The heat of atomisation of methane and ethane are x kJ mol^-1 and y kJ mol^-1 respectively. The longest wavelength () of

Question

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

Accepted Answer

Given: Heat of atomisation of methane is $x \, \text{kJ mol}^{-1}$ and that of ethane is $y \, \text{kJ mol}^{-1}$ .

Find: The longest wavelength $\lambda$ of light capable of breaking the C–C bond.

Bond energy concept: Longest wavelength corresponds to minimum energy required to break a bond.

Step 1: Heat of atomisation of methane gives C–H bond energy, while that of ethane includes both C–H bonds and one C–C bond.

Step 2: Ethane has $6$ C–H bonds and $1$ C–C bond. Hence C–C bond energy is proportional to $4y - 6x$ .

Step 3: Use the relation between photon 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)}

Therefore, the correct option is D.

Answer

Step-by-step solution

Common mistakes

Practice more Enthalpies (Bond, Combustion, Formation…) questions

Related questions