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In a crystalline compound atom A occupy ccp lattices while atoms B occupy

2/3rd tetrahedral voids. Determine formula of the compound.​

User Cartman
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2 Answers

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Final answer:

The crystalline compound where atom A forms a ccp lattice and atom B occupies 2/3rd of the tetrahedral voids has the empirical formula A4B5, based on the consideration that there are twice as many tetrahedral voids as atoms in a ccp lattice and 2/3 of those are occupied by B atoms.

Step-by-step explanation:

To determine the formula of a crystalline compound where atom A occupies the face-centered cubic (ccp) lattice positions and atom B occupies 2/3rd of the tetrahedral voids, we first need to understand the fundamental aspects of ccp lattices and the tetrahedral holes within them. In a ccp lattice, there are 4 atoms per unit cell (considering there's one atom at each corner of the cube and they are shared by 8 other cubes, so ⅛ each, and six half atoms from the face centers).

Since each atom forms 8 tetrahedral voids in ccp, the number of tetrahedral voids is twice the number of atoms in the ccp lattice. With atom A forming the ccp lattice, we have 4 A atoms, leading to 8 tetrahedral voids. If atom B fills 2/3 of these tetrahedral voids, this means 2/3 * 8 = 16/3, which simplifies to approximately 5.33 voids are filled by B. Therefore, for every 4 atoms of A there are about 5.33 atoms of B. By approximation, this ratio is 4:5.33, which requires us to find the smallest whole number ratio, leading us to conclude the empirical formula of the compound is A4B5.

User StevenOjo
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2 votes

Final answer:

The formula of the compound where atom A occupies the CCP lattice and atom B fills 2/3 of the tetrahedral voids is AB4.

Step-by-step explanation:

The question revolves around determining the formula of a compound where atom A occupies a face-centered cubic (CCP) lattice and atom B fills 2/3 of the available tetrahedral voids. In a CCP structure, there are four atoms per unit cell. Since the CCP structure has two tetrahedral voids for each atom, there would be a total of 8 tetrahedral voids per unit cell (2 voids per atom in CCP × 4 atoms per CCP unit cell). If atom B occupies 2/3 of these tetrahedral voids, then the number of B atoms per unit cell equals 2/3 × 8, which is approximately 5.33.

Therefore, for everyone A atom, there are 5.33/4 or approximately 1.33 B atoms. Simplifying the ratio of A to B atoms to the smallest whole numbers gives us the empirical formula AB4 since 1.33 × 3 is approximately 4. Thus, the formula of the compound is AB4.