MHT CET · Chemistry · Solid State

In an ionic crystalline solid, atoms of element \(Y\) forms hep structure. The atoms of element \(X\) occupy one third of tetrahedral voids. What is the formula of compound?

A \(\mathrm{X}_2 \mathrm{Y}_3\)
B \(X Y\)
C \(\mathrm{X}_3 \mathrm{Y}_3\)
D \(\mathrm{XY}_2\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\mathrm{X}_2 \mathrm{Y}_3\)

Step-by-step Solution

Detailed explanation

The atoms of element \(\mathrm{Y}\) form hcp structure. The number of tetrahedral voids generated is twice the number of \(\mathrm{Y}\) atoms. Thus, number of tetrahedral voids \(=2 \mathrm{Y}\) The atoms of element \(X\) occupy (1/3) of these tetrahedral voids.
Hence, number of \(\mathrm{X}\) atoms \(=2 \mathrm{Y} \times 1 / 3=2 / 3 \mathrm{Y}\) Ratio of \(\mathrm{X}\) and \(\mathrm{Y}\) atoms \(=2 / 3 \mathrm{Y}: 1 \mathrm{Y}\) \(=2 / 3: 1=2: 3\)
\(\therefore \quad\) Formula of compound \(=\mathrm{X}_2 \mathrm{Y}_3\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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