Import Question JSON

Current Question (ID: 19847)

Question:

$\text{The root mean square speed of molecules of a given mass of a gas at } 27^\circ\text{C and } 1 \text{ atm is } 200 \text{ m/s.}$ $\text{The root mean square speed of molecules of the gas at } 127^\circ\text{C and } 2 \text{ atm will be:}$

Options:

1. $\frac{200}{\sqrt{3}} \text{ m/s}$
2. $\frac{200}{\sqrt{5}} \text{ m/s}$
3. $\frac{400}{\sqrt{3}} \text{ m/s}$
4. $\frac{100}{\sqrt{5}} \text{ m/s}$

Solution:

$\text{Hint: } v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ $\text{Step: Find the root mean square speed of molecules of the gas at } 127^\circ\text{C and } 2 \text{ atm.}$ $\text{we know that the } v_{\text{rms}} = \sqrt{\frac{\gamma RT}{M}}$ $\Rightarrow \frac{v_1}{v_2} = \sqrt{\frac{T_1}{T_2}} \Rightarrow \frac{200}{v_2} = \sqrt{\frac{27 + 273}{127 + 273}}$ $\Rightarrow v_2 = \frac{400}{\sqrt{3}} \text{ m/s.}$ $\text{Hence, option (3) is the correct answer.}$

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
}