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8.8: Coordination Number

  • Page ID
    53736
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    Anhydrous and hydrated cobalt chloride have very different colors
    Figure \(\PageIndex{1}\) (Public Domain; Martin Walker (Wikimedia: Walkerma) via Anhydrous: http://commons.wikimedia.org/wiki/File:Cobalt%2528II%2529_chloride.jpg; Hydrated: http://commons.wikimedia.org/wiki/File:Cobalt%2528II%2529_chloride_hexahydrate.jpg)

    What makes the colors different?

    Cobalt salts contain \(\ce{Co^{2+}}\) cations. Differences in the color of the salts is due to the species surrounding the cobalt ion. The presence of water molecules in the coordination sphere around the central cobalt ion changes the distances among species and the color of the material.

    Coordination Number

    The coordination number is the number of ions that immediately surround an ion of the opposite charge within a crystal lattice. If you examine the figure below, you will see that there are six chloride ions immediately surrounding a single sodium ion. The coordination number of sodium is 6. Likewise, six sodium ions immediately surround each chloride ion, making the coordination number of chloride also equal to 6. Because the formula unit of sodium chloride displays a 1:1 ratio between the ions, the coordination numbers must be the same.

    Diagram of a cubic crystal lattice with green and blue spheres connected by red lines, representing atoms and bonds.
    Figure \(\PageIndex{2}\): Lattice structure for sodium chloride. The blue balls represent the sodium ions and the green balls represent the chloride ions. (Public Domain; User:Eloy/Wikimedia Commons via Wikipedia)

    The formula unit for cesium chloride is \(\ce{CsCl}\), also a 1:1 ratio. However, as shown in the figure below, the coordination numbers are not 6 as in \(\ce{NaCl}\). The center ion is the \(\ce{Cs^+}\) ion and is surrounded by the eight \(\ce{Cl^-}\) ions at the corners of the cube. Each \(\ce{Cl^-}\) ion is also surrounded by eight \(\ce{Cs^+}\) ions. The coordination numbers in this type of crystal are both 8. \(\ce{CsCl}\) and \(\ce{NaCl}\) do not adopt identical crystal packing arrangements because the \(\ce{Cs^+}\) is considerably larger than the \(\ce{Na^+}\) ion.

    A 3D geometric diagram showing a cubic crystal structure with green spheres at the corners and an orange sphere in the center, connected by rods.
    Figure \(\PageIndex{3}\): In a cesium chloride crystal, the cesium ion (orange) occupies the center, while the chloride ions (green) occupy each corner of the cube. The coordination number for both ions is 8. (CC BY-NC-SA 3.0; Christopher Auyeung via CK-12 Foundation)

    Another type of crystal is illustrated by titanium (IV) oxide, \(\ce{TiO_2}\), which is commonly known as rutile. The rutile crystal is shown below.

    3D model of a chemical compound with red and gray spheres connected by rods, forming a geometric structure.
    Figure \(\PageIndex{4}\): Titanium (IV) oxide forms tetragonal crystals. The coordination number of the \(\ce{Ti^{4+}}\) ions (gray) is 6, while the coordination number of the \(\ce{O^{2-}}\) ions (red) is 3. (Public Domain; Ben Mills (Wikimedia: Benjah-bmm27 via Wikipedia)

    The gray \(\ce{Ti^{4+}}\) ions are surrounded by six red \(\ce{O^{2-}}\) ions. The \(\ce{O^{2-}}\) ions are surrounded by three \(\ce{Ti^{4+}}\) ions. The coordination of the titanium (IV) cation is 6, which is twice the coordination number of the oxide anion, which is 3. This fits with the formula unit of \(\ce{TiO_2}\), since there are twice as many \(\ce{O^{2-}}\) ions as \(\ce{Ti^{4+}}\) ions.

    The crystal structure of all ionic compounds must reflect the formula unit. In a crystal of iron (III) chloride, \(\ce{FeCl_3}\), there are three times as many chloride ions as iron (III) ions.

    A 3D molecular structure with repeating green and purple spheres, arranged in a grid pattern, representing the crystal lattice of sodium chloride (NaCl).
    Figure \(\PageIndex{5}\): Iron (III) chloride. The bluish-gray \(\ce{Fe^{3+}}\) ions are surrounded by green \(\ce{Cl^-}\) ions. (CK-12 Foundation)

    Summary

    • The coordination number of a compound is determined by the type and number of ions or other species surrounding a central ion.
    • Often the color of a compound is affected by the specific materials coordinated to that central ion.

    Review

    1. What is the coordination number for Na+ in NaCl?
    2. What is the coordination number for Cs+?
    3. Why are the packing arrangements for Na+ and Cs+ different?

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