Import Question JSON

Current Question (ID: 18113)

Question:

$\text{A 5 \% solution (by mass) of cane sugar in water has freezing point of 271 K.}$ $\text{Freezing point of 5 \% glucose in water would be: (freezing point of pure water is 273.15 K)}$

Options:

1. $279.24 \text{ K}$
2. $-269.06 \text{ K}$
3. $275.42 \degree \text{C}$
4. $269.06 \text{ K}$

Solution:

$\text{HINT: Use formula for depression in freezing point.}$ $\Delta T_f = (273.15 - 271) \text{ K} = 2.15 \text{ K}$ $\text{5\% solution (by mass) of cane sugar in water means 5 g of cane sugar is present in (100 - 5) g = 95 g of water.}$ $\text{Number of moles of cane sugar} = \frac{5}{342} \text{ mol} = 0.0146 \text{ mol}$ $\text{Therefore, molality of solution, m} = \frac{0.0146 \text{ mol}}{0.095 \text{ kg}} = 0.1537 \text{ mol kg}^{-1}$ $\text{Applying the relation,}$ $273.15 - 271 = k_f \times 0.1537 \quad \text{(1)}$ $\text{For glucose,}$ $273.15 - X = k_f \times 0.2926 \quad \text{(2)}$ $\frac{2.15}{273.15 - X} = \frac{k_f \times 0.1537}{k_f \times 0.2926}$ $0.629 = 41.98 - 0.1537X$ $41.351 = 0.1537X$ $X = 269.06 \text{ K}$ $\text{Freezing point of 5\% glucose in water is 269.06 K}$

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
}