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Current Question (ID: 21032)

Question:

$\text{The value of enthalpy change (}\Delta H\text{) for the reaction}$ $\text{C}_2\text{H}_5\text{OH}_{(l)} + 3\text{O}_2_{(g)} \rightarrow 2\text{CO}_2_{(g)} + 3\text{H}_2\text{O}_{(l)} \text{ at } 27^\circ \text{C is } -1366.5 \text{ kJ mol}^{-1}.$ $\text{The value of internal energy change for the above reaction at this temperature will be:}$

Options:

1. $-1369.0 \text{ kJ}$
2. $-1364.0 \text{ kJ}$
3. $-1361.5 \text{ kJ}$
4. $1371.5 \text{ kJ}$

Solution:

$\text{Hint: Use the formula, that is, } \Delta H = \Delta E + \Delta n_g RT$ $\text{Step 1:}$ $\text{The relation between } \Delta H \text{ and } \Delta E \text{ is as follows:}$ $\Delta H = \Delta E + \Delta n_g RT$ $\text{For given reaction, that is,}$ $\text{C}_2\text{H}_5\text{OH}_{(l)} + 3\text{O}_2_{(g)} \rightarrow 2\text{CO}_2_{(g)} + 3\text{H}_2\text{O}_{(l)}$ $\text{For the above reaction, } \Delta n_g \text{ value is } -1.$ $\text{Step 2:}$ $\text{Calculate the value of } \Delta E \text{ as follows:}$ $\Delta E = \Delta H - \Delta n_g RT$ $= -1366.5 - (-1) \left(8.3 \times 10^{-3}\right) \times 300$ $= -1364.01$ $= -1364 \text{ kJ}$ $\text{Hence, option second is the correct answer.}$

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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
}