Import Question JSON

Current Question (ID: 18318)

Question:

$\text{When the temperature of a reaction increases from } 27^\circ \text{C to } 37^\circ \text{C, the rate increases by } 2.5 \text{ times. The activation energy in the temperature range will be:}$

Options:

1. $53.6 \text{ kJ}$
2. $12.61 \text{ kJ}$
3. $7.08 \text{ kJ}$
4. $70.8 \text{ kJ}$

Solution:

$\text{Use Arrhenius equation at different temperatures.}$ $\log \left( \frac{k_2}{k_1} \right) = \frac{E_a}{2.303 \times R} \left( \frac{T_2}{T_1} \right) - T_1 T_2$ $\text{Given: } k_2 = 2.5 \ k_1; \ T_1 = 27^\circ \text{C} = 300 \text{ K and } T_2 = 37^\circ \text{C} = 310 \text{ K}$ $\log 2.5 = \frac{E_a}{2.303 \times R} \times \left\{ \frac{10}{300 \times 310} \right\}$ $E_a = 70.77 \times 10^3 \text{ J} = 70.8 \text{ kJ}$

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
}