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Current Question (ID: 20787)

Question:

$\text{The molecular formula of a commercial resin used for exchanging ions in water softening is } \text{C}_8\text{H}_7\text{SO}_3\text{Na} \text{ (Mol. Wt. 206).}$ $\text{The maximum uptake of } \text{Ca}^{2+} \text{ ions by the resin when expressed in mole per gram resin is:}$ $\text{C}_8\text{H}_7\text{SO}_3\text{Na} + \text{Ca}^{2+} \rightarrow (\text{C}_8\text{H}_7\text{SO}_3)_2\text{Ca} + \text{Na}^+$

Options:

1. $\frac{1}{103}$
2. $\frac{1}{206}$
3. $\frac{2}{309}$
4. $\frac{1}{412}$

Solution:

$\text{Hint: 1 mole of resin reacts with 1 mole of } \text{Ca}^{2+}$ $2\text{C}_8\text{H}_7\text{SO}_3\text{Na} + \text{Ca}^{2+} \rightarrow (\text{C}_8\text{H}_7\text{SO}_3)_2\text{Ca} + 2\text{Na}^+$ $\therefore \text{ from stoichiometry of the reaction}$ $2 \text{ mole i.e. } (206 \times 2) \text{g of } \text{C}_8\text{H}_7\text{SO}_3\text{Na (resin)}$ $\text{i.e. 412 g of resin exchanges 1 mole of } \text{Ca}^{2+}$ $\therefore 1\text{g of resin exchanges } \frac{1}{412} \text{ mole of } \text{Ca}^{2+}$ $\text{So, maximum uptake of } \text{Ca}^{2+} \text{ ions by the resin is } \frac{1}{412}$

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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
}