Question

Determine whether (a) \(\mathrm{PCl}_{5}\) and (b) \(\mathrm{H}_{2} \mathrm{CO}\) (C double bonded to \(\mathrm{O}\) ) are polar.

Short answer

(a) PCl5 is nonpolar; (b) H2CO is polar.

Step-by-step solution

Determine the Molecular Shape of PCl5

To determine if a molecule is polar, start by identifying its molecular geometry. PCl5 has a central phosphorus atom surrounded by five chlorine atoms. According to VSEPR theory, this arrangement results in a trigonal bipyramidal shape.

Analyze Symmetry in PCl5

A molecule is nonpolar if it is symmetric and all bonds are of the same type, which allows the dipoles to cancel out. In PCl5, the trigonal bipyramidal geometry is symmetric with equivalent P-Cl bonds. Therefore, their dipoles cancel out, making PCl5 nonpolar.

Determine the Molecular Shape of H2CO

For determining the polarity of H2CO, first observe its shape. This molecule has a central carbon atom bonded to two hydrogens and one oxygen atom, with the carbon double-bonded to oxygen. This results in a trigonal planar shape.

Analyze Bond Polarities in H2CO

The C=O bond is significantly polar due to the difference in electronegativity between C and O. The molecule does not have a symmetric arrangement of equivalent bonds that could cancel out these dipoles, leading to an overall dipole moment. Hence, H2CO is polar.

Key concepts

VSEPR Theory

Molecular shape is a key factor in determining the polarity of a molecule, and the VSEPR (Valence Shell Electron Pair Repulsion) Theory is crucial for predicting these shapes. The VSEPR theory helps us understand how electron pairs around the central atom repel each other to create the 3D shape of the molecule.
The principle is simple: electron pairs arrange themselves as far apart as possible to minimize repulsion between them.
For instance, a molecule with two regions of electron density will adopt a linear shape, giving a straight line.

• The shape affects how dipoles either add up to create a polar molecule or cancel out for nonpolar molecules.
• Understanding these shapes allows chemists to predict how a molecule will interact with others.

The VSEPR theory is an essential tool in the chemist's toolbox for understanding molecular interactions.

Trigonal Bipyramidal

The trigonal bipyramidal shape is quite fascinating and can be found in molecules with five bonds around a central atom.
A classic example is \(\mathrm{PCl}_5\), which features phosphorus at the center of five chlorine atoms. This geometry comprises two different types of positions:

• Three equatorial positions, which form a planar triangle around the central atom.
• Two axial positions, which are perpendicular to the plane formed by the equatorial atoms.

These arrangements create a 3D shape where any differences in the surrounding atoms can affect the molecule's symmetry and polarity. However, when all bonds are identical, as in the case of \\mathrm{PCl}_5\, the molecular symmetry allows for the cancellation of individual dipole moments, making the overall molecule nonpolar.

Trigonal Planar

The trigonal planar shape is a basic yet important structure in chemistry.
It occurs when three atoms are bonded to a central atom, all lying in one plane, forming a triangle. This geometry is seen in molecules like \(\mathrm{H}_{2}\mathrm{CO}\) (formaldehyde), where the central carbon atom is double-bonded to oxygen and single-bonded to two hydrogen atoms. This gives the molecule its trigonal planar shape.

• The C=O bond is highly polar due to the difference in electronegativity between carbon and oxygen.
• The trigonal planar shape does not allow for perfect cancellation of the individual bond dipoles since one side of the molecule has a different type of bond.

As a result, formaldehyde becomes polar because the negative charge is skewed toward the oxygen.

Dipole Moment

The dipole moment is a measure of the separation of positive and negative charges in a molecule and a key indicator of polarity.
Dipole moments occur due to differences in electronegativity between bonded atoms.

• In a molecule, the atom with higher electronegativity will attract the shared electrons more strongly than the other atom, resulting in a polar bond.
• These polar bonds can contribute to an overall dipole moment for the molecule, depending on the spatial arrangement of the bonds.

If a molecule’s geometry is symmetric, as with \(\mathrm{PCl}_5\), the dipole moments cancels out, resulting in a nonpolar molecule. However, in asymmetric molecules like \(\mathrm{H}_{2}\mathrm{CO}\), the difference in bond polarities leads to a net dipole moment, making the molecule polar. Knowing the dipole moment helps in predicting the behavior of a molecule in an electric field and in chemical reactions.