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Current Question (ID: 20883)

Question:

$\text{The energy required to break one mole of Cl--Cl bonds in Cl}_2 \text{ is 242 kJmol}^{-1}. \text{ The wavelength of light capable of breaking a single Cl--Cl bond is:}$ $1.\ 494\ \text{nm}$ $2.\ 594\ \text{nm}$ $3.\ 640\ \text{nm}$ $4.\ 700\ \text{nm}$

Options:

1. $494\ \text{nm}$
2. $594\ \text{nm}$
3. $640\ \text{nm}$
4. $700\ \text{nm}$

Solution:

$\text{Hint: Use energy formula, that is, } E = \frac{hc}{\lambda}$ $\text{Step 1:}$ $\text{Calculate the energy required to break one molecule of Cl--Cl bond is as follows:}$ $1\ \text{mole of Cl}_2 = 6.022 \times 10^{23} \text{ molecules of Cl}_2$ $\text{For one molecule of Cl}_2 = \frac{242 \times 10^3}{6.022 \times 10^{23}} = 4.01 \times 10^{-19} \text{ J}$ $\text{Step 2:}$ $\text{Calculate the longest wavelength of light capable of breaking a single Cl--Cl bond is as follows:}$ $E = \frac{hc}{\lambda}$ $4.01 \times 10^{-19} = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{\lambda}$ $\lambda = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{4.01 \times 10^{-19}}$ $\lambda = 4.96 \times 10^{-7} \text{ m} \approx 496 \text{ nm}$ $\text{Hence, option first is the correct answer.}$

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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
}