Import Question JSON

Current Question (ID: 19702)

Question:

$\text{In an isochoric process on an ideal gas, initial temperature is equal to } 27^\circ \text{C with an initial pressure being equal to } 270 \text{ kPa.}$ $\text{Now if the final temperature is made equal to } 36^\circ \text{C then the final pressure is equal to:}$

Options:

1. $298 \text{ kPa}$
2. $270 \text{ kPa}$
3. $360 \text{ kPa}$
4. $278 \text{ kPa}$

Solution:

$\text{Hint: For an isochoric process, volume is constant.}$ $\text{Step: Find the final pressure.}$ $\text{Ideal gas equation is given by } PV = nRT$ $\text{For the isochoric process, volume remains constant.}$ $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ $\frac{270}{300} = \frac{P_f}{309}$ $P_f = 278.1 \text{ kPa}$

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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
}