Import Question JSON

Current Question (ID: 19625)

Question:

$\text{When } M_1 \text{ gram of ice at } -10^\circ\text{C (specific heat = 0.5 cal g}^{-1} \circ\text{C}^{-1}) \text{ is added to } M_2 \text{ gram of water at } 50^\circ\text{C,}$ $\text{It is observed that no ice is left and the water is at } 0^\circ\text{C.}$ $\text{The value of latent heat of ice, in cal g}^{-1} \text{ is:}$

Options:

1. $\frac{50M_2}{M_1} - 5$
2. $\frac{M_1}{50M_2}$
3. $\frac{5M_2}{M_1} - 5$
4. $\frac{50M_1}{M_2} - 5$

Solution:

$\text{Using energy conservation}$ $E_{\text{released by water}} = E_{\text{used by ice}}$ $M_2 S_w (\Delta T)_{\text{water}} = M_1 S_{\text{ice}} (\Delta T)_{\text{ice}} + M_1 L_{\text{fusion}}$ $M_2 (1)(50) = M_1 \left( \frac{1}{2} \right)(10) + M_1 L_{\text{fusion}}$ $L_f = \frac{50 \frac{M_2}{M_1}}{5} + 5M_1$ $L_f = \frac{50 M_2}{M_1} - 5$

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
}