Import Question JSON

Current Question (ID: 18353)

Question:

$\text{The thermal decomposition of a compound is of first order. If 50 \% of a sample of the compound decomposes in 120 minutes, how long will it take for 90 \% of the compound to decompose?}$

Options:

1. $399 \text{ min}$
2. $410 \text{ min}$
3. $250 \text{ min}$
4. $120 \text{ min}$

Solution:

$\text{HINT: Follow first order kinetics.}$ $K = \frac{0.6932}{120} \quad \ldots(1)$ $K = \frac{2.303}{t} \log \frac{a}{0.10a} = \frac{2.303}{t} \log 10 \quad \ldots(2)$ $\text{Equating (1) and (2)}$ $\frac{0.6932}{120} = \frac{2.303}{t}$ $t = 399 \text{ minutes}$

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
}