Import Question JSON

Current Question (ID: 8392)

Question:

$\text{The ratio of }\frac{K_P}{K_C}\text{ for the reaction}$ $\text{CO(g)} + \frac{1}{2}\text{O}_2\text{(g)} \rightleftharpoons \text{CO}_2\text{(g) is:}$

Options:

1. $(\text{RT})^{1/2}$
2. $(\text{RT})^{-1/2}$
3. $\text{RT}$
4. $1$

Solution:

$\text{Hint: Use K}_P \text{ and K}_C \text{ relation.}$ $\text{For gas phase reactions, the relationship between K}_P \text{ and K}_C \text{ is given by:}$ $\text{K}_P = \text{K}_C (\text{RT})^{\Delta n_g}$ $\text{where } \Delta n_g = \text{number of moles of gaseous products} - \text{number of moles of gaseous reactants}$ $\text{Given reaction:}$ $\text{CO(g)} + \frac{1}{2}\text{O}_2\text{(g)} \rightleftharpoons \text{CO}_2\text{(g)}$ $\text{Calculating } \Delta n_g\text{:}$ $\Delta n_g = 1 - (1 + \frac{1}{2}) = 1 - \frac{3}{2} = -\frac{1}{2}$ $\text{Substituting this value in the relation:}$ $\text{K}_P = \text{K}_C (\text{RT})^{-\frac{1}{2}}$ $\text{Therefore:}$ $\frac{\text{K}_P}{\text{K}_C} = (\text{RT})^{-\frac{1}{2}}$ $\text{The ratio of }\frac{\text{K}_P}{\text{K}_C}\text{ for the given reaction is } (\text{RT})^{-1/2}$ $\text{The correct answer is option 2: }(\text{RT})^{-1/2}$

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
}