# B.sc. 2nd Part Chemistry Subsidiary Notes

## Miller Indices

The concept of Miller Indices was introduced in the early 1839s by the British mineralogist and physicist William Hallowes Miller.Miller evolved a method to designate the orientation and direction of the set of parallel planes with respect to the coordinate system by numbers h, k, and l (integers) known as the Miller Indices. The planes represented by the hkl Miller Indices are also known as the hkl planes. Therefore, the Miller Indices definition can be stated as the mathematical representation of the crystallographic planes in three dimensions.

### General Principles of Miller Indices

If a Miller index is zero, then it indicates that the given plane is parallel to that axis.The smaller a Miller index is, it will be more nearly parallel to the plane of the axis.

The larger a Miller index, it will be more nearly perpendicular to the plane of that axis.

Multiplying or dividing a Miller index by a constant has no effect on the orientation of the plane.

When the integers used in the Miller indices contain more than one digit, the indices must be separated by commas to avoid confusions. E.g. (3,10,13)

By changing the signs of the indices 3 planes, we obtain a plane located at the same distance on the other side of the origin.

### Rules for Miller Indices

Determine the intercepts (a,b,c) of the planes along the crystallographic axes, in terms of unit cell dimensions.Consider the reciprocal of the intercepts measured.

Clear the fractions, and reduce them to the lowest terms in the same ratio by considering the LCM.

If a hkl plane has a negative intercept, the negative number is denoted by a bar ( ̅) above the number.

Never alter or change the negative numbers. For example, do not divide -3,-3, -3 by -1 to get 3,3,3.

If the crystal plane is parallel to an axis, its intercept is zero and they will meet each other at infinity.

The three indices are enclosed in parenthesis, hkl and known as the hkl indices. A family of planes is represented by hkl and this is the Miller index notation.

### Q. Determine the Miller Indices of Simple Cubic Unit Cell Plane 1,∞,∞.

Given that,Plane 1,∞,∞

Step 1:

Consider the given plane 1,∞,∞.

Step 2:

Take reciprocals of the intercepts,

1/1, 1/∞, 1/∞

Step 3:

Take LCM of these fractions to reduce them into the smallest set of integers.

1,0,0

Therefore, the miller indices for the given plane is 1,0,0. Isotope Exchange Reaction

Moderators

## Valence Bond Theory For Bonding In Coordination Compounds

This theory is exclusively used to explain the stereochemistry and magnetochemistry of complexes. Some main points of this theory are given below-1. It concern itself with the oxidation number of the central metal atom in the complex compounds.

2. The electronic configuration of the central metal in complex compound is then written in their oxidation state.

3. The outer orbital of the central metal is reperesented by a box. The electrons of the inner orbitals does not participate in the bonding.

4. The central metal electron in outer orbitals is shown by upward (↑) and downward (↓) arrow.

5. The electrons of the ligan is shown by cross (x).

6. Each ligand donates 2 electrons to the cental metal atom for the formation of M ← L coordinate bond.

7. The metal - ligan bond is formed by the overlapping of orbitals. Greater the overlapping, stronger the bond.

8. A σ bond is formed by the overlapping of a vacant metal orbital and a filled ligand orbital.

9. A π bond is formed by the overlapping of a filled metal orbital and a vacant ligand orbital.

10. The hybridization and geometry of complexes are related to the number of ligands(i.e. coordination number).

sp hybridisation – Linear

sp

^{2}hybridisation – Triangular

sp

^{3}hybridisation – Tetrahedral

dsp

^{2}hybridisation – Square planar

dsp

^{3}hybridisation – Trigonal bypyramidal

d

^{2}sp

^{3}hybridisation – Octahedral

d

^{3}sp

^{3}hybridisation – Pentagonal bypyramidal

11. Ligands donating an electron pair easily to the central metal atom are called strong ligands (e.g. CN

^{−},CO etc.) and those donating with difficulty are called weak ligands (e.g. halides, water etc.).

12. Under the influence of strong ligands, metal electrons are forced to pair up even contrary to Hund's rule.

13. The magnetic propertis of complexes are governed by the number of unpaired electrons present in electronic configuration of complexes.

μ

_{s}= n(n+2)

^{1/2}B.M.

where μ

_{s}is spin only magnetic moment, n is the number of unpaired electrons and B.M.(Bohr Magneton) is unit of magnetic moment.

Complexes having unpaired electrons are paramagnetic while having no unpaired electrons are diamagnetic.

Example

Co(NH

_{3})

_{6}]

^{+3}

Co is in +3 oxidation state

Structure of this complex is octahedral in which inner 'd' orbital of central metal atom is used due to strong ligand (NH

_{3}).

μ

_{s}= 0 as this complex does not have any unpaired electron.

### Merits of Valence bond theory

1. Valence bond theory explains the geometrical shape and magnetic properties of complexes satisfactorily.2. It explains the formation of inner complexes in the presence of strong ligands and outer complexes in the presence of weak ligands.

3. It explains the back donation of electrons from metal ions to ligands through dπ pπ overlapping.

### Demerits of valence bond theory

1. Valence bond theory does not give information regarding magnetic moment due to orbital contribution of electrons.2. It can not explain the spectral properties of complexes.

3. It does not explain the relative stability of complex compounds.

## Inner Orbital Complexes

If the complex is formed by the use of inner d-orbitals for hybridisation (written as d^{n}sp

^{3}), it is called inner orbital complex. In the formation of inner orbital complex, the electrons of the metal are forced to pair up and hence the complex will be either diamagnetic or will have lesser number of unpaired electrons. Such a complex is also called low spin complex.

For example, [Fe(CN)

_{6}]

^{-3}and [Co(NH

_{3})

_{6}]

^{+3}are inner orbital complexes.

**[Co(NH**

_{3})_{6}]^{+3}-**Outer Orbital Complexes**

If the complex is formed by the use of outer d-orbitals for hybridisation (written as sp

^{3}d

^{n}), it is called an outer orbital complex. The outer orbital complex will have larger number of unpaired electrons since the configuration of the metal ion remains undisturbed. Such a complex is also called high spin complex.

For example, [Fe(H

_{2}O)

_{6}]

^{+3}, [CoF

_{6}]

^{- 3}and [Co(NH

_{3})

_{6}]

^{+2}are outer orbital complexes.

**[Co(NH**

_{3})_{6}]^{+2}-## 8-Hydroxyquinoline or Oxine

8-Hydroxyquinoline is a chelating agent which has been used for the quantitative determination of metal ions. It reacts with metal ions, losing the proton and forming 8-hydroxyquinolinato-chelate complexes. Its metal chelates have the formula, M(C

_{9}H

_{6}NO)

_{n}, where 'n' is 2 for metals having coordination number 4 (e.g. Mg, Cu, Zn, Cd etc.), 3 for metals having coordination number 6 (e.g. Al, Fe, Bi etc.) and 4 for metals having coordination number 8 (e.g. Zr, Hf etc.).