Question

It takes 242. kJ/mol to break a chlorine-chlorine single bond. Calculate the maximum wavelength of light for which a chlorine-chlorine single bond could be broken by absorbing a single photon. Round your answer to 3 significant digits. Il nm x 5 ?

Answer 1

Consider a Cl - Cl bond. The bond dissociation energy of Cl-Cl bond is 242.0 k J / mol i.e 242000 J / mol.

This is the energy required to break 6.022 $\times$ 10 ²³ Cl-Cl single bonds. Hence, energy required to break single Cl-Cl bond = ( 242000 J / mol. ) ( 1 mol / 6.022 $\times$ 10 ²³ ) = 4.019 $\times$ 10 ^-19 J

We know that, energy (E) of single photon is given as E = h C /

Where, h is a planck constant , C is a velocity of light and is a wavelength of light.

From above relation , it is clear that energy & wavelength are inversely proportional to each other.

4.019 $\times$ 10 ^-19 J is the minimum energy required to break single Cl-Cl bond, hence wavelength associated with this energy will be maximum wavelength required to break the bond.

$\therefore$ maximum = h C / E

$\therefore$ maximum = ( 6.626 $\times$ 10 ^{- 34} J . s ) ( 3.00 $\times$ 10 ⁸ m /s ) / 4.019 $\times$ 10 ^-19 J

$\therefore$ maximum = 4.946 $\times$ 10 ^{- 07} m

We have relation, 1 m = 10 ⁹ nm .

$\therefore$ maximum = 4.946 $\times$ 10 ^{- 07} m ( 10 ⁹ nm / 1 m ) = 494.6 nm = 495 nm

ANSWER : 495 nm