Import Question JSON

Current Question (ID: 19880)

Question:

$\text{What would be the ratio of the root mean square speed of oxygen gas molecules to that of hydrogen gas molecules, if the temperature of both the gases are the same?}$

Options:

1. $1 : 4$
2. $1 : 16$
3. $1 : 32$
4. $1 : 8$

Solution:

$\text{Hint: } v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ $\text{Step: Find the ratio of the root mean square speed of oxygen gas molecules to that of hydrogen gas molecules.}$ $\text{The root mean square speed is given by: } v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ $\text{As the temperature of both gases is the same then; } v_{\text{rms}} \propto \frac{1}{\sqrt{M}}$ $\Rightarrow \frac{(v_{\text{rms}})_{\text{O}_2}}{(v_{\text{rms}})_{\text{H}_2}} = \sqrt{\frac{2}{32}} = \frac{1}{4}$ $\text{Hence, option (1) is the correct answer.}$

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
}