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Current Question (ID: 17940)

Question:

$\text{In a compound, atoms of element Y form ccp lattice, and those of element X occupy } \frac{2}{3} \text{rd of tetrahedral voids. The formula of the compound will be :-}$

Options:

1. $\text{X}_3\text{Y}_4$
2. $\text{X}_4\text{Y}_3$
3. $\text{X}_2\text{Y}_3$
4. $\text{X}_2\text{Y}$

Solution:

$\text{Number of tetrahedral voids} = 2 \times \text{Number of spheres in ccp lattice.}$ $\text{In a cubic close packing, let the number of spheres be } n. \text{ Then the number of tetrahedral voids will be } 2n.$ $\text{Y atom occupies the CCP lattice, hence the effective number of Y atoms} = 4$ $\text{The number of tetrahedral voids generated in any unit cell} = 2n = 2 \times 4 = 8$ $\text{X occupies } \frac{2}{3} \text{rd of tetrahedral voids.}$ $\text{Therefore the effective number of X} = \frac{2}{3} \times 8 = \frac{16}{3}$ $\text{Therefore the ratio of X:Y from the calculation is } \frac{16}{3} : 4$ $\text{Converting the ratio into simplest integer, we get } X:Y = 4:3$ $\text{Hence the formula of the compound will be } \text{X}_4\text{Y}_3$

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Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}