Import Question JSON

Current Question (ID: 11143)

Question:

$\text{The molecular weight of two gases is } M_1 \text{ and } M_2. \text{ At any temperature, the ratio of root mean square velocities } v_1 \text{ and } v_2 \text{ will be:}$

Options:

1. $\sqrt{\frac{M_1}{M_2}}$
2. $\sqrt{\frac{M_2}{M_1}}$ (Correct)
3. $\sqrt{\frac{M_1+M_2}{M_1-M_2}}$
4. $\sqrt{\frac{M_1-M_2}{M_1+M_2}}$

Solution:

$\text{Hint: } v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ $\text{Step: Find the ratio of root mean square velocities.}$ $\text{The RMS speed of any homogeneous gas sample is given by;}$ $v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ $\text{Now at a temperature, the ratio of speeds will be:}$ $\frac{v_1}{v_2} = \frac{\sqrt{\frac{3RT}{M_1}}}{\sqrt{\frac{3RT}{M_2}}}$ $\Rightarrow \frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}}$ $\text{Hence, option (2) is the correct answer.}$

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
}