Import Question JSON

Current Question (ID: 18357)

Question:

$\text{A first-order reaction takes 40 min for 30 \% decomposition. The } t_{1/2} \text{ for this reaction will be:}$

Options:

1. $77.7 \text{ min}$
2. $27.2 \text{ min}$
3. $55.3 \text{ min}$
4. $67.3 \text{ min}$

Solution:

$\text{HINT: } t_{1/2} = \frac{0.693}{k}$ $\text{Explanation:}$ $\text{Extent of reaction = 30\%}$ $\text{Time taken = 40 min}$ $\text{For a first order reaction,}$ $t = \frac{2.303}{k} \log \frac{a}{a-x} = \frac{2.303}{k} \log \frac{1}{1-(x/a)}$ $40 \text{ min} = \frac{2.303}{k} \log \left( \frac{1}{1-0.3} \right)$ $\text{or } k = \frac{2.303}{40} \log 1.428 = 8.92 \times 10^{-3} \text{ min}^{-1}$ $\text{we know, for a first order reaction, } t_{1/2} = \frac{2.303}{k} \log 2$ $\text{then, } t_{1/2} = \frac{2.303}{8.92 \times 10^{-3}} \log 2 = 77.7 \text{ min.}$

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
}