An ionic compound made up of ions A+ and B- has face-centered arrangement in which ions A+ are at the corners and ions B- are at the face centers, if one of the ions is missing from the corner. What is the simplest formula of the compound?

An ionic compound made up of ions A+ and B has face-centered arrangement in which ions A+ are at the corners and ions B are at the face centers, if one of the ions is missing from the corner. What is the simplest formula of the compound?

Answer:

Count the number of ions of element ‘A’ in the FCC arrangement:

Part of ion ‘A’ on corner = 1/8

Number of corners on which ion ‘A’ is present = 8 − 1 = 7

Total number of ion ‘A’ on FCC corners = 1/8 × 7 = 7/8 atom

Count the number of ions of element ‘B’ in the FCC arrangement:

Part of ion ‘B’ on face center = 1/2

Total faces = 6

Total number of atom ‘B’ on cube face centers = 1/2 × 6 = 3 atoms

Hence, the simplest formula of compound is A7/8 B3 or A7 B24

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