Import Question JSON

Current Question (ID: 21433)

Question:

$\text{Consider the given dissociation reaction}$ $\text{HX}_{(\text{aq})} \rightleftharpoons \text{H}^+_{(\text{aq})} + \text{X}^-_{(\text{aq})}$ $\text{with an acid dissociation constant } (K_a) \text{ of } 1.2 \times 10^{-5}. \text{ What is the}$ $\text{osmotic pressure (in atm) of a } 0.03 \text{ M HX solution at } 300 \text{ K?}$

Options:

1. $4 \text{ atm}$
2. $2 \text{ atm}$
3. $1 \text{ atm}$
4. $6 \text{ atm}$

Solution:

$\text{Hint: } K_a = \frac{C \alpha^2}{1 - \alpha}$ $K_a = \frac{C \alpha^2}{1 - \alpha}$ $1.2 \times 10^{-5} = (3 \times 10^{-2})(\alpha^2)$ $\alpha^2 = 0.4 \times 10^{-3}$ $\alpha^2 = 4 \times 10^{-4}$ $\alpha = 0.02$ $\pi = iCRT$ $i = 1 + \alpha = 1.02$ $\pi = (1.02)(0.03)(0.0821)(300)$ $= 0.7536 \text{ atm}$ $\approx 1$

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
}