Import Question JSON

Current Question (ID: 18288)

Question:

$\text{From the following data, the orders with respect to A, B, C, respectively, are:}$ $\begin{array}{|c|c|c|c|} \hline [A] \text{ (mol/L)} & [B] \text{ (mol/L)} & [C] \text{ (mol/L)} & \text{rate (M/sec.)} \\ \hline 0.2 & 0.1 & 0.02 & 8.08 \times 10^{-3} \\ \hline 0.1 & 0.2 & 0.02 & 2.01 \times 10^{-3} \\ \hline 0.1 & 1.8 & 0.18 & 6.03 \times 10^{-3} \\ \hline 0.2 & 0.1 & 0.08 & 6.464 \times 10^{-2} \\ \hline \end{array}$

Options:

1. $-1, 1, 3/2$
2. $-1, 1, 1/2$
3. $1, 3/2, -1$
4. $1, -1, 3/2$

Solution:

$\text{Use general expression of rate law.}$ $\text{If rate} = k[A]^x[B]^y[C]^z$ $\text{From the first two given data}$ $8.08 \times 10^{-3} = k[0.2]^x[0.1]^y[0.02]^z \quad \cdots (1)$ $2.01 \times 10^{-3} = k[0.1]^x[0.2]^y[0.02]^z \quad \cdots (2)$ $\text{Divide (1) by (2) we get, } 4 = 2^x(1/2)^y$ $\text{Similarly, from the second and third data } (9)^y(9)^z = 3$ $2y + 2z = 1$ $\text{From the first and fourth data } 4^z = 8 = 2^3$ $2z = 3, \text{ So } z = 3/2, y = -1, x = 1$

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
}