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Correlation Between Standard Enthalpy of Formation, Structural View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Directory of Open Access Journals J. Serb. Chem. Soc. 78 (2) 241–253 (2013) UDC 547.221/.224:536.77:536.7.004.12 JSCS–4412 Original scientific paper Correlation between standard enthalpy of formation, structural parameters and ionicity for alkali halides ABU NASAR* Department of Applied Chemistry, Faculty of Engineering & Technology, Aligarh Muslim University, Aligarh – 202002, India (Received 13 January, revised 18 April 2012) Abstract: The standard enthalpy of formation (∆H ) is considered to be an interesting and useful parameter for the correlation of various properties of alkali halides. The interrelation between ∆H and structural parameters for the halides of Li, Na, K and Rb has been thoroughly analyzed. When the cationic component element is kept constant in a homologous series of alkali halides, the negative value of ∆H was observed to decrease linearly with increasing interionic distance (d). Accordingly, the following empirical equation ∆H = α + + βd (where α and β are empirical constants) was established. However, for common anionic series of alkali halides, an opposing non-linear trend was observed, with the exception of common fluorides. The correlation study on the standard enthalpy of formation was extended in term of the radius ratio and also discussed in the light of ionization energy of the metal, electron affinity of the halogen, size of the ions, ionic character of the bond and the lattice energy of the compound. Keywords: thermodynamic properties; exothermicity; interionic distance; radius ratio; interrelation. INTRODUCTION Alkali halides are crystalline ionic solids that are of great interest for both theoretical and experimental studies. In recent years, they have gained increased interest due to their prominent applications in the fabrication of various elec- tronic, optical and optoelectronic devices.1 They have also received considerable attention due to their potential role in emerging nano-scale technologies and im- portance in environmental chemistry, such as ozone layer depletion and precipi- tation.2 During the past few years, considerable efforts, e.g., see references3–22, have been made to understand the interrelation between their various structural, optical and electronic properties, such as lattice constants, interionic distance, radius ratio, refractive index, electronic polarizability, dielectric constant, cohe- * Correspondence E-mail: [email protected] doi: 10.2298/JSC120113049N 241 __________________________________________________________________________________________________________________________Available online at shd.org.rs/JSCS/ 2013 Copyright (CC) SCS 242 NASAR sive energy, bond energy, magnetic susceptibility, energy gap, bulk modulus, etc. Although thermodynamic properties are of considerable importance for an under- standing of the nature of a compound against a changing environment, limited attempts have been made to study the interrelation of the thermodynamic proper- ties of alkali halides with their other properties. Shanker et al.23 studied the re- lationship between solid state parameters and melting parameters for alkali ha- lides and reported that melting temperature and relative change in volume after melting vary in a systematic manner with the ionic character of bond. Kanno24,25 observed the relationship between enthalpy of fusion, entropy change upon fu- sion or sublimation upon melting, melting point, electronic polarizability, inter- ionic distance and the ionic radius ratio for some alkali halides. He also deve- loped an empirical relation between the relative volume changes upon melting with the interionic distance.26 In a relatively recent work of Rozman,27 corre- lations between thermodynamic parameters (such as melting point, melting energy and jump in entropy upon melting) and the binding energy of dipolons were esta- blished for the halides of lithium, sodium, potassium and rubidium. Ohashi28 ex- pressed an empirical relation between the heats of formation and the electro- negativity of halogen ions. Recently Vasiliu et al.29 predicted the geometric para- meters, frequencies, enthalpies of formation and bond dissociation energies for some simple alkali metal compounds by employing the coupled cluster theory. A second order empirical polynomial relation between standard enthalpy of forma- tion and refractive index for all the twenty alkali halides has also been deve- loped.30 A literature survey reveals that no systematic effort has hitherto been made to correlate the thermodynamic properties of alkali halides with their structural, physical, optical and electronic properties. The available work in this direction is very limited and scanty. Since structural parameters are basic constants that are involved in most theoretical calculations and also in predicting the behaviour of a compound, it is worth correlating them with the thermodynamic properties of alkali halides. As the enthalpy of formation throws light on the nature of the bond and the intrinsic stability of the compound in the condensed phase, it was decided to study the correlation of the enthalpy of formation with the structural and ionic parameters of alkali halides. BASIC INPUT DATA AND THEIR TREND IN THE HOMOLOGOUS SERIES OF ALKALI HALIDES The values of room temperature standard enthalpy of formation31 and interionic distance1 are listed in Table I for the common cationic and anionic homologous series of alkali halides. The radius ratio in a crystal having the NaCl structure as presented in Table I is calculated from the effective ionic radii of the cationic and anionic constituent elements of the compound with a coordination number 6.31 Table I indicates that the negative value of standard enthalpy of formation (–∆H ), i.e., exothermicity, decreases with increasing of __________________________________________________________________________________________________________________________Available online at shd.org.rs/JSCS/ 2013 Copyright (CC) SCS CORRELATION STUDIES ON AKALI HALIDES 243 interionic distance (d) and decreasing radius ratio (r+/r-) in the homologous series of compounds when the cationic component element is kept constant. On the other hand, for the common anionic homologous series of compounds (Table I), the exothermicity (–∆H ) generally increases with increasing of both d and r+/r-, with the exception of the common fluorides, which obey the reverse trend. TABLE I. Standard enthalpy of formation and structural parameters of alkali halides Compound –∆H / kJ mol-1 d / Å r+/r- Common cationic series LiF 616.0 2.0131 0.5714 LiCl 408.6 2.5699 0.4199 LiBr 351.2 2.7508 0.3878 LiI 270.4 3.0060 0.3455 NaF 576.6 2.3164 0.7699 NaCl 411.2 2.8200 0.5635 NaBr 361.1 2.9865 0.5204 NaI 287.9 3.2364 0.4636 KF 567.2 2.6720 1.0376 KCl 436.5 3.1464 0.7624 KBr 393.8 3.2991 0.7041 KI 327.9 3.5327 0.6273 RbF 557.7 2.8258 1.1429 RbCl 435.4 3.2949 0.8398 RbBr 394.6 3.4454 0.7755 RbI 333.8 3.6710 0.6909 Common anionic series LiF 616.0 2.0131 0.5714 NaF 576.6 2.3164 0.7699 KF 567.2 2.6720 1.0376 RbF 557.7 2.8258 1.1429 LiCl 408.6 2.5699 0.4199 NaCl 411.2 2.8200 0.5635 KCl 436.5 3.1464 0.7624 RbCl 435.4 3.2949 0.8398 LiBr 351.2 2.7508 0.3878 NaBr 361.1 2.9865 0.5204 KBr 393.8 3.2991 0.7041 RbBr 394.6 3.4454 0.7755 LiI 270.4 3.0060 0.3455 NaI 287.9 3.2364 0.4636 KI 327.9 3.5327 0.6273 RbI 333.8 3.6710 0.6909 DISCUSSION The values of the room temperature standard enthalpy of formation are plot- ted against interionic distance for different homologous series of alkali halides in Fig. 1. It could be inferred from Fig. 1 that when the cationic component element __________________________________________________________________________________________________________________________Available online at shd.org.rs/JSCS/ 2013 Copyright (CC) SCS 244 NASAR is kept constant in a given homologous series of the compounds, there is almost linear decrease in the negative value of standard enthalpy of formation with in- creasing d. Thus, the exothermicity of compound formation decreases with in- creasing anion size. Based on the linear variation between ∆H and d, the fol- lowing empirical relation was established: ∆H = α + βd (1) Fig. 1. Plot of the standard enthalpy of formation vs. the interionic distance for alkali halides. where α and β are empirical constants that are presented in Table II for the dif- ferent cationic series of alkali halides. The values of square of the correlation co- efficient, i.e., R2, which can be used to judge the effectiveness of the correlation equation, are also incorporated in this Table. Table II clearly indicates that the R2 value (≥ 0.9980) was very satisfactory for each case. The values for standard en- thalpy of formation (∆H cal) as calculated from Eq. (1) are compared with the known values31 in Table III. The percent deviations for the different compounds, as obtained using the relation: percent deviation = 100│∆H known – ∆H cal│/∆H known (2) __________________________________________________________________________________________________________________________Available online at shd.org.rs/JSCS/ 2013 Copyright (CC) SCS CORRELATION STUDIES ON AKALI HALIDES 245 are also incorporated in Table III. This table clearly shows that there is excellent agreement between the calculated and the known values with the percent de- viation ranging from 0.04 to 2.33. Moreover, the average percent deviation is only 0.65. TABLE II. Empirical constants (α and β) for different series of alkali
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