Question

The bonds in beryllium hydride $\left({\mathrm{BeH}}_2\right)$ molecules are polar, and yet the dipole moment of the molecule is zero. Explain.

Short answer

The linear geometry causes the bond dipoles to cancel each other, resulting in zero dipole moment.

Step-by-step solution

Understanding Molecule Polarity

Beryllium hydride, ${\mathrm{BeH}}_2$, is a linear molecule. It consists of a central beryllium atom bonded to two hydrogen atoms. Each Be-H bond is polar because there is a difference in electronegativity between beryllium and hydrogen, which causes a shift in electron density towards the hydrogen atoms.

Analyzing Molecular Geometry

The geometry of ${\mathrm{BeH}}_2$ is linear, with bond angles of 180 degrees. This configuration is essential in determining the overall dipole moment of the molecule as the molecule's shape influences how individual bond dipoles combine.

Summing Up The Dipole Moments

Although each $\mathrm{Be}-\mathrm{H}$ bond has a dipole moment, the linear arrangement of ${\mathrm{BeH}}_2$ means that the dipole moments are equal in magnitude but opposite in direction. As a result, these dipole moments cancel each other out, resulting in a net dipole moment of zero.

Key concepts

Beryllium Hydride

Beryllium hydride, ${\mathrm{BeH}}_2$, is a compound made up of one beryllium atom bonded to two hydrogen atoms. This molecule features a central beryllium atom to which the hydrogen atoms are directly attached. While typically $\mathrm{Be}$ is a light metal, in ${\mathrm{BeH}}_2$, it forms covalent bonds with hydrogen. Beryllium, being in Group 2 of the periodic table, is less electronegative compared to hydrogen. This results in the $\mathrm{Be}-\mathrm{H}$ bonds being polar. In simple terms, a polar bond is when there is an unequal sharing of electrons between two atoms, which occurs here as the electron density shifts towards the hydrogen atoms. Each of these individual bonds possesses a small dipole moment due to their polarity. However, the molecular geometry of ${\mathrm{BeH}}_2$ plays an important role in determining the overall molecule's polarity.

Dipole Moment

The dipole moment of a molecule is a measure of the overall polarity of the molecule. It arises from the differences in electronegativity between the atoms bonded together. For a simplistic understanding, think of a dipole moment as an arrow pointing from the positive part to the negative part of the molecule. In ${\mathrm{BeH}}_2$, each $\mathrm{Be}-\mathrm{H}$ bond has a dipole moment. However, because the molecule is linear, these dipole moments are in opposite directions and are equal in magnitude. When two dipole moments of equal strength point in opposite directions, they cancel each other out.

• This is why despite having polar bonds, the dipole moment of the entire ${\mathrm{BeH}}_2$ molecule is zero.

This concept of cancelation is crucial to understand why a molecule like ${\mathrm{BeH}}_2$ does not behave as a polar molecule.

Molecular Geometry

Molecular geometry refers to the shape of a molecule, which is determined by the spatial arrangement of the atoms. In the case of ${\mathrm{BeH}}_2$, it has a linear geometry. As mentioned earlier, the $\mathrm{Be}-\mathrm{H}$ bonds are arranged at a 180-degree angle from each other. This linear layout is responsible for the dipole moments directly opposing each other, leading to their cancelation. The overall geometry helps predict how the individual bond dipoles sum up. Understanding that the net dipole moment is zero highlights the importance of molecular geometry in influencing molecular polarity.
Besides affecting polarity, molecular geometry is essential in defining other properties like reactivity and intermolecular forces that the molecule might exhibit.

Electronegativity

Electronegativity is a chemical property that describes an atom's ability to attract and bind with electrons. In a bond, the more electronegative atom will attract electrons more strongly. In ${\mathrm{BeH}}_2$, beryllium $\mathrm{Be}$ has a lower electronegativity compared to hydrogen $\mathrm{H}$. This difference is what leads to the formation of polar bonds in which hydrogen, being more electronegative, pulls electron density towards itself. The polar nature of each $\mathrm{Be}-\mathrm{H}$ bond is critical because it creates partial positive and negative charges within the molecule. But, the combined effect on the total molecule's polarity cannot be overstated. In ${\mathrm{BeH}}_2$, these polarities do not result in a net dipole moment due to the linear geometry.

• This highlights how both electronegativity and molecular geometry together determine the overall dipole moment of a molecule.

Understanding electronegativity helps us break down why molecules have polar or nonpolar characteristics.