Inorganic Chemistry -A Model Chapter

Model Chapter 6 continued



E. Though the sodium metal ignites spontaneously in a chlorine medium, an isolated atom of sodium will never react with another atom of chlorine in vacuum to give two separate ions. The formation of a gaseous Cl^- ion from chlorine atom releases 4eV of energy, while the conversion of a gaseous sodium atom into gaseous sodium ion requires 5.1 eV of energy. Thus, in order that the reaction

Na (g) + Cl (g)                                   Na⁺ (g) +  Cl^- (g) -  1.1 eV

takes place in the forward direction an additional energy of 1.1 eV must be spent. As a pair of separate gaseous ions has a higher energy than a pair of separate atoms, the above reaction would not be expected to occur spon­taneously.

However, when an isolated cation with charge Z⁺ approaches an isolated anion with charge Z^-, both forces of attraction as well as forces of repulsion will operate between them. The forces of attraction are mainly due to the attraction between the two opposite charges. The forces of repulsion are due to the repulsion between the outer electrons of two ions and the repulsion between the two nuclei. At the optimum distance, do, it has been experimen­tally calculated - an approximate calculation only - that the repulsive potential which depends on the electronic configuration of the ions is about 15% of the attractive potential. Thus when a pair of separate sodium and chloride ions approaches each other, the approximate lowering of energy would be

V^°_+- = -e²  (1 - 0.15)

  d₀

71

at the optimum distance. The value of this electrostatic energy is calculated as 4.5 eV. This energy of 4.5eV is higher than the energy required to produce two separate sodium and chloride ions (1.1eV) and hence at the optimum distance the Na⁺ Cl^- "ion pair" becomes stable with respect to the separate gaseous atoms as the initiation point. As the electrostatic force field of a charged particle extends in all directions, (ionic compounds are^. omnidirec­tional )a cluster of two ion pairs will be more stable than two separate ion pairs and the lowering of energy when an ion pair clusters with another ion pair can be calculated easily. In fact, every addition of ion pair with this cluster leads to progressive lowering of energy and in this sense ionic bonding power, in contrast to covalent bonding power, is not saturated at least until crystals that are visible to the naked eye are formed. It is clear that since there is no limitation to the number of Na⁺ - Cl^- ion pairs that can combine to give solid NaCl, every ion in NaCl crystal has many neighbours. Therefore, the binding energy of the ions in a crystal is higher than that in an isolated ion pair. The shape of the crystal is determined by its geometry and the energy released during its formation is expressed by the equation.

                        

where 'U₀' is called the lattice energy of the crystal, 'N' the Avagadro number, 'a' the correction factor to account for the repulsive forces and 'A' the Madelung constant which depends on the geometry of the crystal. U₀ gives the energy released when one mol of an ionic compound condenses into a crystal. It is this energy which is mainly responsible for the production of ionic solids although energy terms such as ionization energy electron affinity, sublimation energy, dissociation energy also must be taken into account.

It must be noted that the ionic compounds are crystalline substances and the concept of two ion molecule of the type of, say, KCl or RbBr does not hold for them and the whole crystal must be regarded as a giant molecule consisting of a large number of K_n⁺ Cl^-_n or Rb_n⁺ Br„ ^-ions.

It must be again noted that the above concept does not apply to covalent compounds. Covalent compounds can be considered as simple molecules provided there is no polymerization.

·  Chemical Bonding and Geometry of Molecules by George E. Ryschkewitsch.

72

F.     The ionic crystals are generally hard. The hardness increases regularly in some of the cases as the distance between the ions decreases. As ,the electrostatic attraction between the ions is strong when the distance between the effective charges on the ions is short, the ions having multiple charges, such as Ca²⁺, A1^3+., P0₄^3-, SO₄^2—, give rise to very strong attractive forces and hence form hard crystal structures provided ionic deformation is not appreci­able.⁽²⁾ It is curious that in a particular set of compounds adopting a particular crystal structure the hardness of the crystal increases as the charge density of the cation increases or when the charge densities of the cation and anion are suitably matched. Thus, the hardness in Mohs of BeO, MgO, CaO, SrO, and BaO - all with NaCl structure - are 9, 6.5, 4.5, 3.5, and 3.3 respectively. Similarly, hardness in Mohs of NaCI, MgO, ScN and TiC - again all with NaCI structure - are 3.2, 6.5, —7.5 and —8.5 respectively. Further, ionic crystals are brittle and are not malleable or plastic. This is because the dislodgement of ions would bring together like charges which because of their repulsion would result in a rupture of the crystal.

G.    Most of the transparent ionic crystals are insulators in the crystalline state. (Transparency is due to the fact that the energy gap separating the valence band and the conductance band is quite large and hence the light from the visible region is not absorbed). Electrons in the insulator crystals are very tightly bound to the atoms. Hence, they cannot be dislodged and made to move easily either by thermal vibration or by ordinary field. On the basis of the band theory, solid insulators are defined as materials wherein the valence band is completely filled while the conductance band is completely empty. The two bands are separated by an energy gap of forbidden zone. The energy gap of the forbidden zone will be normally above 1 electron volt. Hence, only very few electrons from the valence band can be promoted to the conductance band by thermal vibration or by other methods.

If an insulator crystal like NaCI is considered, for Na⁺, the ls, 2s, and 2p levels are full, These levels are deep seated and are hence not important. Similarly, for chloride ion, the ls, 2s, 2p, and 3s levels are not important. The important levels are the 3s level of sodium and the 3p level of chlorine. The 3p level of chlorine can accommodate a maximum of six electrons and it is assumed that the 3p orbitals of chlorine interact and broaden into a 3p band.

⁽²⁾ The fact that diamond and ionic minerals such as calcium carbonate are hard shows that both covalent and ionic bonds are strong and very difficult to break. In liquids and gases the bonds within the molecules may be strong but the forces between the molecules are weak van der Waals forces.

73

It is the valence band and it is completely occupied (ie p⁶ configuration). It is at a lower level than the 3s band formed by the 3s atomic orbitals of the sodium atoms. The 3s band of sodium atoms is the conductance band but it is completely empty. The band gap is calculated as 7eV. Hence, at ordinary temperature electrons are not excited from the valence band to the conduc­tance band. Ionic crystals with energy gap greater than 2eV are considered as good insulators.

Some ionic solids do conduct electricity. For this there must be current carriers. These current carriers are believed to be interstitial ions or vacant ionic cites.

H. Production of colour centres in the space inside the crystals like NaCI by irradiating them with X-rays is well known (refer chapter 18). Now the scientists have succeeded in creating what is called "Spectral holes" in the space inside the crystals by shooting a thin laser beam of a specific colour. Using lasers of different colours, large volume of data is stored in the spectral holes as colour patterns. In fact, it has been found that the space inside a crystal could pack millions of times more information than the same space on the best optical disc developed so far. Recently, adopting a technique developed by the American scientist Thomas Massberg, an Indian scientist Raninder Kachru working in the United States, has devised an apparatus that stores upto 50,000 bits of data in a DoT - sized crystal at superfast speeds.

1. NaC1 crystal has NaC1 structure. CsCl has CsCl structure. NaF adopts NaCl structure. ZnS has zinc blende structure. TiO2 has rutile structure. Ge0₂, SnO₂ and Pb0₂ also adopt rutile structure. Though CaF₂ has fluorite structure, the structure adopted by most of the alkali metal oxides, M₂0, and the corresponding sulphides, selenides and tellurides is the antifluorite structure with 4:8 co-ordination (called so by reason of the fact that the alkali metal ions occupy the F positions and the 0 (S, Se, Te) ions the Ca positions of the CaF₂ structure). Now the question is why does NaCI adopt NaC1 structure and CsCl the CsCl structure? Why does KBr not adopt CsC1 structure? Or why does BeO (wurtzite structure) not adopt the structure of MgO (NaCI structure). Though the polarizability terms have a dominant role in determin­ing the nature of the lattice a substance adopts, the structure of the ionic compounds does not depend on the nature, or the electronic configuration of

74

the element, but it depends on the radii of the ions. If the ratio of the radii of the ions, ie r⁺/r^-, lies between, for example, 0.225 and 0.41, their co-ordination is tetrahedral, if the ratio lies between 0.41 to 0.732, their co-ordination is octahedral, if the ratio is between 0.732 and 1.37 the co-ordination is cubic and so on.

During the interaction of Na⁺ and Cl^- ions (rNa⁺ = 0.98 A^° and rCl^- = 1.81A^°), for example, the ratio of their radii being 0.98/1.81 = 0.54, an octahedral co-ordination as in NaCl structure arises. The ratio of the ionic

radii of Cs⁺ and Cl^- ions (rCs⁺ = 1.65 A^°;                            = 1.81A^°) is 0.91 which
corresponds to cubic co-ordination. Since the K : Br radius ratio (0.68) in KBr is less than the minimum value (0.732) for a stable body centred cubic arrangement, as in CsCl, KBr does not crystallize with CsCl structure. Similarly, the structure of BeO (wurtzite, co-ordination No.4) differs from the structure of MgO (Rock salt, NaCI, co-ordination No.6) because Mg : 0 radius ratio in MgO is 0.47. It is well above the limit of 0.414 for six co-ordination whereas the Be :0 ratio in BeO is 0.23 which is just above the limiting value for tetrahedral co-ordination of four.

Why does the structure adopted by an ionic compound depend on the radii of the ions? We have noted that forces of attraction as well as forces of repulsion will operate between a positive ion and a negative ion when they tend to become an ion pair. Same kinds of forces will operate between the cations and the anions when the ion pairs or better the separate ions tend to cluster together to give new groupings. Obviously, the forces of attraction are those acting between the cations and its closest anions. The forces of repulsion are those acting between the electron clouds of the anion and the surrounding cations, and more importantly those acting between the ions of like charges. The crucial point is that during the formation of an ion pair the question of repulsive forces acting between the ions of like charges does not arise.

The decrease in energy due to attraction between the cation and the surrounding anions will increase with the decrease in the distance between the cations and the anions (of course up to an optimum distance) and with the increase in the number of closest neighbours. When the distance between the cation and the anion decreases, the electrostatic attraction increases and this naturally reflects in the lattice energy. When the number of closest neighbours increases, the number of attractive interactions increases and this also reflects in the Madelung constant and hence in the lattice energy. However, it must

7S

be noted that the variation in the number of closest neighbours accounts for only a few per cent of the lattice energy ⁽³⁾

Table 8

The table showing the effect of co-ordination number on Madelung constant-A. Some Crystal Geometries

Structure	Examples	Co-ord Nos.	A
Wurtzite	ZnS, AIN, BeO	4	1.641
Rock salt	NaCI, CaO, AgCI, NaH	6	1.748
Caesium Chloride	CsCI, TIC', LiHg, CsCN	8	1.763
B - Quartz	SiO2, Ge02	2.4	2.220
Rutile	TiO2, MgF2  .	3.6	2.408
Fluorite	CaF2, SrCl2, Na2O)	4.8	2.519
Corundum	A1203, Fe2O3, Cr2O3	4.6	4.172
Data from Chemical Bonding and Geometry of Molecules by E. Ryschkewitsch.

The tendency of the central ion to have more number of closest neighbours at the shortest possible distance is opposed by the tendency of the surrounding ions to have minimum repulsion between them. The surrounding ions will have like charges and they will repel one another. Hence, if the given clustering is to be stable, there must be sufficient space between the surround­ing ions; and at the same time it is imperative that the surrounding ions must make the optimum contact with the central ion. The combination of conditions means that the number of closest neighbours or the co-ordination number of the central ion will increase with (i) the increase in the size of the central ion and (ii) the decrease in size of the surrounding ions. Therefore, it is evident

⁽³⁾ Ionic size and ionic charge are definitely more important. For instance, though the inter ionic distances are almost the same, Na₂O (-602) has higher lattice energy than NaF (-214) - ie the higher the charge on anions, the higher the polarizability and hence the lattice energy. Again BaF does not exist. But BaF₂ does exist because the :attice energy of BaF₂ is very much higher than that of unstable BaF. Similarly, though NaF and RbI have equal number of charges, lattice energy of NaF (-214) is higher than that of RbI (-147)- ie the larger the ion the lesser the charge density and hence the lesser the stability.

76

that the co-ordination number of the central ion is effectively determined by the sizes or the radii of the positive and negative ions and the radius ratio at which all the ions are in the optimum distance to one another can be calculated in a straight-forward way for each co-ordination number from solid geometry. If the radius ratio is below this geometrical value, then the given clustering will be unstable due to interionic repulsions. Table No 9 gives the list of these limiting radius ratios.

Table 9

Table showing the limiting radius ratios

Co-ordi. No.	Configuration	Limiting radius ratios
3	Trigonal	0.155
4	Tetrahedral	0.225
6	Octahedrat	0.414
8	Cubic	0.732

The maximum co-ordination number of sodium ion with respect to chloride ion is six and therefore in NaCl each ion is surrounded by six other ions of opposite charge. Caesium ion, being bigger than sodium ion, can have eight chloride ions as neighbours and hence in CsCl each ion has eight nearest neighbours. In CaF₂, each Ca²⁺ ion is surrounded by eight F^- ions at the corners of a cube and each F^-. ion by four Ca²⁺ ions at the corners of a regular tetrahedron. We cannot expect a 1:1 compound like NaC1 to adopt the CaF₂ structure simply because NaCl has only half the requisite number of negative ions and even if it is forced to adopt the CaF₂ structure, half of the negative ion positions in CaF₂ lattice must remain empty.

Again, even though larger co-ordination number ensures larger lattice energy, KBr adopts NaCl (1:6) arrangement rather than CsCl (1:8) arrange­ment because there is not enough space around K⁺ ion to accommodate eight Br^- ions.

In this connection, it must be pointed out that the radius ratio criterion cannot be strictly applied to compounds like Si0₂ because there is consider­able covalent character in them. This perhaps indicates the tendency of Si0₂ for polymerization. Further, though the electronegativity of Ge is comparable to Si, Ge0₂with radius ratio close to 0.41 crystallizes with both the 6:3 co-ordinated rut ile structure and the 4:2 co-ordinated quartz structure. Again,

77

though TiO₂ has rutile structure, a distorted structure, ⁽⁴⁾ description of TiCl₄ in terms of ionic bonding is not adequate because of the high positive charge in Ti⁴⁺. In fact, TiC1₄ exists as discrete molecules and its stability is better accounted for in terms of covalent bonding. A metal oxide may have ionic structure. But the corresponding sulphides may often have a layer lattice due to the greater polarizability of the sulphide ion. In fact, polarizable ions do not behave as true spheres. Thus, TiO₂ and SnO₂ have a rutile structure but TiS₂ and SnS₂ have cadmium iodide structure: Similarly, though octahedral co-ordination will be preferred for radius ratios ranging from 0.41 to 0.732 and though BeS with radius ratio 0.35 prefers tetrahedral co-ordination (Be²⁺ ion occupies the tetrahedral holes of the closest - packed lattice adopting wurtzite structure consistent with the fact that the tetrahedral sites will be preferred for radius ratio ranging from 0.225 to 0.41) both forms of ZnS (radius ratio 0.52) - wurtzite and zinc blende-adopt 4 co-ordinated structures violating radius ratio rule. HgS too with radius ratio 0.68, crystallizes with the zinc blende structure. Further, radius ratio criterion fails to explain the structures adopted by some ionic compounds too. For instance, RbCl and RbBr with radius ratio greater than 0.732 do not adopt CsCl structure at atmospheric temperature and pressure (RbBr, RbI and RbCl adopt CsCl structure under a pressure of about 5000 kg/cm² and RbCl also at low temperatures^*) but adopt only NaC1 structure; and KF and RbF with radius⁽⁵⁾

(4)The repulsion between the highly charged metal ions, particularly in the rutile structure, is reduced by distorting a regular structure so as to increase the Ti - Ti interionic distance. This type of distortion is noticed in varying degrees in all crystals where the metal ions carry more than two formal charges. AIF₃, NiAs, A1₂O₃

and CaTiO₃ are examples for such crystals. Still greater distortion is noticed in the lanthanide oxides, M₂0₃.

(5)According to WELLS, (Structural Inorganic Chemistry 1962 Edition)" After the cube (c.no.8) the next highly .symmetrical co-ordination polyhedron is the cubooc­tahedran for 12 co-ordination. When we consider the close packing of equal spheres it can be seen that a close packed arrangement of equal number of oppositely charged ions in which each ion is surrounded by twelve opposite charge is geometrically impossible. There remains the possibility that there might be 9:9 or 10:10 co-or­dinated structures with radius ratio between 0.732 and unity; it seems doubtful if this problem has been studied".

* G. Wagner and L. Lipperet

Table 10.

Atomic Radii / pm of elements

Reference : "The Elements" by John Emsley

Groups of elements

IA

IIA

IIIB

IVB

VB

VIB

VIIB

VIIIB

IB

IIB

IIIA

IVA

VA

VIA

VIIA

VIIIA

1.

H 78

.

He 128

2

Li 152

Be 113.3

B 83

C

N 71

0

F 71.7

Ne

3.

Na 153.7

Mg 160

AI 143.1

Si 117

P 93

S 104

CI

Ar 174

4.

K 227

Ca 197.3

Sc 160.6

Ti 144.8

V 132.1

Cr 124.9

Mn 124

Fe 124.1

Co 125.3

Ni 124.6

Cu 127.8

' Zn 133

Ga 122.1

Ge 122.5

As 125

Se 215.2

Br

Kr

5.

Rb 247.5

Sr 215.1

Y 181

Zr 160

Nb 142.9

Mo 136.2

Tc 135.8

Ru 134

Rh 134.5

Pd 137.6

Ag 144.6

Cd 148.9

In 162.6

Sn 140.5

Sb 182

Te 143.2

I

Xe 218

6

Cs 265.4

Ba 217.3

La 187.7

Hf 156.4,

Ta 143

W 137

Re 137

Os 135

Ir 135.7

Pt 138

Au 144.2

Hg 160

TI 170.4

Pb 175

Bi 155

Po 167

At

Rn

7.

Fr 270

Ra 223

Ac 187.8

Ku

Ha

Ce 182.5

Pr 182.8

Nd 182.1

Pm 181

Sm 180.2

Eu 204.2

Gd 180.2

Tb 178.2

.         Dy 177.3

Ho 176.4

Er 175.7

Tm 174.6

Yb 194

Lu 173.4

Th 179.8

Pa 160.6

U 138.5

Np 131

Pu 151

Am 184

Cm

Bk

Cf

Ks

Fm

Md

No

Lr

Table 11

Covalent Radii / pin of Elements

Reference : "The Elements" by John Emsley.

Groups of elements

IA

IIA

IIIB

IVB .

VB

VIB

VIIB

VIIIB

IB

IIB

IIIA

IVA

VA

VIA

VIIA

VIIIA

1.

H

H 120*

He 122*

2

U 123

Be 89

B 208*

C 185*

N 154*

0 140,*

F 135*

Ne 160

3.

Na 231*

Mg 136

Al 205*

Si 200*

P 190*

S 185*

CI 181*

Ar 191*

4.

K 231*

Ca 174

Sc 144

Ti 132

V

Cr

Mn 117

Fe 116.5

Co 116

Ni 115

Cu 117

Zn 125

Ga 125

Ge 122

As 200*

Se 200*

Br 195*

Kr 198*

5.

Rb 244*

Sr 192

Y 162

Zr 145

Nb 134

Mo 129

Tc

Ru 124

Rh 125

Pd 128

Ag 134

Cd 141

In 150

Sn 140

Sb 220*

Te 220*

I 215*

Xe 209

6.

Cs 262*

Ba 198

La 169

Hf 144

Ta 134

W 130

Re 128

Os 126

Ir 126

Pt 129

Au 134

Hg 144

TI 155

Pb 154

Bi 240*

Po 153

At

Rn

7.

Fr

Ra

Ac

Ku

Ha

Ce 165

Pr 165

Nd 164

Pm

Sm 166

Eu 185

Gd 161

Tb 159

Dy 159

Ho 158

Er 157

Tm 156

Yb 170

Lu 156

Th

Pa

U

Np

Pu

Am

Cm

Bk

Cf

Es

. Fm

Md

No

Lr

80

Table - 12

Ionic Radii of Elements A°

Reference : Inorganic Chemistry by N. Akhmetov.

1.     H^-    = 1.36

2.  He^- = -

3.    Li⁺      = 0.68

4.   Be²⁺  = 0.34

5.   B³⁺   = 0.20

6  C  = -

7.  N^3-.= 1.48

8.  O^2-  = 1.36

9.    F^-      = 1.33

10.  Ne = -

11 . Na⁺ = 0.98

12.       Mg²⁺ = 0.74

13.       Al³⁺ = 0.57

14.       Si⁴⁺ = 0.34

15.       P³    = 1.86

16.       S^2-   = 1.82

17.       Cl^-   = 1.81'

18.       Ar= ‑

19.       K⁺           = 1.33

20.       Ca²⁺ = 4.04

21.       Sc³⁺ = 0.83

22.       Ti⁴⁺ = 0.64

23.       V^s+ = 0.59

24.       Cr⁶⁺ = 0.35

25.       Mn²⁺ = 0.52

26.       Fe²⁺ = 0.80

27.       Co²⁺ = 0.80

28.       Ni²⁺ = 0.79

29.       Cu⁺ = 0.98

30.       Zn²⁺ = 0.83

31.       Ga³⁺ = 0.62

32.       Ge⁴⁺ = 0.44

33.       As^a = 1.92

34.       Se^e = 1.93

35.       Br^-   = 1.96

36.    Kr    = ‑

37.    Rb⁺ = 1.49

38.    Sr²⁺ = 1.20

39.    Y³⁺ = 0.97

40.    Zr⁴⁺ = 0.82

41.    Nb^s+ = 0.66

42.    Mo^s+ = 0.65

43.    Tc⁷⁺ = 0.56

44.    Ru²⁺ = 0.85

45.    Rh³⁺ = 0.78

46.    Pd²⁺ = 0.88

47.    Ag⁺ = 1.13

48.    Cd²⁺ = 0.99

49.    In³⁺ = 0.92

50.    Sn⁴⁺ = 0.67

51.    Sb³ = 2,08

52.    Te^2- = 2.11

53.    I^-    = 2.20

54.    Xe =-

55.    Cs⁺ = 1.65

56.    Ba²⁺ = 1.33

57.    La³⁺ = 1.04

72.   I^-11⁴⁺ = 0.82

73.   Ta^s+ = 0.66

74.   W⁶⁺ = 0.65

75.   Re²⁺ = 0.72

76.   0s²⁺ = 0.89

77.   ir²⁺   = 0.89

78.   Pt²⁺ = 0.90

79.   Au⁺ = 1.37

80.   Hg²⁺ = 1.12

81.   11³⁺ = 1.05

82.   Pb⁴⁺ = 0.76

83.   Bi^3- = 2.13

84.   Po =-

85. At = 2.3

86. Rn = ‑

87. Fr⁺      = 1.75

88. Ra²⁺ = 1.44

89. Ac³⁺ = 1.11

58.   Ce³⁺ = 1.00

59.   Pr^a+ = 1.00

60.   Nd³⁺ = 0.99

61.   Pm³⁺ = 0.98

62.   Sm³⁺ = 0.97

63.   Eu³⁺ = 0.96

64.   Gd³⁺ = 0.94

65.   Tb³⁺ = 0.92

66.   Dy³⁺ = 0.91

67.   Ho³⁺ = 0.89

68.   Er³⁺ = 0.87

69.   Tu³⁺ = 0.86

70.   Yb³⁺ = 0.85

11. Lu³⁺ = 0.84

90. Th³⁺ = 1.08

91. Pa³⁺ = 1.05

92. U³⁺ = 1.03

93. Np³⁺ = 1.01

94. Pu³⁺ = 1.00

95. Am³⁺ = 0.99

96. Cm = -

97. Bk =-

98. Cf   = -

99. Es     = -

100. Fm = -

101. Md =

102. No =

103. Lr          = -

Table - 13

Ionic Radii / pm of elements Reference "The Elements by John Emsley

1.	H-	=	154	36.	Kr+	=	169	85. At-        =	227
2.	He	=	-	37.	Rb+	=	1.49	86. Rn        =	-
3.	Li+	=	78	38.	Sr2+	=	127	87. Fr+       =	180
4.	Be2+	=	34	39.	Y3+	=	106	88. Ra2+ =	152
5.	B3+	=	23	40.	Zr2+	=	109	89: Ac3+ =	118
6.	C4-	=	260	41.	Nb5+	=	69	58. Ce3+ =	107
7.	N3+	=	16	42.	Mo2+ =		92	59. Pr3+      =	106
8.	O2-	=	132	43.	Tc2+	=	95	60. Nd3+ =	104
9.	F-	=	133	44.	Ru3+	=	77	61. Pm3+ = 106
10.	Ne	=	-	45.	Rh2+	=	86	62. Sm3+ = 100
11.	Na+	=	98	46.	Pd2+	=	86	63. Eu3+ =	98
12: Mg2+ =			78	47.	Ag+	=	113	64. Gd3+ =	97
13.	Al3+	=	57	48.	Cd2+	=	103	65. Tb3+ =	93
14.	Si4-	=	271	49.	ln3+	=	92	66. Dy3+ =	91
15.	P3-	=	212	50.	Sn4+	=	74	67. Ho3+ =_89
16.	S4+	=	37	51.	Sb5+	=	62	68. Er3+      =	89
17.	CI-	=	181	52.	Te4+	=	97	69. Tm3+ = 87
18.	Ar	=	-	53.	I-	=	220	70. Yb3+ =	86
19.	K+	=	133	54.	Xe+	=	190	71.  Lu3+    =	85
20.	Ca2+	=	106	55.	Cs+	=	165	90. Th3+ =	101
21.	Sc3+	=	83	56.	Ba2+	=	143	91. Pa3+ =	113
22.	Ti2+	=	80	57.	La3+	=	122	92. U3+       =	103
23.	V5+	=	59	72.	Ht 4+	=	84	93. Np3+ =	110
24.	Cr2+	=	84	73.	Ta5+	=	64	94. Pu3+ =	108
25.	Mn2+ = 91			74.	W4+	=	68	95. Am3+ = 107
26.	Fe2+	=	82	75.	Re4+	=	72	96. Cm3+ = 99
27.	Co2+	=	82	76.	0s2+	=	89	97. Bk3+ =	98
28.	Ni2+	=	78	77.	Ir2+	=	89	98. Cf3+    =	98
29.	Cu+	=	96	78.	Pt2+	=	85	99. Es3+    =	98
30.	Zn2+	=	83	79.	Au+	=	137	100. Fm3+ =	97
31.	Ga3+	=	62	80.	Hg2+	=	122	101. Md3+ =	96
32.	Ge4-	=	272	81.	Ti3+	=	105	102. No3+ =	95
33.	Ass+	=	46	82.	Pb4+	=	84	103. Lr3+  =	94
34.	See'	=	191	83.	Bi5+	=	74
35.	BC	=	196	84.	Po2-	=	230

82

ratio near to unity do not exhibit even higher co-ordination numbers. On the other hand, LiI ⁽⁶⁾ with radius ratio less than 0.414 adopts an octahedral structure (NaCl structure) instead of a tetrahedral structure. Similarly CsC1 has a NaCl structure at 460^°C because of the fact that with rise of temperature more random or distorted structure ie that of high entropy is formed. Further rise in temperature leads to eventual break down of a regular three dimensional structure of CsCl ie the CsC1 crystal will melt leading to still higher entropy. However, these are all exceptions and are, therefore not considered as ex­amples.

J. Though the ions are more stable than atoms (refer section A), the reaction between ions are several times faster than the reaction between atoms. Ionic reactions are so fast that the speed of the ionic reactions can be measured only by steady state principle or by relaxation method. The reason is that in ionic reactions the energy terms such as sublimation energy, ionization energy do not come into the picture. This does not mean that there is possibility for ionic reactions to occur always. This is because, ionic reactions are affected by the nature of the medium. Generally, the reaction proceeds only if the product is insoluble. This means, for example, no reaction will take place between the ions of sodium chloride and potassium sulphate under normal conditions. Reaction takes place between AgNO₃ and KCl because AgCl is insoluble in water. The rate of such precipitation reactions is proportional to the rate of diffusion of the ions. The rate of diffusion of the ions through the medium depends on the nature of the medium. In other words the velocity of the ionic reaction is affected by the nature of the medium. It is clear that ionic reactions are affected by ions which in no way take part in the reaction.^t7

Though the ionic reactions are faster than the reactions between atoms or that between molecules, they are slower than free radical reactions. As the solvation energies of ions are extremely greater than that for neutral species, ionic reactions take place with greater difficulty than the reactions involving neutral reagents such as free radicals.

(6)Another kind of distortion appears to arise when the cation is too small for the anion hole in which it is placed. A simple calculation shows that it would then produce greater lattice energy if it is moved away from the central position of a regular anion environment. This may also account, in part, for the retention of the sodium chloride structure below the radius ratio in LiI.

(7)In physical chemistry it is called neutral salt effect.