Import Question JSON

Current Question (ID: 18364)

Question:

$\text{For a first-order reaction A} \rightarrow \text{Products, the rate of reaction at [A] = 0.2 M is } 1.0 \times 10^{-2} \text{ mol litre}^{-1} \text{ min}^{-1}. \text{ The half-life period for the reaction will be:}$

Options:

1. $832 \text{ sec}$
2. $440 \text{ sec}$
3. $416 \text{ sec}$
4. $14 \text{ sec}$

Solution:

$\text{HINT: For first order reaction, } t_{1/2} = \frac{0.693}{K}$ $\text{Explanation:}$ $r = K[A]$ $K = \frac{10^{-2}}{0.2} = 5 \times 10^{-2}$ $\text{Now, } t_{1/2} = \frac{0.693}{K} = \frac{0.693}{5} \times 10^{-2}$ $t_{1/2} = 13.86 \text{ min} = 832 \text{ sec.}$

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
}