Import Question JSON

Current Question (ID: 21428)

Question:

$\text{If 25 mL of KCl solution requires 20 mL of 1 M AgNO}_3 \text{ solution for complete precipitation of KCl solution. The value of } \Delta T_f \text{ of a KCl solution (} i = 2 \text{) is:}$ $\left( K_f = 1.86 \text{ K} \cdot \text{kg mol}^{-1}. \text{ Assume molarity = molality} \right)$ $\text{(Round off to nearest integer)}$

Options:

1. $5 \text{ K}$
2. $3 \text{ K}$
3. $6 \text{ K}$
4. $1 \text{ K}$

Solution:

$\Delta T_f = i K_f m$ $\Delta T_f = 2 \times 1.86 \times m \quad \text{(Eq - 1)}$ $\text{Let's find } m$ $\text{KCl} + \text{AgNO}_3 \rightarrow \text{KNO}_3 + \text{AgCl} \downarrow$ $\text{From law of chemical equivalence milliequivalents of KCl react with AgNO}_3$ $\left( M \times nf \times V \right)_{\text{KCl}} = \left( M \times nf \times V \right)_{\text{AgNO}_3}$ $M \times 1 \times 25 = 1 \times 1 \times 20$ $M = \frac{20}{25} = \frac{4}{5}$ $\text{Step 3:}$ $\text{Given, molarity = molality}$ $\text{Therefore, molality = } \frac{4}{5} m$ $\text{Putting value of molality in (Eq - 1)}$ $\Delta T_f = 2 \times 1.86 \times \frac{4}{5} \approx 3$ $\text{Thus, option 2 is the correct answer.}$

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
}