Import Question JSON

Current Question (ID: 19846)

Question:

$\text{Initially, a gas of diatomic molecules is contained in a cylinder of volume } V_1 \text{ at a pressure } P_1 \text{ and temperature } 250 \text{ K.}$ $\text{Assume that } 25\% \text{ of the molecules get dissociated, causing a change in the number of moles.}$ $\text{The pressure of the resulting gas at temperature } 2000 \text{ K, when contained in a volume } 2V_1 \text{ is given by } P_2. \text{ The ratio } \frac{P_2}{P_1} \text{ is:}$

Options:

1. $2$
2. $3$
3. $5$
4. $9$

Solution:

$\text{Hint: } PV = nRT$ $\text{Step: Find the ratio of the pressures.}$ $\text{The ideal gas equation is given by:}$ $PV = nRT$ $\Rightarrow P_1V_1 = nR \times 250$ $P_2 (2V_1) = \frac{5n}{4} \times R \times 2000$ $\Rightarrow \frac{P_1}{2P_2} = \frac{4 \times 250}{5 \times 2000}$ $\Rightarrow \frac{P_1}{2P_2} = \frac{1}{5}$ $\Rightarrow \frac{P_2}{P_1} = 5$ $\text{Hence, option } (3) \text{ is the correct answer.}$

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
}