Import Question JSON

Current Question (ID: 21435)

Question:

$\text{The elevation in boiling point for 1 molal solution of a non-volatile solute A is 3 K. The depression in the freezing point for 2 molal solutions of A in the same solvent is 6 K. The ratio of } K_b \text{ and } K_f \text{ i.e., } K_b/K_f \text{ is } 1 : X. \text{ The value of } X \text{ is:}$

Options:

1. $7$
2. $3$
3. $1$
4. $2$

Solution:

$\text{Hint: } \Delta T_b = K_b m$ $\text{Molality of a solution of non volatile solute } (A) = 1$ $\text{Elevation in boiling point is given by}$ $\Delta T_b = K_b m$ $3 = K_b \times 1 \quad \cdots (1)$ $\text{Molality of } (A) \text{ in the same solvent } = 2$ $\text{Depression in freezing point is given by}$ $\Delta T_f = K_f m$ $6 = K_f \times 2 \quad \cdots (2)$ $\text{Dividing } (1) \text{ by } (2)$ $\frac{K_b}{K_f} = \frac{1}{X} = \frac{1}{1}$ $\therefore \quad X = 1$

Import JSON File

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
}