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Current Question (ID: 8158)

Question:

The density of a gas is $1.964 \text{ g dm}^{-3}$ at $273 \text{ K}$ and $76 \text{ cm Hg}$. The gas is:

Options:

1. $\text{CH}_4$
2. $\text{C}_2\text{H}_6$
3. $\text{CO}_2$
4. $\text{Xe}$

Solution:

Hint: Use $\text{M} = \frac{\text{dRT}}{\text{P}}$\n\nStep 1:\nThe formula is given below:\n$\text{M} = \frac{\text{dRT}}{\text{P}}$\n\nStep 2:\nCalculate the molar mass of the gas as follows:\n$\text{M} = \frac{1.964 \times 10^{-3} \times 82.1 \times 273}{1} \approx 44 \text{ g mol}^{-1}$\n\n(Note: Density converted from $\text{g dm}^{-3}$ to $\text{g cm}^{-3}$ by multiplying by $10^{-3}$ and pressure taken as 1 atm = 76 cm Hg)\n\nHence, the gas is $\text{CO}_2$ (molar mass = 44 $\text{g mol}^{-1}$).

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
}