Figure 2. Born–Haber cycle for the preparation of via
preparative route (2).
We now discuss the corresponding enthalpy change ∆H(2) for on the basis
of reaction 2 and Figure 2 by following the procedures described
previously for considering each
salt in turn.
In the case of , the entropy change will be negative (i.e., the products
are more ordered than the reactants) for the corresponding reaction 2
and equal to
S°(,s)–S°(Au,s)–4S°(Ar,g)–S°(F2,g)–4S°(SbF5,g). The
well-established entropies Au(s), Ar(g), and
F2(g)(56) are 11.33, 37.04, and 48.51
kcal/mol, respectively. Based on these values, we obtain an estimate for
the entropy of the corresponding reaction 2, ∆S=−390.24 kcal/mol.
As mentioned in the previous study of , we can estimate the volume of
MNg42+ ions at the MP2 level
without further explanation in the rest of this article because of the
absence of crystal structural data of salt compounds. Here, the
calculated volume of the AuAr42+ ions
at the MP2 level is 0.129 nm3. Thus, we obtain a value
of
V=V(AuAr42+)+2V(Sb2F11−1)=0.129
+2×0.227±0.020 nm3=0.583 nm3±0.040
nm3 (V1/3= 0.835 nm) and a value of
UPOT=1324.681 kJ/mol. The RT terms are corrected by
using Eq. (2), ∆HL=1332.111 kJ/mol=318.686 kcal/mol.
The necessary ancillary thermochemical data are as follows: sublimation
enthalpy of Au(s)(56),
∆Hf(Au(c)→Au(g))=85.7 kcal/mol, ionization potential of
gaseous Ag(56), IE (Au,g)
=I1+I2=684.47 kcal/mol, dissociation
energy of AuAr42+,
D0(AuAr42+)=119.961
kcal/mol (Table 3), and the well-established BE
(F2,g)(56)=37 kcal/mol,
2EA(F,g)=−2×81.1=−162.2 kcal/mol, and
∆Hf298(2SbF5+F−→Sb2F11−)<−111
kcal/mol. The corresponding
enthalpy change ∆H(2) for is estimated to be <−15.477
kcal/mol. Hence, the use of the estimation of the entropy change ∆S
described above leads us to predict that the corresponding free energy
change ∆G(2)=∆H−T∆S is negative when the temperature T is
<48.56 K=−224.43 °C.
Specifically, the salt compound may
exist at temperatures lower than −224.43 °C.
In the case of , the entropy change of the corresponding reaction 2 will
be negative (i.e., the products are more ordered than the reactants) and
equal to
S°(,s)–S°(Ag,s)–4S°(Ar,g)–S°(F2,g)–4S°(SbF5,g). The
well-established entropies Ag(s), Ar(g), and F2(g)(56) are 10.17, 37.04, and 48.51 kcal/mol,
respectively. Based on these values, we can estimate the entropy of the
corresponding reaction 2, ∆S=−389.08 kcal/mol.
The calculated volume of the AgAr42+at the MP2 level is 0.128 nm3. We obtain a value of
V=V(AgAr42+)+2V(Sb2F11−1)=0.128+2×0.227±0.020
nm3=0.582 nm3(V1/3=0.835 nm) and a value of
UPOT=1324.681 kJ/mol. The RT terms are corrected by
using Eq. (2), ∆HL=318.687 kcal/mol.
The necessary ancillary thermochemical data are as follows: sublimation
enthalpy of Ag(s)(56),
∆Hf(Ag(c)→Ag(g))=68.01kcal/mol, ionization potential of
gaseous Ag(56), IE
(Ag,g)=I1+I2=670.35 kcal/mol,
dissociation energy of AgAr42+,
D0(AgAr42+)=121.805
kcal/mol (Table 3), and the well-established BE
(F2,g)(56)=37 kcal/mol,
2EA(F,g)=−2×81.1=−162.2 kcal/mol, and
∆Hf298(2SbF5+F−→Sb2F11−)<−111
kcal/mol. The corresponding enthalpy change ∆H(2) for is estimated to be
<−49.332 kcal/mol. Hence, the use of the estimation of ∆S
described above leads us to predict that the ∆G change is negative, and
∆G(2)=∆H−T∆S <0 when the temperature T is <126.79
K=−146.21 °C. Specifically, the salt may exist at temperatures lower
than −146.21 °C.
In the case of , the entropy change of the corresponding reaction 2 will
be negative (i.e., the products are more ordered than the reactants) and
equal to
S°–S°(Cu,s)–4S°(Ar,g)–S°(F2,g)−4S°(SbF5,g).
The well-established entropies Cu(s), Ar(g), and
F2(g)(56) are 7.923, 37.04, and 48.51
kcal/mol, respectively. Based on these values, we can estimate the
entropy of the corresponding reaction 2, ∆S=−386.833 kcal/mol.
The calculated volume of the CuAr42+at the MP2 level is 0.121 nm3. We obtain a value of
V=V(CuAr42+)+2V(Sb2F11−1)=0.121+2×0.227±0.020
nm3=0.575 nm3 (V1/3=0.831 nm) and a value of
UPOT=1329.299 kJ/mol. The RT terms are corrected by
using Eq. (2), ∆HL=319.792 kcal/mol.
The necessary ancillary thermochemical data are as follows: sublimation
enthalpy of Cu(s)(56),
∆Hf(Cu(s)→Cu(g))=80.86kcal/mol, ionization potential of
gaseous Cu(g)(56), IE
(Cu,g)=I1+I2=7.726+20.292=646.103kcal/mol,
dissociation energy of CuAr42+,
D0(CuAr42+)=134.479
kcal/mol (Table 3), and the well-established BE
(F2,g)(56)=37 kcal/mol,
2EA(F,g)=−2×81.1=−162.2 kcal/mol, and
∆Hf298(2SbF5+F−→Sb2F11−)<−111
kcal/mol. The corresponding enthalpy change ∆H(2) for is estimated to be
<−74.508 kcal/mol. Hence, the use of the estimation of ∆S
described above allows us to predict that the ∆G change is negative, and
∆G(2)=∆H−T∆S<0 when the temperature T is <192.61
K=−80.39 °C. Specifically, the salt may exist at temperatures lower than
−80.39 °C.
The results above show that bulk
salt compounds can be synthesized. Of these, the salt compound is a
promising candidate. The predicted stable temperature of is the highest
among those obtained for the salt compounds, likely because Cu has the
largest binding energy with Ar and the smallest ionic radius among the
systems studied.
Our calculations in the case of indicate that the corresponding enthalpy
change ∆H(2) for , except for , may be estimated to be positive
(Supporting information). This expectation is attributed to the low
M–Ng binding energies in the systems; These energies decrease with
decreasing atomic number of the
noble gas (Ng). The entropy change ∆S for the corresponding reaction 2
will be negative (i.e., the products are more ordered than the
reactants). Accordingly, the
corresponding free energy changes ∆G(2)=∆H−T∆S for , except for ,are
estimated to be positive, which means the corresponding solid salt
compounds cannot be stabilized in the ionic form.
The calculations for indicate that the corresponding enthalpy change
∆H(2) may be estimated to be <−0.666 kcal/mol. This finding
seems to show that the salt compound can be stabilized at extremely cold
temperatures. However, such a small
estimate of enthalpy change
(<−0.666 kcal/mol) is unreliable considering the evaluated
errors. Thus, the outlook for synthesizing the salt compound is also
obscure.