Import Question JSON

Current Question (ID: 8144)

Question:

$ \text{The increase in pressure in order to decrease the volume of a gas by 5\% at a constant temperature will be -} $

Options:

1. $ \text{5\%} $
2. $ \text{5.26\%} $
3. $ \text{10\%} $
4. $ \text{4.26\%} $

Solution:

$ \text{Hint: Boyle's Law} \n\n \text{Applying Boyle's Law, } P_1V_1 = P_2V_2 \n\n \text{Suppose initial pressure is P and initial volume is V, then} \n\n PV = P_2 \times 0.95V \n\n P_2 = \frac{P}{0.95} = \frac{100P}{95} \n\n \text{Increase in pressure} = \left( \frac{100P}{95} \right) - P = \frac{5P}{95} \n\n \% \text{ increase in pressure} = \left( \frac{5P/95}{P} \right) \times 100 = \frac{500}{95} = 5.26\% $

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
}