Tuesday, February 19, 2019

Ionic bond and calculating the lattice energy of ionic compounds (Born-Haber cycle)



Ionic bond:

Ionic bond is an electrostatic bond that forms between positive and negative ions. In ionic bond, one or more electrons transfer from the valence shell of an atom to valence shell of another atom. The atom that loses electrons become positive ion (cation) and the atom that gains electrons become negative ion (anion).
The positive ion -cation- loses electrons, cation has a number of protons larger than the number of electrons. The negative ion -anion- gains electrons, anion has a number of electrons larger than the number of protons.
Any of those positive or negative ions tend to attract a large number of opposite charges forming an ionic solid. The solid normally has a regular, crystalline structure that allows for the maximum attraction of ions, given their particular sizes.

Na [Ne] 3s1 + Cl [Ne]3s23p5 → Na+([Ne]) + Cl-([Ne]3s23p6)

A wide variety of ionic compounds result from the combine of a Group 1A or Group 2A metal with a halogen or oxygen.
To be able to understand how ionic compounds form, we can imagine that the formation of ionic compounds occur in separate steps:
For the reaction of lithium and fluorine atoms to form:
First the lithium loses electron to form positive ion (cation):
Li (1s22s1) → Li (1s22s0) + e-
The electron transfer to fluorine atom:
F (1s22s22p5) + e→ F (1s22s22p6)
Now that would lead to joining between both ions:
Li+ + F- → Li+F-
Another example, the combustion of calcium in presence of oxygen:
2Ca(s) + O2(g) → 2CaO(s)
Ca [Ar]4s2 + O [1s22s22p4] → Ca2+ [Ae] O2-[Ne]
Lattice energy of ionic compounds:
Lattice energy cannot be measured directly. Using Coulomb’s law it is possible to measure crystal energy if we know the structure and composition of the ionic compound. For example the crystal lattice energy of LiF:
Eα QLi+QF-
E= k(QLi+QF-)/r
Where QLi+ and QF- are the charges on the Li+ and F- ions and k is the proportionality constant. E is negative quantity, because QLi+ is positive and QF- is negative so formation of an ionic bond is exothermic process and the lattice energy of LiF is positive and the bonded pair of Li+ and F- ions is more stable than separate Li+ and F- ions.

Born-Haber cycle (the process of determining lattice energy) :

Born-Haber cycle for calculating the lattice energy of fluorine and lithium:
1. The convert solid lithium to lithium vapor (the direct conversion of a solid to a gas is called sublimation): where the enthalpy change is 155.2 (energy needed for sublimation):→
Li(s) → Li(g)                              ∆H1o = 155.2kJ/mol
2- Dissociation of a half mole of F2 gas into gaseous F atoms (breaking of bond):
½ F2(g) → F(g)               ∆H2o = 75.3kJ/mol
3- Ionization of one mole of gaseous Li atoms:
Li(g) → Li+(g) + e-                                  ∆H3o = 520kJ/mol
4- Addition of one mole of electrons to one mole of gaseous F atoms (opposite to electron affinity):
F(g) + e- → F-(g)                                   ∆H4o = -328kJ/mol
5- Combination of 1mole of gaseous Li+ and 1mole of F- forming LiF:
Li+(g) + F-(g) → LiF(s)                             ∆H5o = ?
Reverse step 5:           Energy + LiF(s) → Li+(g) + F-(g)

So,
Li(s) → Li(g)                              ∆H1o = 155.2kJ/mol
½ F2(g) → F(g)                           ∆H2o = 75.3kJ/mol
Li(g) → Li+(g) + e-                      ∆H3o = 520kJ/mol
F(g) + e- → F-(g)                       ∆H4o = -328kJ/mol
                                 Li+(g) + F-(g) → LiF(s)                     ∆H5o = ?
              Sum: Li(s) + ½ F2(g) → LiF(s)                         ∆Hoverallo = -594.1kJ/mol

According to Hiss’s law the total enthalpies equals the sum of enthalpies of each steps:
∆Hoverallo = ∆H1o + ∆H2o + ∆H3o + ∆H4o + ∆H5o
-594.1kJ/mol = 155.2kJ/mol +75.3kJ/mol +520kJ/mol + 328kJ/mol + ∆H5o
∆H5o = -1017kJ/mol

Steps 1, 2 and 3 require energy input were 4 and 5 release energies.
∆H5° is a large negative quantity while the lattice energy of LiF is a large positive quantity. According to Coulomb’s law, the separation of ions is endothermic and for that, the lattice energy is always a positive quantity.

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