Import Question JSON

Current Question (ID: 18349)

Question:

$\text{A first-order reaction takes 40 min for 30 \% decomposition. The half life of the reaction will be:}$

Options:

1. $88.8 \text{ min}$
2. $94.3 \text{ min}$
3. $67.2 \text{ min}$
4. $77.7 \text{ min}$

Solution:

$\text{HINT: Half-life of First order reaction depends only on the rate constant.}$ $\text{STEP 1: For a first order reaction,}$ $t = \frac{2.303}{K} \log \frac{[R]_0}{[R]_t} ; \text{ where } [R]_0 \text{ is the initial conc. of reactant and } [R]_t \text{ is conc. of reactant at time } t$ $K = \frac{2.303}{40 \text{ min}} \log \frac{100}{70}$ $K = 8.92 \times 10^{-3} \text{ min}^{-1}$ $\text{STEP 2: We know that,}$ $\text{Half life } ; t_{1/2} = \frac{0.693}{K}$ $t_{1/2} = \frac{0.693}{8.92 \times 10^{-3} \text{ min}^{-1}}$ $t_{1/2} = 77.7 \text{ min}$

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
}