A crystal is made up of metal ions 'M1' and 'M2' and oxide ions. Oxide ions form a ccp lattice structure. The cation 'M1' occupies 50% of octahedral voids and the cation 'M2' occupies 12.5% of tetrahedral voids of oxide lattice. The oxidation numbers of 'M1' and 'M2' are, respectively :
Solution
O<sup>–2</sup> ions form ccp $\Rightarrow$ O<sub>4</sub>.
<br><br>M<sub>1</sub> = 50% octahedral void = ${{50} \over {100}} \times 4$ = 2
<br><br>M<sub>2</sub> = 12.5% tetrahedral void = ${{12.5} \over {100}} \times 8$ = 1
<br><br>So formula is : (M<sub>1</sub>)<sub>2</sub>(M<sub>2</sub>)<sub>1</sub>O<sub>4</sub>
<br><br>Let charge on M<sub>1</sub> and M<sub>2</sub> are +x and +y respectively. And O<sub>4</sub> has -8 charge.
<br><br>As crystal is neutral. So metals must have +8
charge in total.
<br><br>$\therefore$ +2x + y = 8 ....(1)
<br><br>By checking options we found eq (1) satisfy when
<br>x = +2
<br>y = +4
About this question
Subject: Chemistry · Chapter: States of Matter · Topic: Gas Laws
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