Import Question JSON

Current Question (ID: 8126)

Question:

$\text{A } 200 \text{ mL flask having oxygen at } 220 \text{ mm and a } 300 \text{ mL flask having nitrogen at } 100 \text{ mm are connected in such a way that } \text{O}_2 \text{ and } \text{N}_2 \text{ may combine in their volumes if temperature is kept constant. The total pressure of the gaseous mixture is-}$

Options:

1. $158 \text{ mm}$
2. $138 \text{ mm}$
3. $148 \text{ mm}$
4. $168 \text{ mm}$

Solution:

$\text{Hint: } P_1V_1 = P_2V_2$ $\text{Step 1:}$ $\text{The formula of total pressure is as follows:}$ $P = \frac{P_1V_1 + P_2V_2}{V_1 + V_2}$ $\text{Step 2:}$ $\text{Calculate that total pressure is as follows:}$ $P = \frac{P_1V_1 + P_2V_2}{V_1 + V_2}$ $= \frac{200 \times 220 + 300 \times 100}{200 + 300}$ $P = \frac{44000 + 30000}{500}$ $P = \frac{74000}{500}$ $P = 148$ $\text{Hence, the total pressure is } 148 \text{ mm.}$

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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
}