Question

The bond dissociation energy of a typical C-Cl bond in a chlorofluorocarbon is approximately 330 kJ mol^-1. Calculate the maximum wavelength of light that can photodissociate a molecule of ${\mathbf{CCl}}_{\mathbf{2}}{\mathbf{F}}_{\mathbf{2}}$, breaking such a C-Cl bond.

Short answer

The maximum wavelength of light that can photo dissociate a molecule of is $1.815\times {10}^{-7}m$.

Step-by-step solution

Structure of chlorofluorocarbon

A chlorofluorocarbon is a compound having carbon, chlorine, and fluorine atoms. There are two chlorine and fluorine atoms present.

Calculation of bond dissociation energy

The energy necessary for breaking a chemical bond and produce two separated atoms, each having one electron from the original mutual pair, is referred to as bond dissociation enthalpy.

Given that bond dissociation energy of_C-Clbond is 330 kJ/mol and the total number of_C-Clbonds in${\text{CCl}}_{\text{2}}{\text{F}}_{\text{2}}$is 2.

The total energy required for bond dissociation is calculated as,

$$\begin{gathered} =2\times 330 \\ =660\mathrm{KJ}{\mathrm{mol}}^{-1} \end{gathered}$$

Calculation of maximum wavelength of light

The formula for the energy required to break one _Cl-Clbond is,

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

where, N_Ais Avogadro’s number

h is Planck’s constant

c is speed of light

The known values are substituted.

$$\begin{gathered} \lambda =\frac{hc}{E}\times N_A \\ \lambda =\frac{6.63\times {10}^{-34}\times 3\times {10}^8\times 6.023\times {10}^{23}}{660\times {10}^3} \\ \lambda =1.815\times {10}^{-7}m \end{gathered}$$

Thus, the maximum wavelength of light that can photo dissociate a molecule of CCl₂F₂ is $1.815\times {10}^{-7}m$.