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Q.

In a crystalline solid, anions B are arranged in a cubic close packing. Cations A are equally distributed between octahedral and tetrahedral voids. If all the octahedral voids are occupied, what is the formula of the solid ?

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a

A2B

b

AB

c

A3B

d

A3B2

answer is B.

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Detailed Solution

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  • Suppose the number of anions B = n. 
  • Then number of octahedral voids = n. 
  • Number of tetrahedral voids = 2n. 
  • As octahedral and tetrahedral voids are equally occupied by cations A and all the octahedral voids are occupied (given) therefore, n cations A are present in octahedral voids and n cations A are present in tetrahedral voids. 
  • In other words, corresponding to n anions B, there are n +n = 2n cations A. 
  • Thus, A and anions B are in the ratio 2n: n =2: 1 hence, the formula of the solid will be A2B.
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