Import Question JSON

Current Question (ID: 8237)

Question:

$\text{In which case is the rate of diffusion highest if all are present in the same container at the same temperature:}$

Options:

1. $4 \text{ g H}_2$
2. $32 \text{ g O}_2$
3. $22 \text{ g CO}_2$
4. $56 \text{ g N}_2$

Solution:

$\text{(1) r} \propto 1/\sqrt{m} \propto \text{r} \propto \text{n}$ $\text{According to Graham's law of diffusion, the rate of diffusion is inversely proportional to the square root of the molecular mass.}$ $\text{Let's calculate the rate of diffusion for each gas by comparing their molar masses:}$ $\text{H}_2: \text{Molar mass} = 2 \text{ g/mol}$ $\text{O}_2: \text{Molar mass} = 32 \text{ g/mol}$ $\text{CO}_2: \text{Molar mass} = 44 \text{ g/mol}$ $\text{N}_2: \text{Molar mass} = 28 \text{ g/mol}$ $\text{Since the rate of diffusion r} \propto 1/\sqrt{\text{molar mass}}$, $\text{the gas with the smallest molar mass will have the highest rate of diffusion.}$ $\text{H}_2 \text{ has the smallest molar mass (2 g/mol), so it will have the highest rate of diffusion.}$ $\text{Therefore, 4 g H}_2 \text{ will have the highest rate of diffusion among the given options.}$

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
}