Import Question JSON

Current Question (ID: 11154)

Question:

$\text{At what temperature is the root mean square speed of molecules of hydrogen twice as that at STP?}$

Options:

1. $273 \text{ K}$
2. $546 \text{ K}$
3. $819 \text{ K}$
4. $1092 \text{ K}$ (Correct)

Solution:

$\text{Hint: } v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ $\text{Step: Find the temperature is the root mean square speed of molecules of hydrogen.}$ $\text{The root mean square (RMS) speed of gas molecules is given by;}$ $v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ $\text{We are given that the RMS speed at the new temperature } (T_2) \text{ is twice the RMS speed at STP } (T_1 = 273 \text{ K}):$ $v_{\text{rms},2} = 2 \cdot v_{\text{rms},1}$ $\sqrt{\frac{3RT_2}{M}} = 2 \cdot \sqrt{\frac{3RT_1}{M}}$ $\frac{3RT_2}{M} = 4 \cdot \frac{3RT_1}{M}$ $T_2 = 4 \times T_1$ $\Rightarrow T_2 = 4 \times 273 = 1092 \text{ K}$ $\text{Hence, option (4) is the correct answer.}$

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
}