Question

Fluorine is more electronegative than either boron or phosphorous. What conclusion can be drawn from the fact that \(\mathrm{BF}_{3}\) has no dipole moment but \(\mathrm{PF}_{3}\) does? (1) \(\mathrm{BF}_{3}\) is not spherically symmetrical but \(\mathrm{PF}_{3}\) is. (2) \(\mathrm{BF}_{3}\) moleculc must be linear. (3) The atomic radius of \(P\) is larger than that of \(B\). (4) The \(\mathrm{B} \mathrm{F}_{3}\) molccule must be planar triangular.

Short answer

Option (4)

Step-by-step solution

- Understand Dipole Moments

A molecule has a dipole moment when there is a separation of positive and negative charges. This typically occurs in molecules that are not symmetrical.

- Analyze \(\mathrm{BF}_{3}\) Structure

\(\mathrm{BF}_{3}\) is known to have a trigonal planar structure. All the bond angles are 120° and it is symmetrical. Therefore, any individual dipole moments from the B-F bonds cancel each other out, resulting in no net dipole moment.

- Analyze \(\mathrm{PF}_{3}\) Structure

\(\mathrm{PF}_{3}\) has a trigonal pyramidal structure. Unlike \(\mathrm{BF}_{3}\), \(\mathrm{PF}_{3}\) is not symmetrical because of the lone pair on the phosphorus atom, which causes the dipole moments from the P-F bonds to not cancel out, resulting in a net dipole moment.

- Draw Conclusion

The lack of dipole moment in \(\mathrm{BF}_{3}\) and the presence of a dipole moment in \(\mathrm{PF}_{3}\) indicate that \(\mathrm{BF}_{3}\) must be planar and symmetrical, whereas \(\mathrm{PF}_{3}\) must be non-planar and asymmetrical.

- Match Conclusion with Options

Given our analysis, the only statement that correctly matches our conclusion is (4) \(\mathrm{B} \mathrm{F}_{3}\) molecule must be planar triangular.

Key concepts

Electronegativity

Electronegativity is a measure of how strongly an atom attracts electrons in a chemical bond. It is important because it affects the distribution of electrons between atoms in molecules. Elements with higher electronegativity, such as fluorine, attract electrons more strongly than elements with lower electronegativity, like boron and phosphorus.

In the context of \(\text{BF}_3\) and \(\text{PF}_3\), the high electronegativity of fluorine causes a significant electron pull towards itself from both boron and phosphorus. However, the resulting molecular behavior differs due to their respective geometries.

Dipole Moment

A dipole moment occurs in a molecule when there is a difference in electronegativity between bonded atoms, resulting in a separation of positive and negative charges. It is a vector quantity, having both magnitude and direction. Molecules with symmetrical charge distributions usually have dipole moments that cancel each other out, leading to no net dipole moment.

For example, in \(\text{BF}\_3\), even though each \(\text{B-F}\) bond has a dipole, the molecular symmetry results in these dipoles canceling out. Therefore, \(\text{BF}\_3\) shows no overall dipole moment.

Conversely, \(\text{PF}\_3\) has a trigonal pyramidal geometry, which is asymmetrical due to a lone pair on phosphorus. This asymmetry means the dipoles do not cancel out, and \(\text{PF}\_3\) has a net dipole moment.

Trigonal Planar Structure

In a trigonal planar structure, three atoms are connected to a central atom, forming a flat, triangular shape. The bond angles are 120 degrees, and the structure is typically symmetrical. This symmetry is key to understanding why \(\text{BF}\_3\) has no dipole moment.

Boron trifluoride \(\text{BF}\_3\) is an example of a molecule with a trigonal planar structure. In \(\text{BF}_3\), boron is at the center, with the three fluorine atoms evenly spaced around it. Due to this symmetry, any dipole moments from the \(\text{B-F}\) bonds cancel out, resulting in no net dipole moment.

Trigonal Pyramidal Structure

A trigonal pyramidal structure involves a central atom bonded to three other atoms, with one lone pair on the central atom. This structure is not flat and has bond angles less than 120 degrees. The presence of the lone pair contributes to the asymmetry of the molecule.

Phosphorus trifluoride \(\text{PF}\_3\) exhibits a trigonal pyramidal structure. Due to the lone pair on phosphorus, the molecule is not symmetrically arranged. This asymmetry causes the dipole moments of the \(\text{P-F}\) bonds to not cancel out, resulting in a net dipole moment for the entire molecule.