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Current Question (ID: 17931)

Question:

$\text{The formula of nickel oxide with metal deficiency defect in its crystal is } \text{Ni}_{0.98}\text{O}. \text{ The crystal contains } \text{Ni}^{2+} \text{ and } \text{Ni}^{3+} \text{ ions. The fraction of nickel existing as } \text{Ni}^{2+} \text{ ions in the crystal is-}$

Options:

1. $0.96$
2. $0.04$
3. $0.50$
4. $0.31$

Solution:

$\text{HINT: } \text{Ni}_{0.98}\text{O is neutral so balance the charge.}$ $\text{STEP 1:}$ $\text{Let } \text{Ni}^{+2} \text{ in the crystal } \text{Ni}_{0.98}\text{O be } x$ $\text{Therefore } \text{Ni}^{+3} \text{ in the crystal } \text{Ni}_{0.98} \text{ will be } (0.98-x):$ $\text{Ni}_x^{+2} \text{Ni}_{(0.98-x)}^{+3}\text{O}$ $\text{STEP 2:}$ $\text{By law of conservation of charge -}$ $2x + 3 \times (0.98-x) - 2 = 0$ $x = 0.94$ $\text{STEP 3:}$ $\text{So the fraction of } \text{Ni}^{+2} \text{ ions in the crystal } = \frac{0.94}{0.98} \approx 0.96$

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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
}