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Current Question (ID: 21017)

Question:

$\text{The heat of combustion of ethanol into carbon dioxides and water is } -327 \text{ kcal at constant pressure. The heat evolved (in cal) at constant volume and } 27^\circ\text{C (if all gases behave ideally) is:}$ $\text{(R = 2 cal mol}^{-1} \text{ K}^{-1})$

Options:

1. $316 \text{ kcal}$
2. $326 \text{ kcal}$
3. $365 \text{ kcal}$
4. $342 \text{ kcal}$

Solution:

$\text{Hint: Use the formula, that is, } \Delta H_C = \Delta U_C + \Delta nRT$ $\text{Step 1:}$ $\text{The combustion reaction of ethanol is as follows:}$ $\text{C}_2\text{H}_5\text{OH}_{(l)} + 3\text{O}_2_{(g)} \rightarrow 2\text{CO}_2_{(g)} + 3\text{H}_2\text{O}_{(l)}$ $\text{Calculate the value of } \Delta n_g$ $\Delta n_g = 2 - 3 = -1$ $\text{Step 2:}$ $\text{At constant volume, heat is equal to } \Delta U \text{ and heat at constant pressure is equal to } \Delta H.$ $\Delta H_C = \Delta U_C + \Delta nRT$ $\Delta U_C = \Delta H_C - \Delta nRT$ $\Delta U_C = -327 \times 10^3 - (-1) \times 2 \times 300$ $= -326400 \text{cal}$ $= -326 \text{ kcal}$ $\text{The negative sign indicates the heat has evolved. Thus, 326 kcal amount of energy is released.}$ $\text{Hence, option second is the correct answer.}$

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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
}