Import Question JSON

Current Question (ID: 18304)

Question:

$\text{When the temperature of a reaction increases from } 300 \text{ K to } 310 \text{ K, the rate of the reaction doubles. What is the activation energy for this reaction?}$ $\left( R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1} \text{ and } \log 2 = 0.301 \right)$

Options:

1. $53.6 \text{ kJ mol}^{-1}$
2. $68.6 \text{ kJ mol}^{-1}$
3. $59.5 \text{ kJ mol}^{-1}$
4. $70.5 \text{ kJ mol}^{-1}$

Solution:

$\text{HINT: Use Arrhenius Equation}$ $\log \frac{K_2}{K_1} = \frac{-E_a}{2.303R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right); \; T_2 = 310 \text{K}$ $\frac{K_2}{K_1} = 2$ $T_1 = 300 \text{K}$ $\Rightarrow \log 2 = \frac{-E_a}{2.303 \times 8.314} \left( \frac{1}{310} - \frac{1}{300} \right)$ $\Rightarrow E_a = 53598.6 \text{ J/mol} = 53.6 \text{ KJ/mol}$ $\text{Hence, the answer is option 1.}$

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
}