Import Question JSON

Current Question (ID: 11147)

Question:

$\text{At which temperature the velocity of } \text{O}_2 \text{ molecules will be equal to the velocity of } \text{N}_2 \text{ molecules at } 0°\text{C}?$

Options:

1. $40°\text{C}$
2. $93°\text{C}$
3. $39°\text{C}$ (Correct)
4. $\text{Cannot be calculated}$

Solution:

$v_{\text{rms}} = \sqrt{\frac{3RT}{M}} \Rightarrow T \propto M$ $\text{R} \rightarrow \text{constant}$ $\Rightarrow \frac{T_{\text{O}_2}}{T_{\text{N}_2}} = \frac{M_{\text{O}_2}}{M_{\text{N}_2}} \Rightarrow \frac{T_{\text{O}_2}}{(273 + 0)} = \frac{32}{28}$ $\Rightarrow T_{\text{O}_2} = 312 \text{ K} = 39°\text{C}$

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
}