MHT CET · Chemistry · Solid State
A compound is formed by two elements \(A\) and
B. The atoms of element B form ccp structure.
The atoms of A occupy \(\frac{1}{3}\) of tetrahedral voids.
What is the formula of the compound?
- A \(\mathrm{A}_2 \mathrm{~B}_3\)
- B AB
- C \(\mathrm{AB}_2\)
- D \(\quad \mathrm{AB}_3\)
Answer & Solution
Correct Answer
(A) \(\mathrm{A}_2 \mathrm{~B}_3\)
Step-by-step Solution
Detailed explanation
The atoms of element B form ccp structure. The number of tetrahedral voids generated is twice the number of B atoms. Thus, number of tetrahedral voids \(=2 \mathrm{~B}\)
\(\text {The atoms of element } A \text { occupy }(1 / 3) \text { of these } \)
\( \text {tetrahedral voids. } \)
\( \text {Hence, number of } A \text { atoms }=2 B \times 1 / 3\) \(=2 / 3 B \)
\( \text {Ratio of } A \text { and } B \text { atoms }=2 / 3 \mathrm{~B}: 1 \mathrm{~B} \)
\( =2 / 3: 1=2: 3 \)
\( \therefore \text {Formula of compound }=\mathrm{A}_2 \mathrm{~B}_3\)
\(\text {The atoms of element } A \text { occupy }(1 / 3) \text { of these } \)
\( \text {tetrahedral voids. } \)
\( \text {Hence, number of } A \text { atoms }=2 B \times 1 / 3\) \(=2 / 3 B \)
\( \text {Ratio of } A \text { and } B \text { atoms }=2 / 3 \mathrm{~B}: 1 \mathrm{~B} \)
\( =2 / 3: 1=2: 3 \)
\( \therefore \text {Formula of compound }=\mathrm{A}_2 \mathrm{~B}_3\)
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