The energy required to break one mole of Cl-Cl bonds in `Cl_2` is 242 kJ mol`""^(-1).` The longest wavelength of light capable of breaking a single Cl-Cl bond is

Options

A. 594nm
B. 640nm
C. 700nm
D. 494nm

Answer

To find the longest wavelength of light capable of breaking a single Cl-Cl bond in Cl₂, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Energy Required to Break One Mole of Cl-Cl Bonds:**
The energy required to break one mole of Cl-Cl bonds in Cl₂ is given as 242 kJ/mol.

2. **Convert Energy from kJ to Joules:**
Since 1 kJ = 1000 J, we convert the energy:
\[ 242 \text{ kJ/mol} = 242 \times 10^3 \text{ J/mol} = 242000 \text{ J/mol} \]

3. **Calculate Energy Required to Break One Cl-Cl Bond:**
Using Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mol), we can find the energy required to break one Cl-Cl bond:
\[ \text{Energy per bond} = \frac{242000 \text{ J/mol}}{6.022 \times 10^{23} \text{ molecules/mol}} \approx 40.18 \times 10^{-20} \text{ J} \]

4. **Use the Energy-Wavelength Relationship:**
The relationship between energy (E) and wavelength (λ) is given by the equation:
\[ E = \frac{hc}{\lambda} \]
Rearranging this to solve for λ gives:
\[ \lambda = \frac{hc}{E} \]
where:
- \(h\) (Planck's constant) = \(6.626 \times 10^{-34} \text{ J s}\)
- \(c\) (speed of light) = \(3.00 \times 10^8 \text{ m/s}\)

5. **Substitute Values into the Equation:**
Now we substitute the values into the equation:
\[ \lambda = \frac{(6.626 \times 10^{-34} \text{ J s}) \times (3.00 \times 10^8 \text{ m/s})}{40.18 \times 10^{-20} \text{ J}} \]

6. **Calculate λ:**
Performing the calculation:
\[ \lambda = \frac{1.9878 \times 10^{-25} \text{ J m}}{40.18 \times 10^{-20} \text{ J}} \approx 0.494 \times 10^{-6} \text{ m} \]
Converting to nanometers:
\[ \lambda \approx 494 \text{ nm} \]

### Final Answer:
The longest wavelength of light capable of breaking a single Cl-Cl bond is **494 nm**.

---