Given the dipole moment of water (1.84 D) and the H-O-H bond angle (104.45^∘), justify the state

step 1 M equals to root over of mu1 square plus mu1 square plus 2 mu1, mu1, cos alpha. In H2O, only two

Given the dipole moment of water (1.84 D) and the H-O-H bond...

Given the dipole moment of water $(1.84 \mathrm{D})$ and the $\mathrm{H}-\mathrm{O}-\mathrm{H}$ bond angle $\left(104.45^{\circ}\right)$, justify the statement in Problem 1.42b that the bond dipole moment of the $\mathrm{O}-\mathrm{H}$ bond is $1.52 \mathrm{D}$.

Key Concepts

Molecular Dipole Moment

This concept refers to the overall measure of the separation of charge within a molecule. It is a vector quantity calculated by considering both the magnitude and direction of individual bond dipole moments. The molecular dipole moment helps determine how the molecule interacts with external electric fields and is derived from the vector sum of all individual bond dipoles in the molecule.

Bond Dipole Moment

A bond dipole moment arises from the electronegativity difference between two bonded atoms, leading to an uneven distribution of electron density along the bond. The bond dipole is represented as a vector pointing from the less electronegative atom (partial positive charge) to the more electronegative atom (partial negative charge) and contributes to the overall molecular dipole moment.

Molecular Geometry

Molecular geometry describes the three?dimensional arrangement of atoms within a molecule. In the context of water, the specific bond angle between the hydrogen atoms determines how the individual bond dipoles combine. The non-linear geometry means that the individual dipole vectors do not cancel each other completely, resulting in a net dipole moment.

Vector Addition of Dipole Moments

This concept involves the mathematical addition of bond dipole moment vectors, taking both magnitude and direction into account. In a molecule with more than one bond, like water, the bond angles influence the resultant dipole moment. By resolving each bond dipole into components and summing them, one can explain how the magnitude of each bond dipole relates to the overall measured molecular dipole moment.

Please give Ace some feedback