Import Question JSON

Current Question (ID: 11183)

Question:

$\text{When the gas in an open container is heated, the mean free path:}$

Options:

1. $\text{Increases}$ (Correct)
2. $\text{Decreases}$
3. $\text{Remains the same}$
4. $\text{Any of the above depending on the molar mass}$

Solution:

$\text{Hint: } \lambda = \frac{1}{\sqrt{2\pi n_v d^2}}$ $\text{Step: Find the mean free path of a gas.}$ $\text{The mean free path }(\lambda)\text{ is the average distance of a gas molecule travels between successive collisions with other gas molecules. It is given by;}$ $\lambda = \frac{1}{\sqrt{2\pi n_v d^2}}$ $\text{Here, }n_v = \text{number density}$ $n_v = \frac{\text{molar density}}{\text{volume}}$ $\Rightarrow \lambda \propto \frac{1}{n}$ $\text{i.e., the mean free path is inversely proportional to the molecular density.}$ $\text{At constant volume and pressure, }T \propto \frac{1}{n}\text{. As volume is constant so, }n_v\text{ is decreasing and }\lambda\text{ will increase. As temperature increases moles of gas decrease. When the gas is heated, the effect on the mean free path will increase as the molecular density decreases.}$ $\text{Hence, option }(1)\text{ is the correct answer.}$

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
}