Import Question JSON

Current Question (ID: 19834)

Question:

$\text{In an ideal gas at a temperature } T, \text{ the average force that a molecule applies on the walls of a closed container depends on } T \text{ as } T^q. \text{ A good estimate for } q \text{ is}$

Options:

1. $\frac{1}{4}$
2. $2$
3. $\frac{1}{3}$
4. $1$

Solution:

$\text{Hint: } p = \frac{1}{3} \rho v_{\text{rms}}^2$ $\text{Step 1: The pressure exerted by ideal gas of the walls of the container is given by;}$ $p = \frac{1}{3} \rho v_{\text{rms}}^2 \quad \cdots (1)$ $\text{The rms speed of the ideal gas is given by;}$ $v_{\text{rms}} = \sqrt{\frac{3RT}{M}} \quad \cdots (2)$ $\text{By using above two equations;}$ $\Rightarrow p = \frac{\rho RT}{M}$ $\text{Step 2: Find the average force exerted by the ideal gas;}$ $\frac{F_{\text{avg}}}{A} = \frac{\rho RT}{M}$ $\text{Therefore;}$ $\Rightarrow F_{\text{avg}} = \frac{\rho ART}{M}$ $\text{From the above expression the average force by the ideal gas on the walls of a closed container depends on } T^1.$ $\text{Hence, option (4) is the correct answer.}$

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
}