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Current Question (ID: 8166)

Question:

A 2.24 L cylinder of oxygen at STP is found to develop a leakage. When the leakage was plugged, the pressure dropped to 570 mm of Hg. The number of moles of gas that escaped will be:

Options:

1. 0.050
2. 0.025
3. 0.075
4. 0.01

Solution:

**Step 1:** Determine the initial and final conditions. - Initial pressure at STP (\( P_{\text{initial}} \)) = 760 mmHg - Final pressure (\( P_{\text{final}} \)) = 570 mmHg - Volume (\( V \)) = 2.24 L (constant) - Temperature (\( T \)) = 273 K (STP) - Gas constant (\( R \)) = 0.0821 L atm K\(^{-1}\) mol\(^{-1}\) **Step 2:** Calculate the pressure drop due to leakage. \[ \Delta P = P_{\text{initial}} - P_{\text{final}} = 760 - 570 = 190 \text{ mmHg} \] Convert mmHg to atm: \[ \Delta P = \frac{190}{760} = 0.25 \text{ atm} \] **Step 3:** Use the ideal gas equation to find the escaped moles. \[ n = \frac{\Delta P \times V}{R \times T} = \frac{0.25 \times 2.24}{0.0821 \times 273} \approx 0.025 \text{ moles} \] Hence, the number of moles of gas that escaped is **0.025 moles**.

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
}