Two ions X⁺ and Y^- have the ionic radius 88 pm and 200 pm respectively. In the close packed crystal of compound XY, predict the coordination number of X⁺.

Concept:

Co-ordination number:

• The secondary valencies of a metal are satisfied by co-ordinating with primary ligands.
• The number of ligands satisfying the secondary valency is called the coordination number of the metal.
• The total number of points of attachment to the central element is termed as co-ordination number and this can vary from 2 to 16.

Radius ratio:

• The arrangement of atoms in a crystal system creates vacant spaces in between them known as voids.
• The voids are of two types:
  • Tetrahedral
  • Octahedral

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• The layers are placed alternately, the second layer is placed in the depression of the first layer.
• The "T" represents a tetrahedral void.
• The size of the hole or void is very small compared to the actual size of the molecules.
• The other type of voids formed is tetrahedral voids when the third layer is built the same as the first layer.
• They are indicated as "O", octahedral voids.

• The voids created by anions can accommodate cations in them.
• The ratio of the two ions, cation to the anion is known as radius ratio.
• The ratio is different for different co-ordination numbers.
• The cation to anion ratio of different co-ordination number is shown in the following table:

Given:

• The ionic radius of X+ =  88 pm
• The ionic radius of Y- = 200 pm

Hence, radius ratio =

\(\frac{{{r_ + }}}{{{r_ - }}} = \frac{{88}}{{200}}=.44\)

The radius ratio falls in the range 0.414 – 0.732 which predicts a co-ordination number 6.

Hence, the coordination number of X+ in the crystal system XY is 6.

Additional Information

• The crystal system XY is a NaCl type of crystal that has octahedral voids.