Lattice Enthalpies of lonic Halides, Hydrides, Oxides, and Second-Electron Affinities of Atomic Oxygen and Sulfur Jack B. Holbrook, Ralph Sabry-Grant, Barry C. Smith, and Thakor V. Tandel Birkbeck College (University of London). Gordon House. 29 Gordon Square, London WClH OPP, UK The dissociation of an ionic crystal into ions a t infinity is an endothermic process.
Table 1. Standard Molar Laltlce Enthalples (AHL*) lor Halldes and Hydrldes at 298 K (b)
(a)
(cI
(dl
(e)
(1)
(gl
(hl
AKS/kJ mol-'
The enthalpy change can be obtained from enthalpies of formation of the gaseous ions and solid compound by means of a simplified Born-Haber cycle. At zero temperature, this change is equal to the lattice energy. "Experimental" (cycle) standard molar lattice enthalpies at 298 K for some cubic halides and hydrides appear in column (a) of Tahle 1. Some authorities refer to the formation of crystalline solid from gaseous ions so that the sign of lattice enthalpy is negative.
Compound cycle
AH~*(cycle)= nAH/YMYt, g) + bAH/YXz-, g) - AH/*(M,Xb, s) Columns (b) and (c) of Table 1 contain lattice enthalpies derived from the "theoretical" equations of Born and Lande (I),BL, and Born and Mayer (Z), BM:
KF KC1 KBr KI
AHLYBL)= (A/s.)(l- lln)
RbF RbCl RbBr Rbl
and a similarly extended form of the Bom-Lande equation, XBL:
BM
XBM
XBL
SBL
Ionic
cyc1,ionic
713 675
682 654
-3
LIF LlCl LlBr Lil NaF NaCI NaBr Nal
where A is the attractive constant and s, is the internuclear separation a t equilibrium. Numbers characteristic of ions (3),5< n < 12, and the constant (Z), p = 0.345 A (1A = m), were derived from calculations involving compressibility. These BL and BM lattice enthalpies are closer to each other than to cycle values and are outside the expected limits of experimental error. Extended forms of the Born-Mayer equation, XBM, have been used in attempts to improve accuracy (4-6). Columns (d) and (e) of Tahle 1 contain the results of our calculations for Group 1 halides using the expression:
BL
C8F csc1 CsBr CSI CaFz SrFl SrC12 BaF2 BaCi? LiH NaH KH RbH CsH
-
661 651
696 671
711 678
Hence log [AHL*/A] = -log [s.]
+ log [ l -
lln]
A straight line of gradient -1 and intercept log [I - lln] is where C and D are constants for dipole-dipole and dipolequadrupole interaction, respectively (7),R is the molar gas constant, and OD is Dehye temperature (8)with interpolation for missing values. There is little improvement over the original short equations. Born and Lande used also a simplified equation, SBL, having n = 9 for all compounds (9). The resulting lattice enthalpies in column (0 of Tahle 1 show intermittent improvement. Such simplified forms of the lattice enthalpy equation can be written: AHL'VA= (l/s,)(l- Iln)
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predicted for plots of log [AH~+(cycle)lA]against log [s,]. The results of our plots are shown in the figure. The points for halides fall near a straight line of gradient -0.83, and those for hydrides fall near a straight line of gradient -0.75. Column (g) of Tahle 1 contains our calculations of lattice enthalpies for ionic halides using the relationship: AH~Yioniehalides) = 0.770As,-5n and for ionic hydrides using the relationship: AHL'(ionic hydrides) = 0.644Ase2" Column (h) of Table 1 containing values of.AHLycycle) -
Table 2. Standard Molar Enthalples of Formallon (Ants) of Gaseous Ions at 298 K AH,*W+)
Cation
AHeCW
W mol-'
Anion
685.9. 609.0 514.3
Lif
Na+ Kt Rb+
H-
FCIBrr 1-
490.1
Cs+ Ca2+
458.0 2348.5 1825.9
Sr2+ Baz+
1790.6 1660.5
Mg2+
0-
S-
kJ mol-'
138.0 -255.2 -233.5 -219.0 -194.6 102.0 72.2
This function is real and positive over the range 0 < s < o, provided m is a real, positive, and even integer. All noncou-
.see ten.
AH,.*(ionic) shows ameement within 1%for all compounds except lithium chlorae, bromide, and iodide where increasing polarization of anions is expected and covalent character is indicated (10). Gaseous ions. Table 2 contains standard molar enthalpies of formation forgaseousionsat298K. Valuesfor cations (11, 12) are from NBS 270, except for lithium where the value is anomalous. Our value for lithium is obtained from the standard molar enthalpy of formation of the gaseous atom (12) using the relationship: mre(Mt, g) = AHfTM,g) + 11+ (512)RT where the first molar ionization energy, I,, corresponds to the change in internal energy a t zero temperature (13) for the reaction: M(g) - e-
-
Mt(g)
Values for anions are obtained from standard molar enthalpies of formation of gaseous atoms (14) using the relationship: AHrTX-, g)
and ro is the permittivity of vacuum. Table 4 contains values of M, Myz, and A for five crystalline structures. Repulsive energy. There have been many attempts to relate repulsive energy, which cannot be measured directly or calculated exactly, t o internuclear separation. The most familiar assume that repulsive energy is proportional to s-" (Born-Lande) (I) or exp (-SIP) (Born-Mayer) (2). We propose here that repulsive energy is proportional to a function of internuclear separation that approaches infinity as s approaches zero and decreases monotonically to zero a t distance a,the effective range of repulsive interaction:
= AHre(X, g)
+ 4 - (512)RT
where the first molar electron affinity, Et, corresponds to the change in internal energy a t zero temperature (15) for the reaction:
Our values agree well with those of Morris (16) and Dasent (17), which supersede earlier values. Crystalline solids. Table 3 contains types of structure, internuclear separations derived from unit cell dimensions (18), and standard molar enthalpies of formation a t 298 K from NBS sources (11, 12, 19) except for cesium fluoride where the value of Morris (16) is used.
Table 3. Crystal Types, Internuclear Separallona (s.),and Stsndard Molar Emhalples of Fonnatlon (Ahs) tor Cublc Halldes and Hydrldes at 298 K AH,+
Compomd Type 61 LIF LlCl LiBr Lll
NaF NaCI NaBr NaI
AHe
Compound
kJ molV
kJ mol-'
Type 52
2.013 2.570 2.751 3.006 2.314 2.820
-616.0 -408.6 -351.2 -270.4
CsCl CsBr Csl
3.569 3.720 3.855
-436'7 .
Type 81
Type C1
2.987
3.238 2.672 3.146 3.300 3.533 2.827 3.295 3.445 3.670 3.001
KF KC1 KBr KI RbF RbCl RbBr Rbl
CSF
-393.8 -327.9
LIH
2.043
.
Table 4. Madelung (M, Myr) and Altractlve ( A ) Constants A
Type
M
nnvz
A kJmol-'
6odlum chloride cesium chloride
B1 82
1.74756
calciumdifluorlde dililhium oxide
C1 C1 81
2.51939 2.51939 1.74756
1.74756 1.76267 5.03878
2428 2449 7001 7001 9712
sbuciure
magnesium oxlde
1.76267
5.03878
6.99024
Dlscusslon
These simple empirical relationships, which allow lattice enthalpies of ionic compounds t o be determined readily from observed internuclear separations, are investigated here. The energy of dissociation into infinitely separated gaseous ions is treated as the algebraic sum of coulombic attractive energy and short-range repulsive energy:
lombic interactions are incorporated. Zero-point energy is not considered separately. The repulsive constant, B, is obtained by differentiation: - ~[
