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Current Question (ID: 8432)

Question:

\text{For the reaction:} \text{NO(g) + (1/2)O₂(g) ⇌ NO₂(g)} \text{Given:} \text{ΔfG°(NO₂) = 52.0 kJ/mol} \text{ΔfG°(NO) = 87.0 kJ/mol} \text{ΔfG°(O₂) = 0 kJ/mol} \text{The equilibrium constant for the formation of NO₂ from NO and O₂ at 298K would be:}

Options:

1. $2.36 \times 10^4$
2. $3.10 \times 10^{-7}$
3. $1.36 \times 10^6$
4. $2.18 \times 10^9$

Solution:

\text{Hint: Use the relation between } \Delta G^\circ \text{ and } K_c \text{Explanation:} \text{Step 1: Find } \Delta G^\circ \text{For the given reaction: } \text{NO}_{(g)} + \frac{1}{2}\text{O}_2_{(g)} \rightleftharpoons \text{NO}_2_{(g)} \Delta G^\circ = \Delta G^\circ(\text{products}) - \Delta G^\circ(\text{reactants}) = -35.0 \text{ kJ mol}^{-1} \text{Step 2: Find } K_c \text{ by using Gibbs free energy data} \Delta G^\circ = -RT \ln K_c = -2.303 RT \log K_c \text{Thus, } \log K_c = 6.134 K_c = \text{antilog}(6.134) = 1.36 \times 10^6

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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
}