Import Question JSON

Current Question (ID: 21493)

Question:

$\text{The rate of a reaction is decreased by } 3.555 \text{ times when the temperature was changed from } 40^\circ\text{C to } 30^\circ\text{C.}$ $\text{The activation energy (in kJ mol}^{-1}\text{) of the reaction is:}$ $\text{(Take R=8.314 J mol}^{-1} \text{ K}^{-1} \text{ ln } 3.555=1.268)}$

Options:

1. $100 \text{ kJ/mol}$
2. $120 \text{ kJ/mol}$
3. $95 \text{ kJ/mol}$
4. $108 \text{ kJ/mol}$

Solution:

$\text{Hint: Use the formula, that is, } \ln \left( \frac{K_2}{K_1} \right) = \frac{E_a}{R} \left[ \frac{1}{T_1} - \frac{1}{T_2} \right]$ $\text{Step 1:}$ $\text{Use the formula given below:}$ $\ln \left( \frac{K_2}{K_1} \right) = \frac{E_a}{R} \left[ \frac{1}{T_1} - \frac{1}{T_2} \right]$ $\text{Given values are as follows:}$ $T_1 = 303 \text{K}; \ T_2 = 313 \text{K}$ $\frac{K_2}{K_1} = 3.555$ $\text{Step 2:}$ $\text{Calculate the value of } E_a \text{ as follows:}$ $\ln(3.555) = \frac{E_a}{8.314} \left[ \frac{1}{303} - \frac{1}{313} \right]$ $E_a = 99980.715$ $E_a = 99.98 \text{ kJ/mol}$ $E_a = 99.98 \text{ kJ/mol} \approx 100 \text{ kJ/mol}$

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
}