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Current Question (ID: 18340)

Question:

$\text{For the elementary reaction M} \rightarrow \text{N, the rate of disappearance of M increases by a factor of 8 upon doubling the concentration of M. The order of the reaction with respect to M will be:}$ $1.\ 4$ $2.\ 3$ $3.\ 2$ $4.\ 1$

Options:

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

Solution:

$\text{Consider, rate (r) = k[M]}^n \text{ where n is the order of the reaction.}$ $\text{The rate of disappearance of M increases by a factor of 8 upon doubling the concentration of M. It indicates that if the initial rate (r}_1\text{) is 1 then doubling the concentration rate (r}_2\text{) is 8r}_1\text{. Find the value of n as follows:}$ $r_1 = \text{k[M]}^n$ $r_2 = 8r_1 = \text{k[2M]}^n$ $\frac{r_1}{8r_1} = \frac{\text{k[M]}^n}{\text{k[2M]}^n}$ $\frac{1}{8} = \left(\frac{1}{2}\right)^n$ $\left(\frac{1}{2}\right)^3 = \left(\frac{1}{2}\right)^n$ $n = 3$

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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
}