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Current Question (ID: 18208)

Question:

$\text{The specific conductivity of a saturated solution of KI}_3 \text{ is } 4.59 \times 10^{-6} \text{ ohm}^{-1} \text{ cm}^{-1}$ $\text{and its molar conductance is } 1.53 \text{ ohm}^{-1} \text{ cm}^2 \text{ mol}^{-1}. \text{ The } K_{\text{sp}} \text{ of KI}_3 \text{ will be:}$

Options:

1. $4 \times 10^{-12}$
2. $27 \times 27 \times 10^{-9}$
3. $9 \times 10^{-6}$
4. $4 \times 10^{-6}$

Solution:

$\text{HINT: } K_{\text{sp}} = [\text{K}^+][\text{I}_3^-]$ $\text{Step 1:}$ $\text{Calculate the value of concentration using the molar conductivity formula}$ $\Lambda = \frac{\kappa \times 1000}{\text{M}}$ $1.53 = \frac{4.56 \times 10^{-6} \times 1000}{\text{M}}$ $\text{M} = \frac{4.56 \times 10^{-6} \times 1000}{1.53}$ $\text{M} = 3.0 \times 10^{-3} \text{ M}$ $\text{Step 2:}$ $\text{Calculate the value of } K_{\text{sp}} \text{ as follows:}$ $\text{KI}_3 \rightarrow \text{K}^+ + \text{I}_3^-$ $K_{\text{sp}} = [\text{K}^+][\text{I}_3^-]$ $K_{\text{sp}} = (3 \times 10^{-3})^2$ $K_{\text{sp}} = 9 \times 10^{-6}$

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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
}