Question

The heat of atomisation of methane and ethane are \( x \) kJ mol\(^{-1}\) and \( y \) kJ mol\(^{-1}\) respectively. The longest wavelength (\( \lambda \)) of light capable of breaking the C–C bond can be expressed in SI unit as:

• A. $\dfrac{hc}{1000}\left(\dfrac{y-6x}{4}\right)^{-1}$
• B. $\dfrac{N_A hc}{250(y-6x)}$
• C. $N_A hc\left(\dfrac{y-6x}{4}\right)^{-1}$
• D. $\dfrac{N_A hc}{250(4y-6x)}$

Hint:

Longest wavelength corresponds to minimum energy required to break a bond.

Answer 1

The Correct Option is D

Step 1: Bond energy concept.
Heat of atomisation of methane gives C–H bond energy, while that of ethane includes both C–H and one C–C bond.
Step 2: Extracting C–C bond energy.
Ethane has 6 C–H bonds and 1 C–C bond. Hence C–C bond energy is proportional to $(4y - 6x)$.
Step 3: Relation between energy and wavelength.
\[ E = \frac{hc}{\lambda} = \frac{(4y-6x)\times 10^3}{N_A} \]
Step 4: Rearranging.
\[ \lambda = \frac{N_A hc}{250(4y-6x)} \]