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Current Question (ID: 8167)

Question:

Oxygen is present in a 1-litre flask at a pressure of \( 7.6 \times 10^{-10} \) mmHg. The number of oxygen molecules in the flask at \( 0^\circ C \) is -

Options:

1. \( 2.686 \times 10^{10} \)
2. \( 26.86 \times 10^{10} \)
3. \( 0.626 \times 10^{12} \)
4. \( 4.123 \times 10^8 \)

Solution:

**Step 1:** Convert the given pressure from mmHg to atm. - Given pressure (\( p \)) = \( 7.6 \times 10^{-10} \) mmHg - Conversion factor: 1 atm = 760 mmHg \[ p = \frac{7.6 \times 10^{-10}}{760} = 1 \times 10^{-12} \text{ atm} \] **Step 2:** Use the ideal gas equation to calculate the number of moles (\( n \)) of oxygen. - Volume (\( V \)) = 1 L - Temperature (\( T \)) = \( 0^\circ C \) = 273.15 K - Gas constant (\( R \)) = 0.0821 L atm K\(^{-1}\) mol\(^{-1}\) \[ n = \frac{pV}{RT} = \frac{1 \times 10^{-12} \times 1}{0.0821 \times 273.15} \approx 4.459 \times 10^{-14} \text{ mol} \] **Step 3:** Calculate the number of oxygen molecules (\( N \)) using Avogadro's number (\( N_A \)). \[ N = n \times N_A = 4.459 \times 10^{-14} \times 6.023 \times 10^{23} \approx 2.686 \times 10^{10} \] Hence, the number of oxygen molecules in the flask is \( 2.686 \times 10^{10} \).

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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
}