Import Question JSON

Current Question (ID: 21154)

Question:

$\text{Consider the following reaction,}$ $\text{H}_2\text{O}(g) \rightleftharpoons \text{H}_2(g) + \frac{1}{2} \text{O}_2(g)$ $\text{If } K_{\text{eq}} = 2 \times 10^{-3} \text{ at 2300 K and the initial pressure of H}_2\text{O}(g) \text{ is 1 atm,}$ $\text{then the degree of dissociation of the above reaction will be } x \times 10^{-2},$ $\text{and the value of } x \text{ is:}$

Options:

1. 3 (Correct)
2. 4
3. 2
4. 7

Solution:

$K_{\text{eq}} = \frac{(P_{\text{H}_2})(P_{\text{O}_2})^{1/2}}{P_{\text{H}_2\text{O}}} = \frac{(\alpha)(\frac{\alpha}{2})^{1/2}}{1-\alpha} = 2 \times 10^{-3}$ $\Rightarrow \frac{\alpha^{3/2}}{2^{1/2}} = 2 \times 10^{-3}(1-\alpha \approx 1)$ $\Rightarrow \alpha^{3/2} = 2^{3/2} \times (10^{-2})^{3/2}$ $\alpha = 2 \times 10^{-2}$ $x = 2$

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
}