Lattice energy of MgF2-CaF2-ZrO2 molecule.
Lattice energy is directly proportional to the multiple of ionic charge and inversely proportional to the radius of cation and anion.
In the above compounds, , the extent of charge on’Mg’ ,’Ca’ and ‘Zr’ metal are, +2 ,+2 and +4 respectively.
Again, the extent of charge on ‘F’ and ‘O’ atoms are -1 and -2 respectively.
So, from the data of multiple of ionic charge cationic and anionic charge, it is clear that the for ZrO2 is highest.
Hence, ZrO2 molecule has higher lattice energy among all the above compounds.
The value of lattice energy of MgF2, CaF2 and ZrO2 molecules are, -2913 Kj/mole , -2609 Kj/mole and- 8714.5 kJ/ mole respectively.
In case of molecule, the extent of charge on both ‘Mg’ and’ Ca’ metal is, +2 and the extent of charge on ‘F atom is, -1 .
That is, both cations and anions contain same extent of charge.
Now, both calcium and magnesium are group-II alkaline earth metal. It has been found that, the cationic size of group-II metal decreases from top to bottom.
Therefore, the radius of Mg2+cation is less than Ca2+cation.
Since, the is lattice energy directly proportional to the multiple of ionic charge
and inversely proportional to the radius of cation and anion, hence MgF 2 has higher lattice energy than
is Lattice energy directly proportional to the multiple of ionic charge and inversely proportional to the radius of cation and anion.
Now, in case of ZrO2 molecule, the extent of charge on ‘Zr’ metal atom is very much high, that is, +4 and hence the radius of Zr 4+cation is small.
Metal with high charge and small radius cause the high lattice energy.
The lattice energy of ZrO2 molecule is about, -9714.5 Kj/mole.
can be calculated indirectly by using Born-Haber cycle.
The atomic number of oxygen and zirconium are 8 and 40 respectively.
Hence, the electronic configuration of ‘O’ and ‘Zr’ are[He]2s2,2p4 and [Kr] 4d2,5s2 respectively.
The first and second electron affinities of oxygen atom is +141 kj/mole and — 770 kj/mole respectively. The bond dissociation energy of oxygenmolecule is 498 kj/ mole.
The sublimation energy of Zr(s ) to Zr(g) change is 591 kj/mole and first, second ,
third and forth ionization energy of Zr are about 640 kj/mole, 1270 kj/mole, 2218 kj/mole and 3412 kj/mole respectively.
Applying, the above data, we can calculate the lattice energy of molecule. of ZrO2 molecule is-1080 kj/mole. From Born-Haber cycle,
ΔHf = S + [ I.E1 + I.E2 + I.E3 + I.E4 ] + D + 2 x [ E.A1 + E.A2 ] + U
or,-1080= 591 + [ 640 +1270 +2218 +3412] + 2 x [ +141–770]+U
or, -1080= 591 + 7540 + 2 x (-629)+ U
or,-1080= 591 + 7540–1258+U
Therefore, U= -591–7540 + 1258–1080= - 8451 kj/mole.
That is, the calculated lattice energy of ZrO2 is, -8451 kj/mole.
· Which one has higher lattice energy, MgF2 or CaF2 ?
· Lattice energy calculation for ZrO2 molecule
Originally published at https://chemisfast.blogspot.com.
