Calculating H₂ Dissociation Energy

The dissociation energy of a molecule is the energy required to break it into its constituent neutral atoms.

For the hydrogen molecule ($H_2$), dissociation means splitting it into two hydrogen atoms (H).

The energy balance can be represented as:

$ \text{Energy}(H_2 \text{ molecule}) = 2 \times \text{Energy}(H \text{ atom}) - \text{Dissociation Energy} $

Rearranging the formula to find the dissociation energy ($D_{H_2}$):

$ D_{H_2} = 2 \times \text{Energy}(H \text{ atom}) - \text{Energy}(H_2 \text{ molecule}) $

Applying Given Values

We are given:

• Ground state energy of H atom ($E_H$): -13.6 eV
• Ground state energy of $H_2$ molecule ($E_{H_2}$): -31.7 eV

Step-by-Step Calculation

1. Calculate the total energy of two separate H atoms:

   $ 2 \times E_H = 2 \times (-13.6 \text{ eV}) = -27.2 \text{ eV} $

2. Use the formula to find the dissociation energy:

   $ D_{H_2} = (2 \times E_H) - E_{H_2} $ $ D_{H_2} = (-27.2 \text{ eV}) - (-31.7 \text{ eV}) $ $ D_{H_2} = -27.2 \text{ eV} + 31.7 \text{ eV} $

3. Final Result:

   $ D_{H_2} = 4.5 \text{ eV} $

The calculated dissociation energy for the $H_2$ molecule is 4.5 eV.