Import Question JSON

Current Question (ID: 21501)

Question:

$\text{The half-life period of a first-order chemical reaction is 6.93 minutes.}$ $\text{The time required for the completion}$ $\text{of 99\% of the chemical reaction will be (log 2 = 0.301) -}$

Options:

1. $230.3 \text{ minutes}$
2. $23.03 \text{ minutes}$
3. $46.06 \text{ minutes}$
4. $460.6 \text{ minutes}$

Solution:

$\text{Hint: } k = \frac{2.303}{t} \log \left[ \frac{[A]_0}{[A]} \right]$ $\text{Step 1:}$ $\text{Calculate the value of } k \text{ (rate constant) as follows:}$ $t_{1/2} = \frac{0.693}{k}$ $k = \frac{0.693}{6.93}$ $k = 0.1 \text{ min}^{-1}$ $\text{Step 2:}$ $\text{Calculate the time at which 99\% reaction is completed as follows:}$ $k = \frac{2.303}{t} \log \left[ \frac{[A]_0}{[A]} \right]$ $0.1 = \frac{2.303}{t} \log \left[ \frac{100}{1} \right]$ $t = 46.06 \text{ minutes}$

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
}