Import Question JSON

Current Question (ID: 21031)

Question:

$\text{The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of 10 dm}^3 \text{ to a volume of 100 dm}^3 \text{ at 27}^\circ \text{C is:}$

Options:

1. $38.3 \text{ J mol}^{-1} \text{ K}^{-1}$
2. $35.8 \text{ J mol}^{-1} \text{ K}^{-1}$
3. $32.3 \text{ J mol}^{-1} \text{ K}^{-1}$
4. $42.3 \text{ J mol}^{-1} \text{ K}^{-1}$

Solution:

$\text{Step 1: The given number of moles } = 2$ $\text{Initial volume } (V_1) = 10 \text{ cm}^3, \text{ Final volume } (V_2) = 100 \text{ cm}^3$ $\text{This question aims to calculate the entropy change involved in the isothermal reversible expansion.}$ $\Delta S = 2.303 \times n \times R \times \log \frac{V_2}{V_1}$ $\Delta S = 2.303 \times 2 \times 8.314 \text{ J mol}^{-1} \text{ K}^{-1} \times \log \frac{100 \text{ dm}^3}{10 \text{ dm}^3}$ $\Delta S = 2.303 \times 2 \times 8.314 \text{ J mol}^{-1} \text{ K}^{-1} \times \log (10)$ $\Delta S = 38.3 \text{ J mol}^{-1} \text{ K}^{-1}$ $\text{Hence, option 1 is correct.}$

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
}