The heat of atomization of methane and ethane are 360 kJ/mol and 620 kJ/mol, respectively

• Chemical Thermodynamics

The heat of atomization of methane and ethane are 360 kJ/mol and 620 kJ/mol, respectively. The longest wavelength of light capable of breaking the C - C bond is (Avogadro number = 6.02×10²³, h = 6.62×10^-34 J s):

1. 1.49×10³ nm
2. 2.48×10³ nm
3. 2.48×10⁴ nm
4. 1.49×10⁴ nm

Solution

For methane, CH₄ (g) → C(g) + 4H(g)

4 x E_C–H = 360 kJ/mol 

⇒ E_C–H = 90 kJ/mol

For ethane, C₂H₆ (g) → 2C(g) + 6H(g)

E_C–C + 6 x E_C–H = 620 kJ/mol

E_C–C + 6 x 90 = 620 kJ/mol

⇒ E_C–C = 80 kJ/mol

N_A × hc/λ = = 80 × 1000 J

λ = (6.02×10²³ × 6.62×10^-34 × 3×10⁸)/80000

λ = 1.49 × 10³ nm

The correct option is A.