Pauling’s first rule

Finally, according to Pauling s first rule one would expect lower tetrahedral defect and activation barrier energies in MO2 than in Lii/2M02 for both Co and Mn since the +4 cations have smaller radii than the +2 cations. Again, site-occupancy predictions based on Pauling s first rule run contrary to the results calculated from first principles. 

E4.13 According to Pauling s first rule for predicting the p/C, of a mononuclear oxoacid, pAT, w 8 - 5p (where p is the number of oxo groups attached to the central element). 

Pauling s first rule states that a coordinated polyhedron of anions is formed about each cation, the cation-anion distance being determined by the radius sum and the ligancy of the cation by the radius ratio. 

In general, it is true that successive p values increase (Pauling s first rule). For example, for a diprotic acid, H2A, the two equilibria are... 

It has been found that the most influential factors for ternary compound formation are Z,/(Rj+R ) and R /Rj in this type of systems. Larger zy(R +R ) and larger R /Rj correspond to ternary intermediate compound formation. This fact can be explained as follows According to Pauling s first rule of the crystal structure of complex ionic... 

It can be found that most of the systems without 1 1 compound formation have the radius ratio (Rj/Rx) 0.414. This fact can be explained by Pauling s first rule about the structure of complex ionic crystalline compounds (Rb/Rx) 0.414 means the BXg octahedron unstable, while BXe octahedron is one of the basic parts of perovskite structure. Therefore compounds ABX3 with (Ri/Rx) 0.414 can not form stable perovskite-type lattice, even if the value of tolerance factor t is in the favorable range for perovskite formation. 

Figures 1.4(a) and 1.4(b) show parts of the baddeleyite-type structure of zirconium dioxide ZrO. This structure belongs to the monoclinic space group P2i/c and has a distorted fluorite-type structure. The coordination number (CN) of the Zr cations is seven, which is smaller than that of the fluorite-type oxide (CN = 8). This smaller value (CN = 7) is attributable to the smaller size of Zr cations ( (Zr + s) = 0.84 A) compared to the criterion deduced from Pauling s first rule (r( >8) 1.079 A) for A cations with a CN of eight...

The ionic bond, like the metallic bond, is nondirectional and favors larger coordination numbers than directionally bonded covalent compoimds. The coordination number, however, is limited by Pauling s first rule of ionic crystal formation which requires every ion to be surroimded by a polyhedron of counterions and the stability of the system requires the ion to be in direct contact with each counterion. These requirements establish the allowable coordination number (number of nearest neighbors) based on the ratio of cation/anion size. Since the negatively charged anions have received electrons from the cations, they tend to be the larger of the two. 

Pauling s first rule relates to successive dissociation constants of a polybasic acid. From simple electrostatic considerations, it is easy to predict that successive ionization steps will take place less readily (for example, you might argue that it is easier to lose a proton from a neutral species like H3PO4 than from one, such as H2P04, that already carries a negative charge). The value of the rule is that it allows us to quantify the relationships between successive dissociation constants. 

Use Pauling s first rule to predict (approximately) the dissociation constants for each step in the dissociation of polybasic acids. (Questions 11.5, 11.8 and 12.2)... 

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