. On account of the small accuracy of such a figure, we may consider this value as practically identical with that of the minimum in the interaction of the ionic system (-3.02 V.e.). This result seems to show that the bond in gaseous NaCl is polar. It is unfortunately impossible to compute the interaction curve for neutral atoms of Na and C1, i.e. the curve corresponding to a hypothetical homopolar bond. We may draw such a curve in an approximate way if we suppose that the minimum in the interaction curve of the gaseous system might correspond to a homopolar bond: the appearance of the curve would be that of the upper dotted line I1 in Fig. 3.
IV. Interaction Curve for the Dissolved Ionic System The Coulomb potential in the case of an aqueous solution is very small. I C means that the interaction curve for the dissolved Ka+ and C1- ions is practically identical with the horizontal line a t - 5.95 V.e. from the o level down to quite small distances. Let us suppose that, if Ka+ and C1- form a neutral molecule or a physical aggregate or cluster in Bjerrum’s sense, the equilibrium distanoce between the two constituents is the same as in the NaCl crystal, Le., 2.81 A. For this particular value of r the interaction curve will present a minimum which we can determine from the value given by Sernst’ for the dissociation energy of the molecule or physical aggregate NaC1: 3,500 calories per mole. This dissociation energy corresponds to 0.1j V.e. The minimum is then a t 0. I j \’.e. below the horizontal line of the dissolved F a + and C1- ions, as shown in Fig. 3, curve 1’. We notice that the two minima, the one corresponding to the gaseous state and the one corresponding to the dissolved NaCl are 2.70.V.e. apart. If we consider the calculated minimum of the upper curve as more accurate, those minima are 3.08 V.e. apart. Supposing that this difference of energy content is the one corresponding to the purely hypothetical process gaseous ( S a Cl) +dissolved ( S a Cl), we may draw an horizontal line at 3.08 V.e. below the o-level. In case the minimum in the interaction curve of the system dissolved Ka+ dissolved C1- corresponds to a homopolar molecule, the interaction curve for the system dissolved Ka+ dissolved C1 has the form of the lower dotted line 11’ on Fig. 3. I n aqueous solution, the system (Naf C1-) corresponds to a much lower energy content than the neutral system: it is the stable one. For small distances between the ions, small amounts of molecules (or physical aggregates?) are formed. I n the case of the gaseous state the curves for the neutral and the ionic systems intersect each other in two points. There is a marked tendency to dissociation of sodium chloride into neutral atoms, a fact which allows us to suppose that the molecule may possess a homopolar character.
+
+
+
+
1
W. Nernst: loc. cit.
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PIERRE J. B.4N RTSSELBERGE
V.
Summary
Current ideas about, the structure of compounds of the type of sodium chloride have been reviewed. 2. Curves representing the interaction energy of sodium and chlorine ions and atoms in the gaseous state and in solution in terms of the distance between the nuclei of the t x o constituents have been drawn. 3 . The resulting energy diagram has been discussed. I.
Depnrtirient u j Chemistry. S t a n f o r d C-ilicersity, California.
