Import Question JSON

Current Question (ID: 18366)

Question:

$\text{What is the percentage of the reactant molecules crossing over the energy barrier at 325 K?}$ $\text{Given that } \Delta H_{325} = 0.12 \text{ kcal, } E_{a(b)} = +0.02 \text{ kcal}$

Options:

1. 80.62 \%
2. 85.23 \%
3. 89.27 \%
4. \text{None of the above}

Solution:

$\text{\% of molecule crossing over the barrier} = 100 \times e^{-E_{a,f}/RT}$ $\text{Given,}$ $\Delta H_{325} = 0.12 \times 10^3 \text{ kcal,}$ $E_{a(b)} = +0.02 \times 10^3 \text{ kcal}$ $(E_a) \text{ can never be negative}$ $\Delta H = E_{a(f)} - E_{a(b)}$ $E_{a(f)} = 0.12 \times 10^3 + 0.02 \times 10^3 \text{ cal}$ $= 0.14 \times 10^3 \text{ cal}$ $\text{\% of molecule crossing over the barrier}$ $= 100 \times e^{-E_{a(f)}/RT}$ $= 100 \times e^{-140/(2 \times 325)}$ $= 100 \times 0.8062 = 80.62 \%$

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
}