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Current Question (ID: 21405)

Question:

$\text{Molal depression constant for a solvent is } 4.0 \text{ K kg mol}^{-1} . \text{ The depression in the freezing point of the solvent for } 0.03 \text{ mol kg}^{-1} \text{ solution of } \text{K}_2\text{SO}_4 \text{ is: (Assume complete dissociation of the electrolyte)}$

Options:

1. $0.36 \text{ K}$
2. $0.18 \text{ K}$
3. $0.12 \text{ K}$
4. $0.24 \text{ K}$

Solution:

$\text{Hint: Formula is } \Delta T_f = iK_fm$ $\text{Step 1:}$ $\text{The formula for depression in the freezing point is as follows:}$ $\Delta T_f = iK_fm$ $\text{The given values are as follows:}$ $K_f = 4.0 \text{ K kg mol}^{-1}$ $m = 0.03 \text{ mol kg}^{-1}$ $\text{The } \text{K}_2\text{SO}_4 \text{ is a strong electrolyte hence it will fully dissociate in the solution}$ $\text{K}_2\text{SO}_4 \rightarrow 2\text{K}^+ + \text{SO}_4^{2-}$ $\text{Hence, } i \text{ is } 3.$ $\text{Step 2:}$ $\text{Calculate the value of depression in the freezing point as follows:}$ $= 4 \times 0.03 \times 3$ $= 0.36$ $\text{Thus, } \Delta T_f \text{ is } 0.36 \text{ K}$

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Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

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
}