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Current Question (ID: 18765)

Question:

$\text{The crystal field stabilization energies (CFSE) of high spin and low spin } d^6 \text{ metal complexes in terms of } \Delta_0, \text{ respectively, are:}$

Options:

1. $-0.4 \text{ and } -2.4$
2. $-2.4 \text{ and } -0.4$
3. $-0.4 \text{ and } 0.0$
4. $-2.4 \text{ and } 0.0$

Solution:

$\text{HINT: CFSE for } d^6 \text{ low spin complex is } -2.4 \Delta_0$ $\text{Explanation:}$ $\text{STEP 1: Configuration of } d^6 \text{ in high spin is:}$ $d^2_{xy}d^1_{yz}d^1_{xz} \ (t_{2g}) \ d^1_{z^2}d^1_{x^2-y^2} \ (eg)$ $CFSE = (-0.4 \times 4 + 0.6 \times 2) \Delta_0 = -0.4 \Delta_0$ $\text{STEP 2: Configuration of } d^6 \text{ in low spin is:}$ $d^2_{xy}d^2_{yz}d^2_{xz} \ (t_{2g}) \ d^0_{z^2}d^0_{x^2-y^2} \ (eg)$ $CFSE = (-0.4 \times 6 + 0.6 \times 0) \Delta_0 = -2.4 \Delta_0$

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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
}