Import Question JSON

Current Question (ID: 18345)

Question:

$\text{A first-order reaction was started with a decimolar solution of the reactant.}$ $\text{After 8 minutes and 20 seconds, its concentration was found to be } M/100. \text{ The}$ $\text{rate constant of the reaction will be:}$

Options:

1. $4.6 \times 10^{-3} \text{ sec}^{-1}$
2. $16.6 \times 10^{-3} \text{ sec}^{-1}$
3. $24.6 \times 10^{-3} \text{ sec}^{-1}$
4. $40.6 \times 10^{-3} \text{ sec}^{-1}$

Solution:

$\text{Here } a = 0.1 \text{ M}$ $a - x = \frac{M}{100} = 0.01 \text{ M}$ $t = 8 \text{ minutes } 20 \text{ seconds} = 500 \text{ seconds}$ $\text{Substituting the values in the first-order reaction}$ $k = \frac{2.303}{t} \log \frac{a}{a-x}$ $= \frac{2.303}{500} \log \frac{0.1}{0.01} = \frac{2.303}{500} \log 10$ $= \frac{2.303}{500} \times 1 = 4.6 \times 10^{-3} \text{ sec}^{-1}$

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
}