How is electric dipole moment calculated for a molecule?

The calculation of a molecule's net electric dipole moment depends on its geometry and the polarity of its individual bonds. It is the vector sum of all individual bond dipole moments within the molecule.

1. For Diatomic Molecules (e.g., HCl, CO):
   The calculation is simple. The dipole moment is the product of the partial charge (δ) on one of the atoms and the bond length (d).
   • Formula: p = δ × d
   • The vector points from the partially positive (δ+) atom to the partially negative (δ-) atom (in the chemistry convention, which is often used in this context). For example, in HCl, the vector points from H to Cl.
2. For Polyatomic Molecules (e.g., H₂O, CO₂):
   This requires considering the molecule's 3D shape (VSEPR theory).
   • Step 1: Determine the dipole moment vector for each individual bond (e.g., for each O-H bond in water).
   • Step 2: Add these individual bond vectors together using vector addition (head-to-tail), considering the angles between them.
   • Example (H₂O): Water has a "bent" shape (approx. 104.5°). The two O-H bond dipoles (pointing from H to O) are at an angle. When added together, they result in a large net dipole moment (p ≠ 0). This makes water a highly polar molecule.
   • Example (CO₂): Carbon dioxide has a "linear" shape (O=C=O). The two C=O bond dipoles are equal in strength but point in exact opposite directions (180° apart). As a result, they cancel each other out perfectly, and the net dipole moment for CO₂ is zero (p = 0). This makes CO₂ a non-polar molecule, even though its individual bonds are polar.