Import Question JSON

Current Question (ID: 19844)

Question:

$\text{Nitrogen gas is at a certain temperature } 300^\circ\text{C. At what temperature (in Kelvin) will the root mean square (rms) speed of a hydrogen molecule be equal to the rms speed of a nitrogen molecule?}$ $\text{(Given: molar mass of nitrogen molecule is } 28 \text{ g/mol and molar mass of hydrogen molecule is } 2 \text{ g/mol)}$

Options:

1. $21 \text{ K}$
2. $41 \text{ K}$
3. $52 \text{ K}$
4. $76 \text{ K}$

Solution:

$\text{Hint: } v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ $\text{Step: Find the temperature at which a hydrogen molecule's root mean square (rms) speed equals the rms speed of a nitrogen molecule.}$ $v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ $\Rightarrow v_{\text{N}_2} = v_{\text{H}_2}$ $\Rightarrow \sqrt{\frac{3RT_{\text{N}_2}}{M_{\text{N}_2}}} = \sqrt{\frac{3RT_{\text{H}_2}}{M_{\text{H}_2}}}$ $\Rightarrow \frac{573}{28} = \frac{T_{\text{H}_2}}{2}$ $\Rightarrow T_{\text{H}_2} = 40.928 \approx 41.$ $\text{Hence, option (2) is the correct answer.}$

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
}