Question

The longest wavelength of light with enough energy to break the Cl-Cl bond in Cl2(g) is 495 nm.

Answer 1

Explanation:

The longest wavelength of light with enough energy to break the Cl-Cl bond = 495 nm = $495\times 10^{-9} m$

1) The frequency of the light:

$\lambda =495\times 10^{-9} m$

$\nu=\frac{c}{\lambda }$

c = speed of light= $3\times 10^8 m/s$

$\nu=\frac{3\times 10^8 m/s}{495\times 10^{-9} m}$

$=6.0606\times 10^{14) s^{-1}$

The frequency of the light is $6.0606\times 10^{14) s^{-1}$.

2)The energy of a photon of the light:

The energy of the photon is given by : E

$E=h\nu$

h =  Planck's constant = $6.626\times 10^{-34} J/s$

$E=6.626\times 10^{-34} J/s\times 6.0606\times 10^{14) s^{-1}$

$=4.016\times 10^{-19} J$

The energy of a photon of the light is $4.016\times 10^{-19} J$.

3) The minimum energy of the Cl-Cl bond :

To break single bond of Cl-Cl bond we need energy E= $4.016\times 10^{-19} J$

1 mole = $N_A=6.022\times 10^{23} mol^{-1}$

So, in order to break 1 mole of Cl-Cl bond we will need:

$E\times N_A=4.016\times 10^{-19} J\times 6.022\times 10^{23} mol^{-1}$

$=241,828.92 J/mol=241,828.92\times 0.001 kJ/mol=241.83 kJ/mol$

The minimum energy of the Cl-Cl bond is 241.83 kJ/mol.