Question

(a) The \(\mathrm{PH}_{3}\) molecule is polar. How does this offer experimental proof that the molecule cannot be planar? (b) It turns out that ozone, \(\mathrm{O}_{3}\), has a small dipole moment. How is this possible, given that all the atoms are the same?

Short answer

(a) PH3 is a polar molecule due to the higher electronegativity of phosphorus compared to hydrogen. If the molecule were planar, the bond dipoles would cancel each other out, resulting in a nonpolar molecule. However, since PH3 is polar, its structure cannot be planar. (b) Ozone (O3) has a small dipole moment due to its resonance structure, with double and single bonds alternating between the oxygen atoms. Although all atoms are the same, the V-shaped structure creates a localized difference in electron density, leading to slight polarity.

Step-by-step solution

Understand Polarity and Structure of PH3

In order to answer part (a), we need to understand the basics of molecular polarity. A molecule is polar when there is an uneven distribution of electron density, leading to a net dipole moment. For a molecule to be planar, all its atoms must lie in the same plane. PH3 consists of one phosphorus atom and three hydrogen atoms. Since phosphorus has higher electronegativity than hydrogen, electron density tends to accumulate towards the phosphorus atom, creating a dipole moment. This uneven distribution of electron density implies that the molecule is polar.

Prove that PH3 cannot be planar with its polarity

If PH3 were planar, the bond dipoles from the hydrogen atoms would cancel each other out because they would be evenly distributed with respect to the phosphorus atom, resulting in a nonpolar molecule. However, since we know that PH3 is polar, this scenario cannot happen. Therefore, the molecular structure of PH3 cannot be planar.

Understand the Polarity and Structure of O3

In order to answer part (b), we need to discuss the molecular structure of ozone (O3). O3 consists of three oxygen atoms. It has a resonance structure, where the three oxygen atoms are bonded in a V-shape with double and single bonds alternating between the atoms. The resonance structure suggests that each double and single bond is equal and contributes to the dipole moment.

Explain the small dipole moment in O3

Although all three oxygen atoms are the same, the uneven distribution of electron density due to the resonance structure leads to a small dipole moment in O3. The overall dipole moment would be small because the electrons are shared equally among the atoms, but the V-shaped structure creates a localized difference in electron density. This difference is what leads to the slight polarity in ozone.

Key concepts

Dipole Moment

A dipole moment arises when there is an unequal distribution of electron density in a molecule, resulting in a separation of positive and negative charges. This separation gives the molecule a polar nature.
In molecules like phosphine (\( \text{PH}_3 \)), even though phosphorus and hydrogen do not have a huge electronegativity difference, the arrangement of atoms matters. Phosphine has a lone pair of electrons on the phosphorus atom. This lone pair significantly contributes to the overall polarity by affecting how electron density is distributed in the molecule.
The dipole moment is a vector quantity, which means it has both magnitude and direction. In \( \text{PH}_3 \), the dipole moment points towards the phosphorus atom, making this molecule polar. If \( \text{PH}_3 \) were planar, the vectors from each \( \text{H-P} \) bond could have canceled out. However, the actual shape ensures a net dipole moment, confirming its polarity.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. It plays a crucial role in determining the molecule's physical and chemical properties, including its dipole moment.
For example, phosphine (\( \text{PH}_3 \)) is not planar due to its geometry, which is influenced by the lone pair on the phosphorus atom. This lone pair forces the hydrogen atoms into a trigonal pyramidal shape, resulting in a polar molecule.
Ozone (\( \text{O}_3 \)), on the other hand, has a bent molecular shape. Despite having three identical oxygen atoms, the geometric arrangement results in a small net dipole moment. The unequal sharing of electron density creates a localized region of negative charge that contributes to the molecule's polarity. Hence, even molecules that involve atoms of the same type can be polar due to molecular geometry.

Resonance Structure

Resonance structures are different Lewis structures for the same molecule that depict the possible arrangements of electrons. They help highlight molecules like ozone (\( \text{O}_3 \)) where the reality is a hybrid of all possible structures.
In ozone, resonance structures illustrate alternating single and double bonds between the oxygen atoms. This sharing of electrons among different configurations stabilizes the molecule. The resonance hybrid, or the average of these structures, contributes to the understanding of ozone's slight polarity.
Despite the equal sharing of electrons in theory, in practice, resonance creates an electron distribution where the regions connected by double bonds tend to have more electron density. This gives ozone a small, but crucial, dipole moment. In this manner, resonance structures are vital for visualizing real electron distribution and understanding a molecule’s polarity.