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Current Question (ID: 21108)

Question:

$\text{The standard Gibbs energy change at 300 K for the reaction}$ $2\text{A} \rightleftharpoons \text{B} + \text{C is } 2494.2 \text{ J. At a given time, the composition of the reaction mixture is }$ $[\text{A}] = \frac{1}{2}, \ [\text{B}] = 2 \text{ and } [\text{C}] = \frac{1}{2}. \text{ The reaction proceeds in the: [assume } R = 8.314 \text{ J/K/mol; } e^{-1} = 0.37]$

Options:

1. $\text{Forward direction because } Q > K_C$
2. $\text{Reverse direction because } Q > K_C$
3. $\text{Forward direction because } Q < K_C$
4. $\text{Reverse direction because } Q < K_C$

Solution:

$\text{Hint: Use the relation between } Q_C \text{ and } K_C$ $\text{Step 1:}$ $\text{First calculate the value of equilibrium constant as follows:}$ $\Delta G^\circ_{rxn} = -RT \ln K_{equ}$ $2494.2 = -8.314 \times 300 \times \ln K_{equ}$ $K_{equ} = e^{-1}$ $= 0.37$ $\text{Step 2:}$ $\text{Calculate the value of } Q_C \text{ as follows:}$ $Q = \frac{[\text{B}][\text{C}]}{[\text{A}]^2} = \frac{(2) \times (\frac{1}{2})}{(\frac{1}{2})^2} = 4$ $\therefore \ Q > K_{equ}.$ $\text{The value of } Q_C \text{ is more than the equilibrium constant value. The reaction proceeds in the reverse direction.}$

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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
}