Import Question JSON

Current Question (ID: 21518)

Question:

$\text{The activation energy of one of the reactions in a biochemical process is } 532611 \text{ J mol}^{-1}. \text{ When the temperature falls from } 310 \text{ K to } 300 \text{ K, the change in rate constant observed is }$ $k_{300} = x \times 10^{-3} k_{310}. \text{ The value of } x \text{ is:}$ $\text{[Given: } \ln 10 = 2.3, R = 8.3 \text{ JK}^{-1}\text{mol}^{-1} ]$

Options:

1. 1 (Correct)
2. 5
3. 2
4. 8

Solution:

$\text{Hint: } \log \frac{k_2}{k_1} = \frac{E_a}{2.303R} \left[ \frac{T_2 - T_1}{T_1 T_2} \right]$ $\log \left( \frac{K_{310}}{K_{300}} \right) = \frac{532611}{8.3} \left( \frac{1}{300} - \frac{1}{310} \right)$ $\frac{K_{310}}{K_{300}} = 10^3 \Rightarrow K_{300} = 1 \times 10^{-3} \times K_{310}$

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
}