Question

A common way of initiating certain chemical reactions with light involves the generation of free halogen atoms in solution. if δh for the reaction cl2(g) → 2cl(g) is 242.8 kj/mol, what is the longest wavelength of light that will produce free chlorine atoms in solution?

Answer 1

Answer: The longest wavelength of light that will produce free chlorine atoms in solution is 493 nm.

Explanation:

$Cl_2\overset{h\nu}\rightarrow Cl^-,Delta H_{rxn}=242.8kJ/mol$

Energy required to produce free chlorine atoms from one mole of chlorine gas :

= 242.8kJ = $242.8\times 1000=242800 Joules$ (1kJ=1000J)

1 mole = $6.022\times 10^{23}$ molecules

For $6.022\times 10^{23}$ molecules = 242,800 Joules

For one molecule of chlorine gas =  $\frac{242800 Joules/mol}{6.022\times 10^{23} mol^{-1}}=40,318.83\times 10^{-23}Joules$

According to photoelectric equation:

$E=h\nu=\frac{hc}{\Lambda }$

E = Energy of the photon of light used to produce free chlorine atoms

$\nu$= frequency of the light used to produce free chlorine atoms

h = Planck's constant =$6.626\times 10^{-34}J.s$, c = speed of light=$3\times 10^8 m/s$

$\lambda$ = wavelength of the light used to produce free chlorine atoms

$40,318.83\times 10^{-23}J=\frac{hc}{\Lambda }=\frac{6.626\times 10^{-34} J.s\times 3\times 10^8 m/s}{\lambda }$

$\lambda=0.0004930203\times 10^{-3} m=493.0203\times 10^{-9} m=493 nm$

The longest wavelength of light that will produce free chlorine atoms in solution is 493 nm.