Question

The energy required to break one mole of $Cl-Cl$ bond in ${Cl}_{2}$ is 242 kJ/mol. The longest wavelength of light capable of breaking single $Cl-Cl$ bond is: $c = 3 \times {10}^{8} m/s, {N}_{A} = 6.023 \times {10}^{23} {mol}^{-1}$
a.) 700 nm
b.) 494 nm
c.) 594 nm
d.) 640 nm

Answer 1

The strength of a covalent bond depends upon the amount of energy that would be required to break the bond. This energy is known as bond energy.

Complete step by step answer:
The bond energy also known as the bond enthalpy or the bond strength is the amount of energy that is required to break a bond or a mole of a molecule into its constituent atoms.

A small atom will have a large nuclear force of attraction with the electrons on the outermost shell of the nucleus, hence more bond energy would be required to break the bond.

It is given that the energy required to break one mole of $Cl-Cl$ bond in ${Cl}_{2}$ is 242 kJ. And we are required to find out the energy required to break a single $Cl-Cl$ bond and its wavelength.
We know that in 1 mole, the no. of molecules is equal to the Avogadro number which is $6.023 \times {10}^{23}$.

Therefore, 1 mole = $6.023 \times {10}^{23}$ molecules
Energy required for 1 mole = 242 kJ

Thus, $Energy\quad required\quad for\quad 1\quad molecule\quad =\cfrac { 242\quad \times \quad { 10 }^{ 3 } }{ 6.023\quad \times \quad { 10 }^{ 23 } }$
$\implies Energy\quad required\quad for\quad 1\quad molecule\quad =\quad 40.18\quad \times \quad { 10 }^{ -20 }\quad J$

Therefore, the energy required to break 1 molecule of ${Cl}_{2}$ is $40.18 \times {10}^{-20} J$.
Thus, the wavelength can be calculated as follows.
$\lambda = \cfrac {hc}{E}$,
where, $\lambda is the wavelength$, h is the Planck's constant which is equal to $6.626 \times {10}^{-34}$, E is the energy of 1 molecule, and c is the speed of light which is equal to $3 \times {10}^{8} m$.

Substituting these values in the above equation, we get,
$\lambda \quad =\quad \cfrac { 6.626\quad \times { \quad 10 }^{ -34 }\quad \times \quad 3\quad \times \quad { 10 }^{ 8 } }{ 40.18\quad \times { \quad 10 }^{ -20 } }$
$\implies \lambda \quad =\quad 494\quad \times \quad { 10 }^{ -9 }m\quad =\quad 494\quad nm$
So, the correct answer is “Option B”.

Note: The wavelength that is found out here represents the wavelength of the photon or light which has the energy $40.18 \times {10}^{-20} J$ to break one molecule of ${Cl}_{2}$. Take care of the units while calculating such huge numbers. It can be a tedious thing but if the units are not taken care of, we might end up getting the wrong answers.