Which of the following structural descriptions is/are...

Which of the following structural descriptions is/are inconsistent with the stoichiometry of the salt being described? 22.1 $\mathrm{CdCl}_2$ adopts a hep lattice of chloride ions in which all the octahedral holes are occupied by cadmium ions. $22.2 \mathrm{CdCl}_2$ adopts a ccp lattice of chloride ions in which half of the octahedral holes are occupied by cadmium ions. 22.3 $\mathrm{Li}_2 \mathrm{SO}_4$ adopts a hep lattice of sulfate ions in which all the tetrahedral holes are occupied by lithium ions. $22.4\left(\mathrm{CH}_3\right)_4 \mathrm{NF}$ adopts a cep lattice of tetramethylammonium ions in which all the octahedral holes are occupied by fluoride ions.

Which of the following structural descriptions is/are inconsistent with the stoichiometry of the salt being described?
22.1 $\mathrm{CdCl}_2$ adopts a hep lattice of chloride ions in which all the octahedral holes are occupied by cadmium ions.
$22.2 \mathrm{CdCl}_2$ adopts a ccp lattice of chloride ions in which half of the octahedral holes are occupied by cadmium ions.
22.3 $\mathrm{Li}_2 \mathrm{SO}_4$ adopts a hep lattice of sulfate ions in which all the tetrahedral holes are occupied by lithium ions.
$22.4\left(\mathrm{CH}_3\right)_4 \mathrm{NF}$ adopts a cep lattice of tetramethylammonium ions in which all the octahedral holes are occupied by fluoride ions.

Key Concepts

Ionic Stoichiometry

Ionic stoichiometry is the fundamental principle that ensures the ratio of cations to anions in a compound matches its chemical formula. It requires that the number of ions occupying the lattice sites accounts for the charges and proportions specified by the empirical formula, meaning that the occupation of interstitial sites must yield numbers of ions that correctly balance to form the compound.

Close-Packed Lattices

Close-packed lattices, such as cubic close-packed (ccp) and hexagonal close-packed (hcp), describe the efficient arrangements of ions or atoms where the constituent particles are as densely packed as possible. These lattice types determine the geometry and distribution of interstitial sites like tetrahedral and octahedral holes that can be occupied by ions.

Interstitial Sites

Interstitial sites, including tetrahedral and octahedral holes present in close-packed lattices, are the gaps between the packed ions that can be occupied by smaller ions. The number and type of these sites are inherent properties of the lattice structure and have to be considered when assigning positions to different ions to maintain the overall stoichiometry.

Structure-Stoichiometry Consistency

Structure-stoichiometry consistency is the concept that the arrangement of ions within the lattice – particularly the fraction of occupied interstitial sites – must be in agreement with the compound's overall formula. This means that if a structural description indicates all or half of certain interstitial sites are filled by cations, the resulting ratio should precisely reflect the stoichiometry of the compound as determined by its formula.

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