Import Question JSON

Current Question (ID: 21061)

Question:

$\text{The solubility of Ca(OH)}_2 \text{ in water is:}$ $\text{[Given: } K_{sp} \text{ Ca(OH)}_2 \text{ in water = } 5.5 \times 10^{-6}\text{]}$

Options:

1. $1.77 \times 10^{-6}$
2. $1.11 \times 10^{-6}$
3. $1.11 \times 10^{-2}$
4. $2.77 \times 10^{-2}$

Solution:

$\text{Hint: The solubility product of Ca(OH)}_2 \text{ is } K_{sp} = [\text{Ca}^{2+}][\text{OH}^-]^2$ $\text{STEP 1: The reaction is as follows:}$ $\text{Ca(OH)}_2 \rightarrow \text{Ca}^{2+} + 2\text{OH}^-$ $K_{sp} = [\text{Ca}^{2+}][\text{OH}^-]^2$ $\text{STEP 2: If } s \text{ is the solubility. Then,}$ $K_{sp} = s(2s)^2 = 4s^3$ $5.5 \times 10^{-6} = (4s)^3$ $\left( \frac{5.5 \times 10^{-6}}{4} \right)^{1/3} = (s)$ $\text{or } s = 1.11 \times 10^{-2}$ $\text{Thus, option 3 is the correct answer.}$

Import JSON File

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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
}