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Current Question (ID: 11016)

Question:

$\text{One mole of an ideal gas expands at a constant temperature of 300 K from an initial volume of 10 litres to a final volume of 20 litres. The work done in expanding the gas is equal to:}$ $(R = 8.31 \text{ J/mol-K})$

Options:

1. $750 \text{ J}$
2. $1728 \text{ J}$ (Correct)
3. $1500 \text{ J}$
4. $3456 \text{ J}$

Solution:

$\text{Hint: } W = 2.303nRT\text{Log}\left(\frac{V_f}{V_i}\right)$ $\text{Step: Find the work done in expanding the gas.}$ $\text{The work done in the isothermal process is given by:}$ $W = 2.303nRT\text{Log}\left(\frac{V_f}{V_i}\right)$ $\text{Given:}$ $\text{Number of moles } n = 1 \text{ mol}$ $\text{Temperature } T = 300 \text{ K}$ $\text{Gas constant } R = 8.31 \text{ J/mol-K}$ $\text{Initial volume } V_i = 10 \text{ litres}$ $\text{Final volume } V_f = 20 \text{ litres}$ $\text{Substituting the values:}$ $W = 2.303 \times 1 \times 8.31 \times 300 \times \text{Log}\left(\frac{20}{10}\right)$ $W = 2.303 \times 1 \times 8.31 \times 300 \times \text{Log}(2)$ $W = 1728.15 \text{ J} \quad [\text{Log}(2) = 0.301]$ $W = 1728 \text{ J}$ $\text{Hence, option (2) is the correct answer.}$

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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
}