Import Question JSON

Current Question (ID: 8155)

Question:

At a certain temperature for which $\text{RT} = 25 \text{ L atm mol}^{-1}$, the density of a gas, in $\text{g L}^{-1}$, is $\text{d} = 2.00\text{P} + 0.020 \text{P}^2$, where $\text{P}$ is the pressure in atmosphere. The molecular weight of the gas in $\text{g mol}^{-1}$ is:

Options:

1. $25$
2. $50$
3. $75$
4. $100$

Solution:

Hint: $\text{M (molar mass)} = \frac{\text{dRT}}{\text{P}}$\n\nStep 1:\nThe formula of density for an ideal gas is as follows:\n$\text{PV} = \text{nRT}$\n$\frac{\text{d}}{\text{P}} = \frac{\text{M}}{\text{RT}}$\n\nStep 2:\nCalculate the molecular weight of the gas as follows:\n$\text{M (molar mass)} = \frac{(2.00\text{P} + 0.020\text{P}^2) \text{RT}}{\text{P}}$\n$\text{M (molar mass)} = (2.00 + 0.020\text{P})\text{RT}$\n\nThe value of $0.020\text{P}$ is very small compared to $2.00$. Thus, $2.00 + 0.020\text{P} \approx 2.00$.\n\n$\text{M} = 2\text{RT}$\n$\text{M} = 2 \times 25 = 50 \text{ g mol}^{-1}$

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
}