Import Question JSON

Current Question (ID: 10739)

Question:

$150\text{ g of ice at } 0°\text{C is mixed with } 100\text{ g of water at a temperature of } 80°\text{C. The latent heat of ice is } 80\text{ cal/g and the specific heat of water is } 1\text{ cal/g°C. Assuming no heat loss to the environment, the amount of ice that does not melt is:}$

Options:

1. $100\text{ g}$
2. $0$
3. $150\text{ g}$
4. $50\text{ g}$ (Correct)

Solution:

$\text{Hint: Heat gained by ice = Heat lost by water}$ $\text{Step 1: Assume final temperature of mixture as } 0°\text{C}$ $Q_w = mC\Delta T$ $= 100 \times 1 \times (80 - 0)$ $= 8000\text{ cal}$ $Q_w = Q_{ice}$ $8000 = mL_f$ $m = \frac{8000}{80} = 100\text{g}$ $\text{Step 2: Find mass of ice that does not melt}$ $m_{un} = 150 - 100$ $= 50\text{ ice } (0°\text{C})$

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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
}