Import Question JSON

Current Question (ID: 8375)

Question:

$\text{In the reaction A(g) + 2B(g)} \rightleftharpoons \text{2C(g) + D(g), the initial concentration of B is twice that of A and, at equilibrium, the concentrations of A and D are equal. The value of the equilibrium constant will be:}$

Options:

1. $4$
2. $16$
3. $2$
4. $1$

Solution:

$\text{Hint: K} = \frac{[\text{C}]^2 \times [\text{D}]}{[\text{A}] \times [\text{B}]^2}$ $\text{Step 1: The reaction is as follows:}$ $\text{A(g) + 2B(g)} \rightleftharpoons \text{2C(g) + D(g)}$ $\text{Initial conc.} \quad 1 \quad 2 \quad - \quad -$ $\text{equilibrium conc.} \quad 1-x \quad 2-2x \quad 2x \quad x$ $\text{Step 2: At equilibrium concentration of A and D are equal}$ $[\text{A}] = [\text{D}] = x = 1-x$ $2x = 1$ $x = \frac{1}{2}$ $\text{Concentration of A, B, C and D at equilibrium is}$ $[\text{A}] = 1 - \frac{1}{2} = \frac{1}{2}$ $[\text{B}] = 2 - (2 \times \frac{1}{2}) = 1$ $[\text{C}] = 2 \times \frac{1}{2} = 1$ $[\text{D}] = \frac{1}{2}$ $\text{K}_c = \frac{[\text{C}]^2 \times [\text{D}]}{[\text{A}] \times [\text{B}]^2}$ $\text{K}_c = \frac{(1)^2 \times \frac{1}{2}}{\frac{1}{2} \times (1)^2}$ $\text{K}_c = 1$ $\text{Hence, option 4 is the answer}$

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
}