Import Question JSON

Current Question (ID: 18267)

Question:

$\text{During the formation of ammonia by Haber's process } \text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3, \text{ the rate of appearance of NH}_3 \text{ was measured as } 2.5 \times 10^{-4} \text{ mol L}^{-1} \text{ s}^{-1}. \text{ The rate of disappearance of H}_2 \text{ will be:}$

Options:

1. $2.5 \times 10^{-4} \text{ mol L}^{-1} \text{ s}^{-1}$
2. $1.25 \times 10^{-4} \text{ mol L}^{-1} \text{ s}^{-1}$
3. $3.75 \times 10^{-4} \text{ mol L}^{-1} \text{ s}^{-1}$
4. $15.00 \times 10^{-4} \text{ mol L}^{-1} \text{ s}^{-1}$

Solution:

$\text{Rate of reaction is rate of disappearance of any of the reactants or the rate of appearance of products is divided by their respective stoichiometric coefficients.}$ $\text{Given: } \text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3,$ $\text{Thus,}$ $-\frac{1}{3} \frac{d[\text{H}_2]}{dt} = \frac{1}{2} \frac{d[\text{NH}_3]}{dt}$ $\Rightarrow -\frac{d[\text{H}_2]}{dt} = \frac{3}{2} \times 2.5 \times 10^{-4}$ $\Rightarrow -\frac{d[\text{H}_2]}{dt} = 3.75 \times 10^{-4} \text{ mol L}^{-1} \text{ s}^{-1}$ $\text{Hence, the correct answer is the third option.}$

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
}