Is there a pattern in the magnitude of lattice enthalpy of dissociation as we go down Group -1 (alkali metals) and Group -17 (Halogens)?

Chemistry is an interesting subject, i solemnly believe. I was introduced to this subject when I was in fourth grade. It was not in the school curriculum. We had a compiled science book then with no specific physics, chemistry or biology.

 

My cousin brother, quite older than me, was into research then. He is a chemistry doctorate now. Back then he used to stay with us for his bachelor's degree. In the area we lived in, there were hardly enough children of my age I could play with. As a result, my cousin brother was my only companion then. I love spending time with him. He spoke to me about his dreams and that's how I was introduced to this wonderful subject, chemistry.

 

Though I was too young to understand his studies, it used to give me immense pleasure to hear him speak of the subject. With every passing day, the subject grew more and more interesting.

 

In grade six, chemistry classes started in school. I already knew the chapters so well that I gradually became the star of the class. I started spending more time exploring the subject.

 

I was in grade 8 when I was first taken to the chemistry lab in school. No words can describe that feeling! It opened a whole new dimension of interests for me. My brother was doing his masters. After much persuasion, he took me to his lab, but just twice. School then did not permit us to do experiments on our own to avoid risks.

 

I would visualize myself experimenting with those colourful compounds all day. It made me wonder how two elements stay together and form a whole new compound. Finding resources and studying them, I came across the term lattice enthalpy.

 

Lattice enthalpy is a measure of the strength of the forces between the ions in an ionic solid. The more I read about it, the more I was intrigued. So, decided to share my views.

 

In this IA, I have decided to show the lattice enthalpy trend of the elements of group 1 and group 16 of the periodic table.

Born Haber cycle (Treptow et al) is a cycle of enthalpy change of process that leads to the formation of a solid crystalline ionic compound from the elemental atoms in their standard state and of the enthalpy of formation of the solid compound such that the net enthalpy becomes zero.

 

Hess Law of Thermodynamics (Wrobleski, Henry et al) states that change in enthalpy in a chemical reaction does not depend on the pathway of the process.

 

Any ionic compound is not fully ionic in nature and similarly, any covalent compound is not fully covalent in nature (Su et al). In case of any Ionic Compound, the ionic bond is formed due to transfer of electron between two atoms resulting in the formation of an anion and a cation. Ionic radius of cation is less than that of the atom and ionic radius of anion is greater than that of the atom. As a result, in any ionic compound, two ions are present in vicinity. Due to this, cations attract the anions due to presence of opposite charge. As a result, the electron cloud present around the anion change its shape and partly moves towards the cation. This phenomenon is called Polarisation (Rao et al). As a result, the electrons present in the anion are partially shared with the cations. More the polarisation, more will be the covalent character of the ionic compound. Polarisation depends upon two factors. They are – Polarising power of the cation and the polarizability of the anion. Polarising power of the cation depends on the amount of positive charge present in the cation with respect to size of the cation. Lesser the size, greater will be the polarisation power since, the charge density will be maximum. On the other hand, more the size of the anion, lesser will be the distance between the anion and the cation. As a result, polarizability of anion will increase. Fajan’s Rule (Stone et al) is essential to state the qualitative analysis of covalent character in any Ionic compound. Using this rule, we can state which compound is more covalent when compared between two such compounds.

 

In the proceedings of the IA, the lattice enthalpy of NaCl, NaBr, NaI, KCl, KBr, KI, LiCl, LiBr and LiI are essential to be found. In the subsequent paragraphs, I will find the lattice enthalpy of these ionic compounds using Hess Law and Born Haber Cycle.

In a research article titled as – ‘Lattice dynamics of covalent ionic compounds’ published in the journal Wiley, increase in covalent character of ionic compounds was studied as the elements move down the group of periodic table. The compounds chosen for this paper are Magnesium, Oxygen and Halogens. It was studied that the covalency of ionic compounds increase as we move down the groups. The correlation was expressed as a “linear equation y = 1.7647x -1.5023 with a R² value of 0.9963” (A. M. Altshuer et al).

This IA is mainly focussing on the lattice enthalpy change of alkali metals and halogens as we move down these groups in the periodic table. It mainly involves polarisation of ions resulting in an increase in covalent character in the compounds. Since, covalent compounds have less lattice enthalpy than ionic compounds, the ions with more polarising strength will exhibit lesser lattice energy and vice versa. As the charge of cation (Group 1) and size of anions (Group 17) increases down the group, their polarising strength will increase down the group. Thus, it is predicted Lattice enthalpy will decrease as we move down the groups 1 and 17.

Different Ionic compounds

In this IA, I will develop a comparative analysis on the study of Lattice Enthalpy of the ionic compounds, such as, of NaCl, NaBr, NaI, KCl, KBr, KI, LiCl, LiBr and LiI. I will draw two comparison based on the Groups. Firstly, I will try to derive the trendline of Lattice Enthalpy among the compounds taking the cation (Group 1) constant. Such as, one graph for NaCl, NaBr and NaI and similarly graphs for each of the Group 1 elements with different halogens will be constructed. Secondly, I will try to derive the trendline of Lattice enthalpy among the compounds taking the anions (Group 17) constant. Such as, one graph for NaCl, KCl, LiCl and similarly graphs for each of the Group 17 elements with different alkali metals will be constructed. Thus, these different compounds are the independent variable for this comparative study.

Lattice Enthalpy is the dependent variable of this comparative study which is analysed for different compounds.

In order to find the trendline of Lattice Enthalpy for different compounds made up of the ions of Group 1 and Group 17, the lattice enthalpies of all such compounds that are considered in this IA should be found. I will find the lattice enthalpy of the above-mentioned compounds using Hess Law. The energy which is required by an anion and a cation in gaseous state to combine in order to form an ionic compound is called its Lattice Enthalpy. Though, the Heat of formation of ionic compounds involves all the energy that is absorbed or released in the course of the reaction.

 

Lattice Enthalpy of NaCl:

 

Heat of formation of NaCl is -411 kJ/ mol.

 

Na (s) + \(\frac{1}{2}\) Cl²  (g) → Nacl (s)

 

Heat of sublimation of Na is +107 kJ/ mol.

 

Na (s) → Na (g)

 

Ionisation Enthalpy of Na is +502 kJ/ mol.

 

Na (g) → Na⁺ (g)

 

Heat of dissociation of Cl is +242 kJ/ mol.

 

Cl₂ (g) → 2Cl (g)

 

Heat of dissociation of Cl for half mole of Chlorine is +121 kJ/ mol.

 

Electron affinity of Cl is -355 kJ/ mol.

 

Cl (g) → Cl^- (g)

 

Let the Lattice enthalpy be x kJ/ mol.

 

Na⁺ (g) + (Cl^- (g) → Nacl (s)

 

Now, we can write,

 

∴ 107 + 502 + 121 - 355 + x = -411

 

=> x = -786kJ/mol

 

Lattice Enthalpy of NaBr:

 

Heat of formation of NaBr is -362 kJ/ mol.

 

Na (s) + \(\frac{1}{2}\) Br2 (l) → NaBr (s)

 

Heat of sublimation of Na is +107 kJ/ mol.

 

Na (s) → Na (g)

 

Ionisation Enthalpy of Na is +502 kJ/ mol.

 

Na (g) → Na⁺ (g)

 

Heat of vaporisation of Br₂ is +31 kJ/ mol.

 

Br₂ (l) → Br₂ (g)

 

Heat of vaporisation of Br for half mole of Bromine is +15.5 kJ/ mol.

 

Heat of dissociation of Br is +190 kJ/ mol. 

 

Br₂ (g) → 2Br (g)

 

Heat of dissociation of Br for half mole of Bromine is +95 kJ/ mol.

 

Electron affinity of Br is -325 kJ/ mol.

 

Br (g) → Br^-(g)

 

Let the Lattice enthalpy be x kJ/ mol.

 

Na⁺ (g) + Br^- (g) → NaBr (s)

 

Now, we can write,

 

∴ 107 + 502 +15.5 + 95 - 325 + x = -362

 

=> x = - 756kJ/mol

 

Lattice Enthalpy of NaI:

 

Heat of formation of NaI is -287 kJ/ mol.

 

Na (s) + \(\frac{1}{2}\) l₂ (l) → Nal (s)

 

Heat of sublimation of Na is +107 kJ/ mol.

 

​ Na (s) → Na (g) ​

 

Ionisation Enthalpy of Na is +502 kJ/ mol.

 

Na (g) → Na⁺ (g) ​

 

Heat of sublimation of I 2 is +62 kJ/ mol.

 

l₂(s) → l₂(g) ​

 

Heat of vaporisation of I for half mole of Iodine is +31 kJ/ mol.

 

Heat of dissociation of I is + 152 kJ/ mol.

 

l₂(g) → 2l(g)

 

Heat of dissociation of I for half mole of Iodine is +76 kJ/ mol.

 

Electron affinity of I is -295 kJ/ mol.

 

l(g) → l^-(g)

 

Let the Lattice enthalpy be x kJ/ mol.

 

Na⁺(g)+l^-(g)→Nal(s)

 

Now, we can write,

 

∴ 107 + 502 + 31 + 76 − 295 + x = −287

 

=>x = − 708kJ/mol

 

Lattice Enthalpy of KCl:

 

Heat of formation of KCl is - 436 kJ/ mol.

 

K(s)+\(\frac{1}{2}\) Cl₂(g)→KCl(s)

 

Heat of sublimation of K is +72 kJ/ mol.

 

K(s)→K(g)

 

Ionisation Enthalpy of K is +420 kJ/ mol.

 

K(g)→K⁺(g)

 

Heat of dissociation of Cl is +242 kJ/ mol.

 

Cl₂ (g) → 2Cl(g)

 

Heat of dissociation of Cl for half mole of Chlorine is +121 kJ/ mol.

 

Electron affinity of Cl is -355 kJ/ mol.

 

Cl (g) → Cl^- (g)

 

Let the Lattice enthalpy be x kJ/ mol.

 

Na⁺ (g) + Cl^- (g) → NaCl (s)

 

Now, we can write,

 

∴ 72 + 420 + 121 − 355 + x = −436

 

=> x = − 694kJ/mol

 

Lattice Enthalpy of KBr:

 

Heat of formation of KBr is -392 kJ/ mol.

 

K(s) +\(\frac{1}{2}\)Cl₂ (g) → KCl (s)

 

Heat of sublimation of K is +72 kJ/ mol.

 

K (s) → K(g)

 

Ionisation Enthalpy of K is +420 kJ/ mol.

 

K (g) → K⁺(g)

 

Heat of vaporisation of Br₂ is +3 1 kJ/ mol.

 

Br₂ (l) → Br₂ (g)

 

Heat of vaporisation of Br for half mole of Bromine is +15.5 kJ/ mol.

 

Heat of dissociation of Br is +190 kJ/ mol.

 

Br₂ (g) → 2Br (g)

 

Heat of dissociation of Br for half mole of Bromine is +95 kJ/ mol.

 

Electron affinity of Br is - 3 25 kJ/ mol.

 

Br (g) → Br^- (g)

 

Let the Lattice enthalpy be x kJ/ mol.

 

Na⁺ (g) + Br^- (g) → NaBr (s)

 

Now, we can write,

 

∴ 72 + 420 + 15 . 5 + 95 − 325 + x = −392

 

=> x = − 669kJ/mol

 

Lattice Enthalpy of KI:

 

Heat of formation of K I is -32 8 kJ/ mol.

 

k (s) + \(\frac{1}{2}\) l_{2 (g) → Kl (s)} 

 

Heat of sublimation of K is +72 kJ/ mol.

 

k (s) → k (g)

 

Ionisation Enthalpy of K is +420 kJ/ mol.

 

k (g) → k+ (g)

 

Heat of sublimation of I 2 is +62 kJ/ mol.

 

l₂(s) → l₂(g)

 

Heat of vaporisation of I for half mole of Iodine is +31 kJ/ mol.

 

Heat of dissociation of I is +152 kJ/ mol.

 

l₂ (g) → 2l (g)

 

Heat of dissociation of I for half mole of Iodine is +76 kJ/ mol.

 

Electron affinity of I is -295 kJ/ mol.

 

l (s) → l^-(g)

 

Let the Lattice enthalpy be x kJ/ mol.

 

K⁺ (g) + → l^-(g) → Kl (s)

 

Now, we can write, 

 

∴ 72 + 420 + 31 + 76 - 295 + x = -328

 

= > x = −632kJ/mol

 

Lattice Enthalpy of LiBr:

 

Heat of formation of LiBr is -350 kJ/ mol.

 

Li (s) + \(\frac{1}{2}\) Cl₂ (g) → LiCl (s)

 

Heat of sublimation of K is +159 kJ/ mol.

 

Li (s) → Li (g)

 

Ionisation Enthalpy of Li is +520 kJ/ mol.

 

Li (g) → Li⁺ (g)

 

Heat of vaporisation of Br₂ is +31 kJ/ mol.

 

Br₂ (l) → Br₂ (g)

 

Heat of vaporisation of Br for half mole of Bromine is +15.5 kJ/ mol.

 

Heat of dissociation of Br is +190 kJ/ mol.

 

Br₂ (g) → 2Br (g)

 

Heat of dissociation of Br for half mole of Bromine is +95 kJ/ mol.

 

Electron affinity of Br is - 3 25 kJ/ mol.

 

Br (g) → Br^- (g)

 

Let the Lattice enthalpy be x kJ/ mol.

 

Na⁺ (g) + Br^- (g) → NaBr (s)

 

Now, we can write,

 

∴ 159 + 520 + 15.5 + 95 - 325 + x = -350

 

=> x = -814.5kJ/mol

 

Lattice Enthalpy of LiI:

 

Heat of formation of LiI is -271 kJ/ mol.

 

Li (s) + \(\frac{1}{2}\) l2 (g) → Lil (s)

 

Heat of sublimation of Li is +159 kJ/ mol.

 

Li (s) → Li⁺ (g)

 

Ionisation Enthalpy of Li is +520 kJ/ mol.

 

Li (s) → Li⁺ (g)

 

Heat of sublimation of I 2 is +62 kJ/ mol.

 

l₂ (s) → l₂ (g)

 

Heat of vaporisation of I for half mole of Iodine is +31 kJ/ mol.

 

Heat of dissociation of I is +152 kJ/ mol.

 

l₂ (g) → 2l (g)

 

Heat of dissociation of I for half mole of Iodine is +76 kJ/ mol.

 

Electron affinity of I is -295 kJ/ mol.

 

l (g) → l^- (g)

 

Let the Lattice enthalpy be x kJ/ mol.

 

K+ (g) + l- (g) → Kl (s)

 

Now, we can write,

 

∴ 159 + 520 + 31 +76 - 295 + x = -271

 

=> x = -762kJ/mol

Absolute error = ±10

 

Lattice enthalpy = −854 ± 10 kJ/mol

 

Fractional error = \(\frac{10}{854}\) = 0.0158 ≈ 0.016

 

Percentage error = 0.016 x 100 = 1.6

In Figure 2, 3 and 4, the lattice enthalpy of the compounds for each of the graphs decreases as we move down the group 17. This indicates that, the lattice enthalpy of halogens decreases down the group and increases as we move from bottom of any group to top of Periodic Table.

 

In Figure 5, 6 and 7, the lattice enthalpy of the compounds for each of the graphs decreases as we move down the group 1. This indicates that, the lattice enthalpy of alkali metals decreases down the group and increases as we move from bottom of any group to top of Periodic Table.

Lattice Enthalpy of Lithium Halides

In this graph, it has been observed that, keeping the cation same, when the halides (anions) are changed in the ionic compound, the lattice enthalpy of the compound decreases when we moving down the Halogen group. It is assumed to be a linear relationship and the value of R² of the equation came out to be as 0.99 with an equation:

 

y = -46x + 902

 

Lattice Enthalpy of Sodium Halides

In this graph, it has been observed that, keeping the cation same, when the halides (anions) are changed in the ionic compound, the lattice enthalpy of the compound decreases when we moving down the Halogen group. It is assumed to be a linear relationship and the value of R² of the equation came out to be as 0.98 with an equation:

 

y = -39x + 828

 

Lattice Enthalpy of Potassium Halides

In this graph, it has been observed that, keeping the cation same, when the halides (anions) are changed in the ionic compound, the lattice enthalpy of the compound decreases when we moving down the Halogen group. It is assumed to be a polynomial relationship and the value of R² of the equation came out to be as 1 with an equation:

 

y = -6x² - 7x + 707

 

Lattice Enthalpy of Metal Chloride

In this graph, it has been observed that, keeping the anion same, when the alkali metal (cations) are changed in the ionic compound, the lattice enthalpy of the compound decreases when we moving down the Halogen group. It is assumed to be a polynomial relationship and the value of R² of the equation came out to be as 1 with an equation:

 

y = -12x² - 32x + 898

 

Lattice Enthalpy of Metal Bromide

In this graph, it has been observed that, keeping the anion same, when the alkali metal (cations) are changed in the ionic compound, the lattice enthalpy of the compound decreases when we moving down the Halogen group. It is assumed to be a polynomial relationship and the value of R² of the equation came out to be as 1 with an equation:

 

y = -14.5x² - 14.5x + 843

 

Lattice Enthalpy of Metal Iodide

In this graph, it has been observed that, keeping the anion same, when the alkali metal (cations) are changed in the ionic compound, the lattice enthalpy of the compound decreases when we moving down the Halogen group. It is assumed to be a polynomial relationship and the value of R² of the equation came out to be as 1 with an equation:

 

y = -11x² - 21x + 794

• The trend obtained can be explained using two different perspectives. One with respect to the cation and another with respect to the anion. It is evident that every ionic compound exhibit partial covalency. With the increase in covalent character, the melting point, boiling point etc. decreases of the compound. Consequently, the lattice energy also decreases. In each of the above-mentioned graphs, it has been observed that, the lattice energy of the compounds decreases as we move down the group 1 and group 17. This is because of polarisation of the ionic compound. More the polarisation, more will be the covalent character in the compound. As a result, lesser will be the lattice energy.
• With respect to the cations (metal ions), moving down the Group 1, increases the strength of positive charge in the nucleus. Though the atomic radii also increase as we move down the group, the charge density of the metal ions also increases. As the charge density of Potassium is more than Sodium and charge density of Lithium is even less that the above two, Polarising power also follows the same order. Potassium has the maximum polarising power; Sodium has a polarising power greater than Lithium. As a result, covalent character in Lithium halide is minimum, Potassium halide is maximum and Sodium halide lies between the two. Thus, Lithium halide has maximum lattice enthalpy, Potassium halide has minimum and Sodium halide lies between the two.
• With respect to the anions (halogen ions), moving down the Group 17, increases the radius of ion. Larger the ionic radii be, closer will be the electron cloud of anion with respect to the nucleus of cation. As a result, the force of attraction between the anions and cations will be more. As the ionic radii of Iodine is more than Bromine and ionic radii of Chlorine is even less that the above two, Polarizability also follows the same order. Iodine has the maximum polarizability; Bromine has a Polarizability greater than Chlorine. As a result, covalent character in Metal chloride is minimum, metal iodide is maximum and Sodium halide lies between the two.

In the graphs 1 to 6, the co-relation values are mentioned. The value of R² is 0.99 and 1 in most of the graphs. Being positive, it supports the fact that the lattice enthalpy of ionic compounds decreases as we move down the group 1 and group 17. The value of R² is high; 1 which justifies the correlation. Thus, the hypothesis predicted stands valid.

Is there a pattern in the magnitude of lattice enthalpy of dissociation as we go down Group -1 (alkali metals) and Group -17 (Halogens)?

• In the study of lattice enthalpy of Lithium Halides, the lattice enthalpy decreases down the group 17 from -854 kJ/mol for LiCl, -814 kJ/mol for LiBr and -762 kJ/mol for LiI with a trendline of equation: y = -46x + 902.
• In the study of lattice enthalpy of Sodium Halides, the lattice enthalpy decreases down the group 17 from -786 kJ/mol for NaCl, -756 kJ/mol for NaBr and -708 kJ/mol for NaI with a trendline of equation: y = -39x + 828.
• In the study of lattice enthalpy of Potassium Halides, the lattice enthalpy decreases down the group 17 from -694 kJ/mol for KCl, -669 kJ/mol for KBr and -632 kJ/mol for KI with a trendline of equation: y = -6x2 - 7x + 707.
• In the study of lattice enthalpy of Metal Chlorides, the lattice enthalpy decreases down the group 1 from -854 kJ/mol for LiCl, -786 kJ/mol for NaCl and -694 kJ/mol for KCl with a trendline of equation: y = -12x2 - 32x + 898.
• In the study of lattice enthalpy of Metal Bromides, the lattice enthalpy decreases down the group 1 from -814 kJ/mol for LiBr, -756 kJ/mol for NaBr and -669 kJ/mol for KBr with a trendline of equation: y = -14.5x2 - 14.5x + 843.
• In the study of lattice enthalpy of Metal Iodides, the lattice enthalpy decreases down the group 1 from -762 kJ/mol for LiI, -708 kJ/mol for NaI and -632 kJ/mol for KI with a trendline of equation: y = -11x2 - 21x + 794.
• The decrease in lattice enthalpy of Group 1 metals as we move down the group is gradual and polynomial of degree 2 in nature.
• The decrease in lattice enthalpy of Group 17 halogens as we move down the group is gradual and polynomial of degree 2 in nature.
• The value of R² (0.99) or (1) and the positive value of the gradient confirms that the hypothesis predicted is valid.

• The investigation has been designed in a simple and easy procedure which do not demands the use of any chemical or apparatus which is forbidden or difficult to procure.
• The independent variable chosen has no error that needs to be considered
• Any external factors that can question or alter or influence the reliability of the data like room temperature, humidity, pressure and so on have been controlled in a justified scientific procedure.
• The magnitude of percentage error indicates that the data collected claims reliable accuracy and significant preciseness as well.

This experiment can be conducted for metal fluorides. Fluoride atoms, being very small in size, show extensive electronegativity as well as least polarizability. As a result, the ionic character in metal fluoride is much greater than that of any other metal halides. Thus, it often disturbs the usual trendline. Though, further analysis of lattice enthalpy can be done considering Metal fluorides.

References has been done in MLA 8 format. As per MLA 8 guidelines the citations are listed below in alphabetical order and the in-text citations are inserted at appropriate places. Access date and time are not mentioned for research articles as per latest MLA 8 guidelines.

• Treptow, Richard S. "Determination of δh for reactions of the Born-Haber cycle." Journal of Chemical education 74.8 (1997): 919.
• Wrobleski, Henry, and Kären hess. Introduction to law enforcement and criminal justice. Cengage learning, 2005.
• Su, z. H. E. N. G. W. E. I., and P. Coppens. "on the calculation of the lattice energy of ionic crystals using the detailed electron-density distribution. I. Treatment of spherical atomic distributions and application to naf." acta crystallographica section a: foundations of crystallography 51.1 (1995): 27- 32.
• Rao, Daas Narayana. "ionic polarisation in crystals: additivity in double salts." proceedings of the indian academy of sciences-section a. Vol. 30. No. 6. Springer india, 1949.
• Stone, h. E. N., and stone hen. "the incidence of inter-transition metal phases and fajan's rule." (1978).
• Altshuler, A. M., Yu Kh Vekilov, and A. D. Izotov. "Lattice dynamics of covalent ionic compounds (b)." physica status solidi (b) 68.1 (1975): 165-172.