Import Question JSON

Current Question (ID: 21028)

Question:

$\text{An ideal gas is allowed to expand from 1 L to 10 L against a constant external pressure of 1 bar. The work done in kJ is:}$

Options:

1. $+10.0$
2. $-9.0$
3. $-2.0$
4. $-0.9$

Solution:

$\text{Hint: The formula of work done is } W = -P_{\text{ext}} \Delta V$ $\text{Step 1:}$ $\text{The formula of work done is as follows:}$ $W = -P_{\text{ext}} \Delta V$ $W = -P_{\text{ext}} (V_2 - V_1)$ $= -1 \times (10 - 1)$ $W = -9 \text{ bar L}$ $\text{Step 2:}$ $\text{Work done value must be multiplied and divided by the value of R so that work done can be calculated in J.}$ $R = 0.08314 \text{ L bar mol}^{-1} \text{ K}^{-1} = 8.314 \text{ J mol}^{-1} \text{ K}^{-1}$ $W = -9 \text{ bar L} \times \frac{8.314 \text{ J mol}^{-1} \text{ K}^{-1}}{0.08314 \text{ L bar mol}^{-1} \text{ K}^{-1}}$ $W = -900 \text{ J}$ $W = -0.9 \text{ kJ}$

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
}