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Current Question (ID: 8278)

Question:

$\Delta U^{\circ} \text{ for combustion of methane is } -x \text{ kJ mol}^{-1}. \text{ The value of } \Delta H^{\circ} \text{ for the same reaction would be:}$

Options:

1. $= \Delta U^{\circ}$
2. $> \Delta U^{\circ}$
3. $< \Delta U^{\circ}$
4. $= 0$

Solution:

$\text{Hint: } \Delta H^{\circ} = \Delta U^{\circ} + \Delta n_g RT$ $\text{Step 1: Write down the relation between } \Delta H^{\circ} \text{ and } \Delta U^{\circ}$ $\Delta H^{\circ} = \Delta U^{\circ} + \Delta n_g RT;$ $\text{The combustion reaction of methane is as follows:}$ $\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l)$ $\text{The } \Delta n_g \text{ value is } -2$ $\text{Step 2: Substitute the given data in the above equation.}$ $\Delta U^{\circ} = -x \text{ kJ mol}^{-1}$ $\Delta n_g = -2$ $\Delta H^{\circ} = -x - \frac{2RT}{1000} \text{ (divide by 1000 to convert in kJ mol}^{-1}\text{)}$ $\Delta H^{\circ} < \Delta U^{\circ}$

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
}