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.