Question

It has been found that a gaseous iodine molecule just dissociates into iodine atoms after absorption of light at wavelength $4995{{A}^{{}^\circ }}$. The energy required to dissociate 1 mole of iodine molecules is
(1) 52.2 Kcal/mole
(2) 93.4 Kcal/mole
(3) 63.4 Kcal/mole
(4) 57.3 Kcal/mole

Answer 1

Hint: Recollect the basic concepts of spectroscopy. We have been given a wavelength at which iodine molecules split into iodine atoms. We need to find the energy of dissociation for one mole of iodine molecules. Use the formula, $E=h\nu $ and calculate the energy for one mole of dissociation of iodine molecules.

Complete step by step solution:
- Let’s have a look at the question. It says gaseous iodine molecules dissociate into iodine atoms after absorption of electromagnetic radiation having the wavelength $4995{{A}^{{}^\circ }}$.
- We have been given a wavelength at which dissociation takes place.
- Energy is directly proportional to frequency and the formula is given as, $E=h\nu $ where h is Planck’s constant.
- For dissociation of one molecule, $E=h\nu $
- For dissociation of one mole, we will have to multiply energy by Avogadro’s number because one mole consists of Avogadro’s number of molecules.
- So now we get, $E=h\nu \times {{N}_{A}}$ …. (1)
- Now, we know that frequency is inversely proportional to wavelength and so we have the relation, $\nu =\dfrac{c}{\lambda }$ where c is the velocity of light …. (2)
- From (1) and (2) we get, $E=\dfrac{hc}{\lambda }\times {{N}_{A}}$
- Now substituting the values we get,
\[\begin{align}
  & E=\dfrac{hc}{\lambda }\times {{N}_{A}} \\
 & =\dfrac{6.626\times {{10}^{-34}}Js\times 3\times {{10}^{8}}m{{s}^{-1}}\times 6.023\times {{10}^{23}}mo{{l}^{-1}}}{4945\times {{10}^{-10}}m} \\
 & =0.024\times {{10}^{7}}J/mol \\
 & =2.4\times {{10}^{5}}J/mol \\
 & E=240kJ/mol
\end{align}\]
- Now, in the options the unit used is kcal/mol so we need to convert energy in terms of kilocalories per mole.
1kJ/mol = 0.239kcal/mol
- Therefore, $E=240\times 0.239kcal/mol=57.36kcal/mol$
- Therefore, the energy required to dissociate 1 mole of iodine molecules is 57.36kcal/mol.

- Therefore, the answer is option (D).

Note: Remember energy for dissociation of one molecule is $E=h\nu $. For one mole, multiply energy with Avogadro’s number. 1kJ/mol = 0.239kcal/mol is the conversion factor for kilojoules per mole to kilocalories per mole.