Question

(a) The \(\mathrm{PH}_{3}\) molecule is polar. Does this offer experimental proof that the molecule cannot be planar? Explain. (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) The $\mathrm{PH}_{3}$ molecule has a trigonal pyramidal geometry and a small net molecular dipole due to the non-cancellation of bond dipoles and the slight difference in electronegativity values (2.19 for P and 2.20 for H). This provides experimental evidence against it being planar. (b) Ozone, $\mathrm{O}_{3}$, has a bent geometry and is a resonance hybrid with an average bond characteristic between single and double bonds. This results in an unequal distribution of electrons between the central oxygen and two terminal oxygens, giving rise to a small dipole moment, even though all atoms are the same.

Step-by-step solution

Understand the PH3 molecule's polarity

The PH3 molecule consists of a central phosphorus (P) atom bonded to three hydrogen (H) atoms. To determine if the molecule is polar, we need to examine both the geometry of the molecule and the electronegativity difference between the P and H atoms.

Assess the geometry of the PH3 molecule

A central component in this assignment is the geometrical shape of the molecules. PH3 has 3 regions of electron density (single bonds) around the central phosphorus atom. According to VSEPR (valence shell electron pair repulsion) theory, these regions of electron density will assume a tetrahedral arrangement to minimize electron-electron repulsion, making the P-H bonds form an angle of about 109.5º between each other. As a result, PH3 has a trigonal pyramidal geometry, which is not a planar shape.

Evaluate electronegativity differences and molecular dipoles

The next step is to consider the electronegativity values for both phosphorus and hydrogen. The electronegativity of phosphorus is 2.19, while the electronegativity of hydrogen is 2.20. The difference in electronegativity values is very small (0.01), suggesting very weak polar bonds. However, since the geometry of the PH3 molecule is trigonal pyramidal, the bond dipoles do not cancel, giving rise to a net molecular dipole.

Conclude PH3's planarity from its polarity

In conclusion, since the PH3 molecule has a net molecular dipole and a trigonal pyramidal geometry, its non-zero net dipole moment does provide experimental evidence against it being a planar molecule.

Analyze ozone (O3) molecule geometry

The ozone (O3) molecule contains three oxygen atoms. It is a resonance hybrid of two structures, where one of the oxygen atoms has a double bond with the central oxygen atom, and the other has a single bond. In reality, the bond lengths are an average between the lengths of a single and double bond. The geometry of the O3 molecule is bent with bond angles of about 116.8º.

Examine dipole moments in ozone

Though all atoms in the O3 molecule are the same, there is an unequal distribution of electrons. This occurs because of the resonance hybrid’s average bond characteristics, causing a small difference in electron density between the central oxygen atom and the two terminal oxygen atoms. This results in a small, nonzero molecular dipole moment.

Conclusion

In summary, the polarity of the PH3 molecule and its trigonal pyramidal geometry provide experimental evidence against the molecule being planar. On the other hand, ozone (O3), despite having all identical atoms, exhibits a small dipole moment due to its bent geometry and delocalization of electrons across the resonance hybrid.

Key concepts

VSEPR Theory

The VSEPR theory stands for Valence Shell Electron Pair Repulsion theory. It is used to predict the shape of individual molecules based on the number of electron pairs surrounding their central atoms. Each pair of electrons, whether involved in a bond or existing as a lone pair, is negatively charged and repels other electron pairs. This repulsion affects the geometry of the molecule, as the electrons arrange themselves to minimize these repulsive forces.
In the case of the PH3 molecule, the central phosphorus atom has three bonds with hydrogen atoms and one lone pair. According to VSEPR theory, this arrangement forms a pyramidal shape, with the lone pair forcing the bonded pairs slightly closer together, resulting in a bond angle less than the typical tetrahedral angle of 109.5°. This is why PH3 takes on a trigonal pyramidal shape rather than being flat or planar. The bent geometry because of VSEPR theory contributes significantly to the polarity of the molecule.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. It is determined by the electron arrangement predicted by VSEPR theory. The geometry dictates many of the molecule's properties, including reactivity, polarity, and physical state.
For PH3, the molecular geometry is trigonal pyramidal. This means that there are regions of electron density that occur due to the bonds between phosphorus and hydrogen, plus one lone pair on phosphorus. The presence of this lone pair slightly alters the geometry, preventing it from being flat. This shape plays a crucial role in establishing the overall dipole moment and thus the molecule’s polarity.

• The trigonal pyramidal shape indicates that PH3 cannot be planar.
• It affects how molecular dipoles add up to create a net dipole moment.

The slightly unequal distribution of electron density results in PH3 being a polar molecule.

Dipole Moment

The dipole moment is a vector measurement of a molecule's overall polarity. It depends on both the differences in electronegativities between bonded atoms and the shape of the molecule. A dipole arises when there is a separation of charges within a bond due to differences in electronegativity.
In PH3, although the electronegativity difference between phosphorus and hydrogen is negligible, the molecule still exhibits a dipole moment. This is because of its trigonal pyramidal structure, which does not allow the bond dipoles to cancel out entirely, resulting in a net dipole moment.
As for ozone (O3), each oxygen atom has the same electronegativity, but the molecule's bent shape causes an uneven electron distribution. This shape and the resonance structures contribute to a tiny dipole moment. Ozone’s geometry causes a non-zero dipole despite having atoms of identical electronegativity.
The dipole moment is critical as it explains why molecules with similar atoms, like ozone, can be polar due to molecular geometry.