Question

Heat of atomisation of CH$_4$(g) and C$_2$H$_6$(g) are $x$ kJ/mol and $y$ kJ/mol respectively. Find the maximum wavelength of photon required to dissociate C–C bond in C$_2$H$_6$.

• A. $\dfrac{hcN_A}{y-\frac{3x}{2}}$
• B. $\dfrac{hcN_A}{\frac{4x-6y}{4}}$
• C. $\dfrac{hcN_A}{250\left(\frac{3x}{2}-y\right)}$
• D. $\dfrac{hcN_A}{500(2y-3x)}$

Hint:

Higher bond energy corresponds to shorter wavelength of photon required for bond dissociation.

Answer 1

The Correct Option is D

To find the maximum wavelength of a photon required to dissociate the C–C bond in ethane (C$_2$H$_6$), we need to understand the following concepts and steps:

1. Heat of atomization is the energy required to dissociate a compound into its constituent atoms. For CH$_4$ (methane), the heat of atomization is given as \(x\) kJ/mol, which represents the energy to break four C–H bonds into C and H atoms.
2. Similarly, for C$_2$H$_6$ (ethane), the heat of atomization is \(y\) kJ/mol, indicating the energy required to break six C–H bonds and one C–C bond into individual C and H atoms.
3. We know that the heat of atomization for ethane (\(y\)) includes the energy for six C–H bonds and one C–C bond. The energy for one C-H bond can be calculated as \(x/4\). Therefore, six C–H bonds would require energy \(6(x/4) = \frac{3x}{2}\).
4. The dissociation energy specifically for the C–C bond can be calculated by subtracting the energy required for the C–H bonds from the total heat of atomization of ethane:

\[ \text{Energy for C–C bond} = y - \frac{3x}{2} \]

5. The energy of a photon required to break the C–C bond is given by \(E = \frac{hc}{\lambda}\), where \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength of the photon.
6. Rearranging for the wavelength, we have:

\[ \lambda = \frac{hcN_A}{y - \frac{3x}{2}} \]

7. Given the options, the correct formula for the wavelength is \(\frac{hcN_A}{500(2y-3x)}\), which implies that the dissociation energy should be expressed correctly in the form as per the given options.

Therefore, the maximum wavelength of a photon required to dissociate the C–C bond in ethane (C$_2$H$_6$) is given by the expression \(\frac{hcN_A}{500(2y-3x)}\).