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Current Question (ID: 8169)

Question:

The pressure of 1 gm of an ideal gas A at 27 °C is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at the same temperature, the pressure becomes 3 bar. The correct relationship between their molecular masses is -

Options:

1. M_A = M_B
2. 4M_A = M_B
3. M_A = 2M_B
4. 2M_A = M_B

Solution:

\text{Step 1: Analyze the initial condition with gas A only.} \\ \text{Mass of gas A: } m_A = 1 \text{ g} \\ \text{Pressure due to gas A: } P_A = 2 \text{ bar} \\ \text{Using the ideal gas equation:} \\ P_A V = \frac{m_A}{M_A} RT \\ 2V = \frac{1}{M_A} RT \quad \text{...(1)} \\[0.5em] \text{Step 2: Analyze the condition after adding gas B.} \\ \text{Mass of gas B: } m_B = 2 \text{ g} \\ \text{Total pressure: } P_{total} = 3 \text{ bar} \\ \text{Pressure due to gas B: } P_B = 3 - 2 = 1 \text{ bar} \\ \text{Using the ideal gas equation for gas B:} \\ P_B V = \frac{m_B}{M_B} RT \\ 1V = \frac{2}{M_B} RT \quad \text{...(2)} \\[0.5em] \text{Step 3: Relate equations (1) and (2)} \\ \text{Divide equation (1) by equation (2):} \\ \frac{2V}{1V} = \frac{1/M_A \cdot RT}{2/M_B \cdot RT} \\ 2 = \frac{M_B}{2M_A} \\ 4M_A = M_B

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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
}