16.3 |
Problems |
16.1 |
Identify the four C3 axes of the cubic unit cell in Fig 16.1 (a). One of them is the line joining the points 3 and 5. How many C2 axis does a cubic unit cell have? In the same manner (by labeling the corners or additional points by numbers) identify the C2 axis in monoclinic and orthorhombic lattices, the C3 axis in a rhombohedral lattice, the C4 axis in a tetragonal lattice and the C6 axis in a hexagonal lattice. Can you show that the four C3 axes in the cubic lattice are in a tetrahedral arrangement relative to each other? |
16.2 |
Give an example for each one of the fourteen Bravais Lattices (other than the examples given in Table (16.3) |
16.3 |
Parallelograms can be repeated periodically (by repeatedly translating through the edge lengths a and b) to fill up the whole of two dimensional space. Satisfy yourself that a regular pentagon can not be repeated (by using translations and rotations) so as to fill the whole of a 2-dimensional space. Can you fill up a two dimensional space using triangles? |
16.4 |
Distinguish between a lattice and a unit cell. |
16.5 |
Why do substances exist in different allotropic forms at different temperatures? e.g., monoclinic and rhombohedral forms of sulphur.
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16.6 |
For the repulsive potential of the form B / rn, we have derived the equation for Lattice energy UL = - NAM z1, z2e2 r0-1 (1- 1/n) where NA is the Avogadro number, M the Madelung constant and r0 the closest cation - anion separation. If the repulsive potential has the form Ce -r/r0, what is the expression for the Lattice energy? |
16.7 |
For NaCl, r0 = 2.8 * 10 -10 m. The value of n in the repulsive form B/rn can be estimated from the close shell configuration of the ions. FOr close shells like He, n = 5; Ne, n = 7; Ar, n = 9; Kr, n = 10; xe, n =1. If the cations and anions have different closed shells, as in NaCl. The average value of n over the two closed shells is used. If the cations and anions have different closed shells is used. If the average is a fraction, (as in the case of NaCl again), the larger value of n (of the two) can be used. Estimate the lattice energy of NaCl from the Born Lande equation and compare that with the value of UL obtained from the Born Haber cycle given in Example 1. |
16.8 |
The alkaline earth oxides of group II - A (MgO, CaO,...) have the NaCl crystal structure (ie, two interpenetrating FCC Lattices of anions and cations). Using the value of the nearest neighbour separation (r0) for the oxides given below (in pm = 10 -12m), calculate their lattice energies (using Born Lande eq) MgO (210pm), CaO (240pm), SrO(257pm), BaO(276pm). |
16.9 |
Why are the lattice energies of the above oxides greater than those of the corresponding chlorides? |
16.10 |
Using the energy data given below (in kJ/mol) calculate the electron affinity of fluorine |
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H dissociation (F2) = 160, Hf (NaF) = -571, 1E(Na) = 494 |
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Hvaporization (Na) = 101, UL (NaF) = -894 |
16.11 |
To extend the Born Haber cyle to bivalent oxides MO, where M is divalent metal ion, we need the second ionization potential (M+ M2+ + e-) and the second electron affinity (O2- O-). Calculate the heat of formation of MO (solid) using the following data (in kJ/ mol). |
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Hdissociation (O2 = 309 H vaporization (M) = 309 |
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First 1.E of M (M m+ + e-) = 900, second 1.E of M = 1760 |
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First electron affinity of O (o - o +e) = 142 |
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Second electron affinity of 0 = -879 |
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Madelung constant = 1.747, Born exponent n = 8 |
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r0 (M-0) = 1.75*10 -10m |
16.12 |
To calculate the heat of formation of gaseous MO, we can use the Born Haber cycle except that, instead of Lattice energy M 2+ +O2- MO(lattice), we have the gas phase energy for M2+ + O2- MO(g). We can use the Born Lande formula for the above process without the factor of Madelung constant. The calculation reveals that MO(solid) is a more stable than MO(gas).can you rationalize this fact?can use the Born Land formation. |
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