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Current Question (ID: 18379)

Question:

$\text{The mechanism of a hypothetical reaction}$ $\text{X}_2 + \text{Y}_2 \rightarrow 2\text{XY} \text{ is given below:}$ $\text{(i) X}_2 \rightarrow \text{X} + \text{X (Fast)}$ $\text{(ii) X + Y}_2 \rightleftharpoons \text{XY + Y (slow)}$ $\text{(iii) X + Y} \rightarrow \text{XY (Fast)}$ $\text{The overall order of the reaction will be:}$

Options:

1. $2$
2. $0$
3. $1.5$
4. $1$

Solution:

$\text{The overall reaction rate depends on the rate of the slowest step.}$ $\text{i.e., The overall rate is equal to the rate of the slowest step (ii)}$ $=k[\text{X}][\text{Y}_2] \ldots (1)$ $\text{where, k= rate constant}$ $\text{Assuming step (i) to be reversible, the equilibrium constant can be given as,}$ $K_{eq} = \frac{[\text{X}]^2}{[\text{X}_2]} = [\text{X}]^2$ $[\text{X}] = \sqrt{K_{eq}[\text{X}_2]} \ldots (2)$ $\text{From eq (1) and (2)}$ $rate = k \sqrt{k_{eq}[\text{X}_2]} [\text{Y}_2]$ $\text{Overall order=} \frac{1}{2} + 1 = \frac{3}{2} = 1.5$

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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
}