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Current Question (ID: 21395)

Question:

$1$ $\text{molal aqueous solution of an electrolyte } \text{A}_2\text{B}_3 \text{ is } 60\% \text{ ionised.}$ $\text{The boiling point of the solution at } 1 \text{ atm is-. (Rounded-off to the nearest integer)}$ $\text{[Given } K_b \text{ for (H}_2\text{O)} = 0.52 \text{ K kg mol}^{-1}]$

Options:

1. $373 \text{ K}$
2. $380 \text{ K}$
3. $375 \text{ K}$
4. $377 \text{ K}$

Solution:

$\text{Hint: Use the formula } \Delta T_b = i K_b m$ $\text{Step 1:}$ $\text{First, calculate the value of } i \text{ using alpha value, that is } 60\%. $ $\text{The relation between } i \text{ and } \alpha \text{ for } \text{A}_2\text{B}_3 \text{ is as follows:}$ $\text{A}_2\text{B}_3 \leftrightarrow 2\text{A}^{3+} + 3\text{B}^{2-}$ $\frac{1}{1-\alpha} \quad \quad 2\alpha \quad \quad 3\alpha$ $i = \frac{1 - \alpha + 2\alpha + 3\alpha}{1}$ $i = 1 + 4 \times \frac{60}{100}$ $i = 3.4$ $\text{Step 2:}$ $\text{Calculate the boiling point of the solution}$ $\Delta T_b = i K_b m$ $T_b - T_b^0 = 3.4 \times 0.52 \times 1$ $T_b - 373 = 3.4 \times 0.52 \times 1$ $T_b = 1.768 + 373$ $T_b = 1.768 + 373 = 374.918 \text{ K} = 375 \text{ K}$ $\text{Hence, option third is the correct answer.}$

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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
}