Which Color Breaks Cl₂ Bond? Visible Spectrum NSEC Olympiad

The light frequency required to break the Cl-Cl bond can be determined using bond dissociation energy and Planck's equation. A chemical bond remains stable until it absorbs a photon with sufficient energy to overcome its bond dissociation energy.  

By converting the bond energy into joules per molecule, calculating the corresponding frequency, and then determining the wavelength, we can identify the colour of visible light capable of supplying the required energy. This concept is commonly tested in NSEC and other chemistry Olympiad examinations. 

Calculation of Light Frequency for Cl-Cl Bond Dissociation

Calculating the light frequency required for Cl-Cl bond dissociation involves converting bond energy into energy per molecule and applying Planck’s equation. This method helps you determine the frequency and wavelength of light capable of breaking the chlorine bond effectively and accurately. 

 Problem Statement

Calculate the frequency of the light required to break the Cl-Cl bond.

Given Data

• Bond Dissociation Energy (BDE) = 58 kilocalories per mole (kcal/mol)

• Conversion Factor: 1 kilocalorie (kcal) = 4.18 × 10^3 Joules (J)

• Planck's constant (h) = 63 × 10^-13 (as used in the calculation, implicitly in J.s)

• Speed of light (c) = 3 × 10^8 m/s

Core Formulas

• Energy (E) = Planck's constant (h) × frequency (ν)

• Therefore, frequency (ν) = Energy (E) / Planck's constant (h)

• Speed of light (c) = wavelength (λ) × frequency (ν)

Solution Steps

1. Convert Bond Dissociation Energy from kilocalories per mole to Joules per particle:

• First, convert kilocalories to Joules per mole:
  E (J/mol) = 58 kcal/mol × (4.18 × 10^3 J / 1 kcal)
  E (J/mol) = 242440 J/mol

• Next, convert Joules per mole to Joules per particle by dividing by Avogadro's number (6.02 × 10^23 particles/mol):
  E (J/particle) = (242440 J/mol) / (6.02 × 10^23 particles/mol)
  E ≈ 4.03 × 10^-19 J/particle

2. Calculate the frequency (ν) of the light:

• Using the formula ν = E / h:
  ν = (4.03 × 10^-19 J) / (63 × 10^-13)
  ν ≈ 6.08 × 10^14 Hz

3. Calculate the wavelength (λ) of the light (for further interpretation):

• Using the formula λ = c / ν:
  λ = (3 × 10^8 m/s) / (6.08 × 10^14 Hz)
  λ ≈ 493 nanometers (nm)

Interpretation

The calculated wavelength is approximately 493 nm, which lies in the blue-green region of the visible spectrum. A photon of this wavelength possesses approximately the same energy as the Cl-Cl bond dissociation energy. Therefore, if chlorine molecules absorb photons of this energy, the Cl-Cl bond can dissociate.