Import Question JSON

Current Question (ID: 8296)

Question:

$\text{To calculate the amount of work done in joules during reversible isothermal expansion of an ideal gas, the volume must be expressed in:}$

Options:

1. $\text{m}^3 \text{ only}$
2. $\text{dm}^3 \text{ only}$
3. $\text{cm}^3 \text{ only}$
4. $\text{All of the above}$

Solution:

$\text{Hint: All units of volume are applicable}$ $\text{Step 1: Consider the formula for work in reversible isothermal expansion}$ $\text{The work done during reversible isothermal expansion of an ideal gas is given by:}$ $W_{\text{rev}} = -nRT\ln\frac{V_2}{V_1}$ $\text{or using base-10 logarithm:}$ $W_{\text{rev}} = -2.303\,nRT\log\frac{V_2}{V_1}$ $\text{Step 2: Analyze the units in this formula}$ $\text{In this formula:}$ $\bullet \, n \text{ is the number of moles (mol)}$ $\bullet \, R \text{ is the universal gas constant (J mol}^{-1}\text{ K}^{-1}\text{)}$ $\bullet \, T \text{ is the temperature (K)}$ $\bullet \, \frac{V_2}{V_1} \text{ is the ratio of final volume to initial volume}$ $\text{Step 3: Examine the volume ratio term}$ $\text{Looking at the volume ratio } \frac{V_2}{V_1}\text{, notice that:}$ $\text{• This is a dimensionless ratio}$ $\text{• The units of } V_2 \text{ and } V_1 \text{ must be the same, but the specific unit doesn't matter}$ $\text{• Whether volumes are expressed in m}^3\text{, dm}^3\text{, or cm}^3\text{, the ratio remains the same}$ $\text{For example, if } V_1 = 1\text{ m}^3 \text{ and } V_2 = 2\text{ m}^3\text{, the ratio is 2.}$ $\text{Similarly, if } V_1 = 1000\text{ dm}^3 \text{ and } V_2 = 2000\text{ dm}^3\text{, the ratio is still 2.}$ $\text{And if } V_1 = 1,000,000\text{ cm}^3 \text{ and } V_2 = 2,000,000\text{ cm}^3\text{, the ratio remains 2.}$ $\text{Step 4: Confirm the units of the final result}$ $\text{The units of the terms in the work equation are:}$ $\bullet \, n \text{ in mol}$ $\bullet \, R \text{ in J mol}^{-1}\text{ K}^{-1}$ $\bullet \, T \text{ in K}$ $\bullet \, \ln\frac{V_2}{V_1} \text{ is dimensionless}$ $\text{Therefore, the work will be in joules regardless of which volume unit is used, as long as the same unit is used for both } V_1 \text{ and } V_2\text{.}$ $\text{Hence, the volume can be expressed in m}^3\text{, dm}^3\text{, cm}^3\text{, or any other unit of volume, as long as the same unit is used consistently.}$ $\text{The correct answer is: All of the above.}$

Import JSON File

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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
}