Import Question JSON

Current Question (ID: 18114)

Question:

$\text{A solution of 18 g of glucose in 1000 g of water is cooled to -0.2 } ^\circ \text{C. The amount of ice separating out from this solution is -}$ $[K_f(\text{H}_2\text{O}) = 1.86 \text{ K molal}^{-1}]$

Options:

1. $70 \text{ g}$
2. $140 \text{ g}$
3. $90 \text{ g}$
4. $210 \text{ g}$

Solution:

$\text{Hint: } \Delta T = K_f \times m'$ $\text{Step 1:}$ $\text{Calculate the amount of solvent (water) as follows:}$ $\Delta T = K_f \times m'$ $m' = \frac{\Delta T}{K_f} = \frac{0.2}{1.86} = 0.1075$ $0.1075 = \frac{18}{180} \times \frac{1000}{X}$ $X = \frac{100}{0.1.75} = 930.2 \text{ g}$ $\text{Step 2:}$ $\text{Calculate the amount of ice separating out from this solution.}$ $\text{At } -0.2 ^\circ \text{C, the solution has 930.2 g of solvent (water)}$ $\therefore \text{amount of ice separated out} = 1000 - 930 = 70 \text{ g}$

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
}