The Thermochemical Stability of lonic Noble Gas Compounds Gordon H. Purser Glendale College, 1500 No. Verdugo Road, Glendale, CA 91208 All known noble gas compounds fall into one of two classes: (1) species in which a heavy noble gas atom is bonded covalently tu fluorine, oxygen, or nitrogen and (2) clathraces resultine from dioole-induced dioole attraction. Althoueh studies bf reactions between thd lighter noble gases a i d metals have been reoorted. none have resulted in the isolation or characteriz&m df a well-defined compound. In 1895,a year after the discoverv of argon. Troost and Ouvrard reported the combinationof riagnesjum with argon and with helium (11. Crooke suggested a reaction between a zinc melt and helium in 1Wfi (2).The first "characterized helide" was reported in 1924 by Manley (3). The compound was wepared by an electrical discharge and was proposed to have the formula HgHelo. The tungsten belide, "WHe2", reportedlv was ~roducedbv electron bombardment of tunesten in an atmosphere of heiium a year later (4). For over aodecade, beginning in the late 1920's, Damianovicb and co-workers published numerous papers on proposed helides of various metals including uranium, platinum, palladium, bismuth, and iron (5,6).Many of the preparations involved the formation of a "deposit" during electrical discharge (6).Waller. in 1960, reported that he was unable to reprohuce any of the electric discharge preparations (7), and suggested that each of the reported "helides" may have been the result of occlusion of the noble gas hy the metal. This explanation is likely, especially in view of known metallic absorption of hydrogen to produce "alloys" exhibiting properties very similar to the reported helides. The first nrenaration of a eenuine noble gas compound was published in19fi2 by Neil nartlett at the University of British Columbia (81. Shor!lv thereafter in a review ofnoble gas compounds the followhg statement in reference to helidesappeared (9): Now that the existence of true chemical compounds (containing noble gas atoms) is known, and some inhibitions have been removed, a number of these earlier experiments might bear repeating although the chances of forming noble gas-metal compounds must be considered remote. Presented here are calculations that suggest stoichiometric, ionic, noble gas-metal compounds indeed may be stable. Thermochemlcal Calculations' Since a monovalent, anionic noble gas ion will have a ground state configuration ns2np6(n 1)s' (or ls22s' in the case of helium), the ion will have a spherically symmetrical electron distribution; thus, the interionic forces involved can he described in simple coulombic terms. Enthalpy cycles, especially the Born-Haber thermochemical cycle, have been useful in predicting the stability of chemical compounds (11-13). Such cvcles also have been used to demonstrate the instabhity of ionic solids containing noble gas cations (13). Using the Born-Haber thermochemical cvcle. . .the follow. ing steps are involved:
+
M(s) M(g)
--
M(g) Mt(g) + e-
Due to the low enthalpy of suhlimation and the low ionization energy of cesium, i t will be used as the reactive metal, M, in this example. Neon will be used as the noble gas. To calculate AHfthe lattice enthalpy must be estimated for the hypothetical CsNe crystal. For the estimate, eq 1will be used. where NAVis Avogadro's number, A is the Madelung constant, e is the charge on the electron, z, and z, are the charges on the cation and anion, respectively. Ro is the sum of the ionic radii, n is the Born exponent, R is the gas constant, and T is the kelvin temperature. Since the entropy change for the overall process of forming one mole of crystalline CsNe is negative, formation of the ionic solid would be possible only when AHr is negative. A treatment of the entropy change is given below. The requirement for exothermicity is represented by the eq 2.
where RN.- is the radius of the neonide anion in meters. The values of AHelffuonatfinity, RN~-,and n have not been measured directlv: however. certain reasonable estimates can be made. The d u e of A depends on the assumed structure of the compound which in turn depends upon the value used for the radius of the neonide ion. Electron Affinity Within the past two decades, several investigators have renorted electron affinites of noble gas atoms based on oeriodic trends and calculations (14.15j. The values range &om -21 kJ mol-I for helium to -41 kJ mol-' for radon. Since these values are reported as internal energies, R T (2 kJ mol-I at 25 OC) must be added to produce enthalpies. The electron affinity given for neon is about -29 kJ moi-l; therefore, the value of +31 kJ mol-' will be used as the "best estimate" for AHeleCt,,.%.ity. This value is not assumed to be without error, and the stability plot, to be presented, is drawn for the electron affinity range 0 to -200 kJ mol-l. Born Exponent The Born exponent is usually evaluated experimentally from the comnressibilitv of the ionic crvstal. Without an existing cryst2 of CsNe on which to makekeasurements, an appropriate value of the Born exponent for use in eq 2 must be obtained. When calculated lattice enthalpies and measured ionic radii2 of the cesium halides are substituted into the appropriate form of eq 2 above, calculated values of n range from 16 for CsCl to 9.6 for CsI. Although the range, 9Ifi, seems large, the correction factor to the lattice entha~py introduced by the Rornexponent over this rangeonly differs
AH/VIub~imtion AHioDization
' Thermodynamic data used throughout this paper are from Circular of the Natlonal Bureau of Standards 500 ( 10). lonic radl' used lhrougnout thns paper from -. H. Ahrens (16). Volume 65 Number 2
February 1988
119
reasonable values) of ionic radii for the noble gas anions can he estimated. The average decrease in ion; radius with increasing nuclear charge is a l m t 16ro, although the values ranee from about a 2"odecrease IS2- and CI-I ( 4 , about a 42% &crease (Nsand M g 9 in size. Taking the radius of the sodium atom as 0.186 nm.. the predicted size of the neonide . ion would he0.221 nm. Extreme values for the radius of Nebased on theextreme values in Tahlr I fall in theranee0.190 nm and 0.274 nm. This entire range of radii falls within the fllnity region of stahility for CsNe where n = 10 and AH.l.&,, = +31 kJ mol-I. The crystal structure of a complex containing the sodium anion, Na-, has been determined (18).By examining various interatomic distances, and from various calculations, the radius of the sodium anion is predicted to he -0.217 nm, smaller, as expected, than the predicted radius of Ne-. Similarities between the size of the sodium anion and iodide anion are found, and although the sodium anion and neonide anion are not isoelectronic. the findines of Dve and co-workers provide added suppok to the predicted value of the neonide anion made in this work. ~
1.5 0
20
40
60
80
100
I20
1M
140
180
200
AH electron oft in it^ LJ m i - '
Stabili plot at 0 K of CsNe fw Born values 8, 9, 10. . . . 16. and m. The r indicates me predicted position of CsNe on the plot.
by about 5%.The neonide anion will he quite large, so 10, a value close to that for Csl, will he used as the best estimate for the Born exponent. As with the electron affinity, the Hornexponent is not assumed to be without error, and several values are indicated on the stability plot. Stability Plot
A plot of the maximum radius of the neonide ion that allows exothermic formation of CsNe as a function of AHe~.,,,,m.ity a t various values of the Born exponent divides the graph into a region of stability and a region of instability. The stability plot of CsNe is shown in the figure. The area ahove and to the right of the n = curve is the reeion of instahilitv for anv value of the Born exponent. ~ & curve h below the n = --curve represents the maximum radius for which AH?would he negative a t that value of the Born exponent. In this figure, oniy the values deemed reasonable for theBorn exponent of CsNe, 8-16, are shown. The regim below and to t h i left of each curve indicates a comhination of radius and electron affini~yfor which CsNe would hestatde. In thisexample each curve ofstahilityaccounts for the ~ h a n g e i nthe Madelung constant when the radiusof Nereaches0228 nm. the radius at which the coordination number of the ions would he expected to change. If the "hest" values for the electron affinitv (-31 k J mol-') and Born exponent (n = 10) are used, the maximum radius of Ne- for which the solid would he formed exothermicallv is 0.290 nm. This value of ionic radius appears to he enormous: however. the estimated radius for the Ne- ion determined helow is just slightly smaller than this value.
-
Radius of the Neonlde Anion Predicting the radius of the neonide ion is a critical step in determining whether the ionic solid would he stable or unstable. onemethod for predicting the size of an ion would he to look at the trends among species that are isoelectronic with the ion for which the size is to he estimated. Unfortunately there are no accurate values of ionic radii for ions isoelectronic with the sodium atom. However, the trends in ionic radii for several pairs of isoelectronic species that contain 10 or more electrons allow estimatinu of a rance " of factors by which ioniclatomic radii decrease with increasing nuclear charee for elements hevond carbon. The ionic radius of He- is predicted from the series confined to isoelectronic pairs with two electrons. A summarv of ionic radii is found in able 1. By the appropriate application to the next alkali metal atomic radius3 (specifically Nan in this example) of the factors so determined, a value (and range of Atomic radii used throughout this paper from L. E. Sunon (17). 120
Journal of Chemical Education
~~~
Results from the CsNe Example The values used to solve eq 2 ahove for CsNe are: R N ~=0.221 nm, AHeiecMnaffinity= +31 kJ mol-', n = 10, and A = 1.76. Based on these values the enthalpy of formation of CsNe from the constituent elements is about -85 kJ mol-'. This value can he determined from the stability plot by measuring the horizontal distance from the point defined by the estimated radius and electron affinitv assumed for the CsNe system to the point at which the s t a h i t y curve for the estimated Born exponent intersects that radius. For everv 1 kJ mol-' that the electron affinity value is in error, the enthalov of formation will he in error 1kJ mol-I. Thus the stability plot provides a means by which the thermochemical stability of a hypothetical ionic solid can be predicted. Alternate Calculation The predicted radius of the neonide ion (0.221 nm) is within 0.5% that of the iodide ion (0.220 nm). If one chooses Table 1. Radlus Rallos of Selected lsoelectronic Species that Dltfer by One Unlt ol Nuclear Charge
10 w more
electrons
Mg2+
AI3+
Kt
Ca2+
d shell
CU+
Zn2+
Ag+ HgZ+ TI3+
sshe11
Pd A"+ Hgzt ~g TIt Pb2+ Sn2'
n+ Pbzr Bi3+
Sb3+
0.066 0.133
0.051 0.099
0.773 0.744
0.096 0.138 0.137 0.110
0.074 0.128 0.110 0.095
0.771 0.913 0.803 0.864
0.150 0.147 0.120 0.093
0.147 0.120 0.096 0.076
0.980 0.816 0.800 0.817
-
average 0.836 range 0.680-0.984 variance 0.093 2 electron^
Li+
H-
Be2+ Liz+
0.068 0.208
0.035 0.068
0.515 0.572" average 0.553
Table 2. Parameters Used In Lattice Enthalpy and Enthalpy of Formatlon Calculations for the Alkali Metal-Noble Gas Crystals Metal Li
Na K Rb Cs
Al&VkJ ml-'
AM..m,mVkJ
155 109 90 86 79
mol-'
r+'Inm
523 496 421 405 376
0.066 0.097 0.133 0.147 0.167
Table 5. Calculated LaUlce Enthalples and Enthalples of Formation ol Alkall Metal-Noble Gas Crystals
n 7 6 9 9 10
Li
Lanice Enthalpy (kJ mol-')IAMW mol-')* Na K Rb
Cs
Noble $as predicted r ~ ~ l n r nA ~ l ~ o n s n n n r dmol-' lkJ He
Ne Ar
Kr Xe
0.276 0.222 0.271 0.296 0.316
+23 t31 +37 +41 +43
.Ref 70wIlh factors of Rrwhere spproprlam. a Ref 7 6 *mep d i o t e d lmk radius d me noble gas snlon Is based on 1.19times the m i o factn 1.75. radius of the next alkali metal except Hs, which was calculated using %ef 15 wRh facta of R7.
to assume that the lattice parameters for the neonide are t6e same as those for the iodide, the stability of cesium neonide can he determined relative to cesium iodide. In the thermochemical cycle, the following steps are the same in both cases: Csk) Cs(s) Csk) Cst(g) + eCst(g) + X-(g) CsXM
--
For iodine there is a sublimation step and a dissociation step that is not reauired for the formation of the neonide. These two steps represent 107 kJ mol-I that the neonide would be morr stable than the iodide. Theelertron affinity of iodine is exothermic hy 297 kJ mol-I and that ofthenesn isendothermic by about 31 kJ mol-l. The result is adifference of 3% kJ mol-1 that the neonide would he less stable than the iodide. The overall enthalpv difference between the two ionic solids yields the iodide 22i kJ mol-I more stable than the neonide. The standard enthalpy of formation of CsI is -347 kJ mol-I; consequently, the enthalpy of formation of CsNe would he about -126 kJ mol-'. This value is 41 kJ mol-' more stable than predicted in the calculation above but only represents an error of -8% in the calculated lattice enthalpy of CsNe. Other Noble Gas Ionic Solids The procedure outlined above was employed for 24 other ionic, alkali metal-noble gas rompounds.~Thevalues used in the calculation of the lattice enthalpiea are found in Tahle 2, and the calculated values of lattice enthalnv. and AH
