Kapustinskii approximation

The results obtained by using Equation 1 are summarized in Table I. The heats of formation given for the isolated anions were computed from the standard heat of formation of the corresponding potassium salt by means of the Kapustinskii approximation. The value thus derived from F (using a radius of 1.33 A.) falls within 5 kcal./mole of that from the heat of formation and measured electron affinity of F. The value for BF4 differs by 19 kcal./mole from that obtained in a detailed lattice-energy calculation by Altschuller (I) his value is very close to that derived by Kapustinskii and Yatsimirskii (11) by modifying the Kapustinskii equation. 

Despite the uncertainties inherent in the Kapustinskii approximation and in the estimated heat of formation of NF4+(g), it seems safe to conclude that the hypothetical salts NF4+F, NF4C104 and (NF4)2S04 are unstable relative to their possible decomposition products. The compound NF4BF4 i also likely to be unstable at one atmosphere and all temperatures, but may possibly be capable of existence at low temperatures. 

Salt Experimental (Born-Haber cycle) Simple model (Eq.4.13) "Best values Kapustinskii approximation ... 

As an example, let us pose the question why does BF3 adopt a molecular structure, while A1F3 is apparently ionic As shown in Table 5.2, the ionic model (using the Kapustinskii equation) gives a fair approximation to the thermochemistry of formation of A1F3. Let us estimate the enthalpy of formation of a hypothetical ionic substance BF3(s), having a structure similar to that of A1F3. The lattice energy can be estimated by means of the Kapustinskii equation. We require the... 

Kapustinskii noted that if the Madelung constant A is divided by the number of ions per formula unit for a number of crystal structures, nearly the same value is obtained. Furthermore, as both A/n and re increase with the coordination number, their ratio A/nre is expected to be approximately the same from one structure to another. Therefore, Kapustinskii proposed that the structure of any ionic solid is energetically equivalent to a hypothetical rock-salt structure and its lattice energy can be calculated using the Madelung constant of NaCl and the appropriate ionic radii for (6,6) coordination. 

Although values of lattice energies for heteropoly compounds are not known, estimates have been obtained from the Kapustinskii equation102,103). The lattice energy of K4[SiMo12040] was calculated to be approximately 800 kcal/mole104. ... 

Let us turn now to the question of the lattice energy of salts of NF4+. For tetrahedral ions such as this one, the simplest approach, though an approximate one, is that proposed many years ago by Kapustinskii (10). 

The method outlined above is capable of extension to a number of groups though no very wide use has been made of it. Sherman (114) calculated the proton affinity of water by assuming that the lattice energy of hydroxonium perchlorate (Hs0+C104 ) was the same as that of NH4+C104 since the unit cells of the two solids are isomorphous and very nearly the same size. He obtained a value of 182 kcal/mole. The proton affinities of the methylamines could be obtained by this method if their lattice energies were known. Certainly, approximate values could be obtained by the use of the Kapustinskii equation. 

Pauling (1940) related ionic size to co-ordination number, and Kapustinskii (1943) used the relationship to eliminate the Madelung constant and obtained an approximate general result ... 

Q Use the Kapustinskii equation to calculate an approximate lattice energy for calcium chloride, CaCl. ... 

The compound FrF cannot be isolated owing to short half-life of Fr. Use the Kapustinskii equation to calculate an approximate lattice energy for FrF, given that the sum of the francium and fluorine ionic radii is 4.2 A... 

From data tables, the ionic radius for Sr = 113 pm and for q2- = 140 pm. This gives an approximate minimum cation-anion distance of 253 pm. Using the Kapustinskii equation as in question 1 gives t/j = 3315 kJ mol . ... 

Theoretical estimates of lattice energies using the Bom-Lande or Bom-Mayer equations agree well with Bom-Haber values for many compounds. The Kapustinskii equation gives a useful approximate estimate. Both experimental and theoretical lattice energies increase as ions become smaller or more highly charged. 

Even though ionic model calculations do not always give accurate predictions of lattice energies (and especially when the approximate Kapustinskii equation is used) the trends predicted are usually reliable and can be used to rationalize many observations in inorganic chemistry. 

This expression has its origins in the Born-Lande equation, with a value of 9 for the Born exponent (the value for NaCl) and half the value of the Madelung constant for NaCl the inclusion of the factor v shows why half of A is included. Although the Kapustinskii equation is useful, it is a gross approximation and values obtained in this way must be treated with caution. 

If the lattice type and Madelung constant for an ionic solid are not yet known, the lattice energy can still be approximated using an empirical equation developed by Kapustinskii, shown in Equation (12.7). Only the charges on each ion, the stoichiometric total number of ions (v), and the interionic separation need to be known in order to make the calculation. If Tq is entered into Equation (12.7) in units of pm, the calculated lattice energy will be in units of kj/mol. Using the values in Example 12-1 for NaCI and v = 2,Uq = -746 kj/mol, a difference of only 5% from the experimental value is obtained. 

It is believed that known relationships, including Kapustinskii s equation, yield approximate values of the lattice energy. As a rule, these values do not converge with the results of Born-Haber calculations. The term "thermochemical radius" appeared, meaning the radius that is derived from the lattice energy found on the basis of thermochemical data. 

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