Question

The heat of atomization of methane and ethane are 360 kJ/mole and 620 kJ/mole, respectively. The longest wavelength of light capable of breaking the C-C bond is :
(Avogadro number = $6.023X{{10}^{23}},h=6.62X{{10}^{-34}}Js$ )
(A) $2.48X{{10}^{4}}nm$
(B) $1.49X{{10}^{3}}nm$
(C) $2.48X{{10}^{3}}nm$
(D) $1.49X{{10}^{4}}nm$

Answer 1

Hint: Every spontaneous process is the formation of new products. Out of All processes, some are the evaluation of energy, and some are released during the process. There is a change in enthalpy that will observe during the completion of the process.

Complete step by step solution:
The heat of atomization or enthalpy of atomization is the change in energy gained when one mole of bonds is completely broken atoms in the gas phase. The heat of atomization is always an endothermic reaction.
The heat of atomization of methane (given) = 360 kJ/mol
This value belongs to breaking four C-H bonds in methane.
Hence, the heat required for breaking one C-H bond = $\dfrac{360kJ/mol}{4}=90kJ/mol$
Similarly, given that the heat of atomization of ethane = 620 kJ/mol
This value is related to six C-H bonds and one C-C bond in ethane.
The heat required to breaking one C-C bond = \[620-6X90\] = 80 kJ/mol
Hence, 80 kJ energy is required to break one C-C bond per one mole.
For one single bond, the required energy by Avogadro's number, E = $\dfrac{80X1000}{6.023X{{10}^{23}}}$ -- (1)
The energy-related to wavelength, $E=\dfrac{hc}{\lambda }$ --(2)
Equation (1) and (2) represents same energy equation,
$\dfrac{80X1000}{6.023X{{10}^{23}}}=\dfrac{6.62X{{10}^{-23}}X3X{{10}^{8}}}{\lambda }$
$\lambda =1.49X{{10}^{-6}}m=1.49X{{10}^{3}}nm$
Hence, The longest wavelength of light capable of breaking the C-C bond = $1.49X{{10}^{3}}nm$

The correct answer is option B


Note: When a process of dissolving one mole of a substance in a solution, the enthalpy change is called enthalpy of solution. The enthalpy change observed when a substance transforms from one phase to another phase is enthalpy change during phase transition.