Question

The energy required to break one mole of $\mathrm{Cl}-\mathrm{Cl}$ bonds in ${\mathrm{Cl}}_2$ is $242\mathrm{kJ}/\mathrm{mol}$ . The longest wavelength of light capable of breaking single $\mathrm{Cl}-\mathrm{Cl}$ bond is__________ $(\mathrm{c}=3\times {10}^8\mathrm{m}/\mathrm{s},{\mathrm{N}}_{\mathrm{A}}=6.023\times {10}^{23}{\mathrm{mol}}^{-1})$.

• A. $700\mathrm{nm}$
• B. $640\mathrm{nm}$
• C. $594\mathrm{nm}$
• D. $492\mathrm{nm}$

Answer 1

The correct option is D

$492\mathrm{nm}$

Explanation for correct option :

(D) $492\mathrm{nm}$

Step 1: Bond energy :

• It is also known as the bond enthalpy.
• It is a measure of the bond strength of a chemical bond,
• It is also the amount of energy required to break one mole of the bond.

Step 2: Given Information:

• The bond energy = $242\mathrm{kJ}/\mathrm{mol}$

Step 3: Formula used for calculation of wavelength:

• The formula to calculate the wavelength is :

$\lambda =\frac{\mathrm{hc}}{\mathrm{E}}$

Where, $\mathrm{h}$ is Plank's constant, whose value is $6.626\times {10}^{-34}\mathrm{Js}$, $\mathrm{c}$ is the speed of light, which is $3\times {10}^8\mathrm{m}/\mathrm{s}$, and $\mathrm{E}$ is the energy of a photon.

Step 4: Calculation for wavelength:

The bond energy of ${\mathrm{Cl}}_2$ is $242\mathrm{kJ}/\mathrm{mol}$, the bond energy of single $\mathrm{Cl}-\mathrm{Cl}$ bond is :

$$\begin{gathered} \mathrm{E}=\frac{\mathrm{Bond}\mathrm{energy}\mathrm{of}{\mathrm{Cl}}_2}{{\mathrm{N}}_{\mathrm{a}}} \\ \mathrm{E}=\frac{242{\text{kJ mol}}^{-1}}{6.023\times {10}^{23}{\mathrm{mol}}^{-1}} \\ =\frac{242\times {10}^3\text{J}}{6.023\times {10}^{23}} \\ =4.017\times {10}^{-19}\mathrm{J} \end{gathered}$$.

Substituting all the values in the wavelength formula :

$\lambda =\frac{(6.626\times {10}^{-34}\mathrm{Js})\times (3\times {10}^8\mathrm{m}/\mathrm{s})}{4.017\times {10}^{-19}\mathrm{J}}$

$\lambda =492\mathrm{nm}$

Explanation for incorrect options:

As the value of wavelength is $492\mathrm{nm}$. Thus options A, B, and C stand incorrect.

Hence the correct option is D i.e. the wavelength is $492\mathrm{nm}$.