Question

\(\mathrm{BH}_{3}\) and \(\mathrm{PH}_{3}\) each contain four atoms, with the three hydrogens surrounding the central atom. Do the two molecules have the same electron-group geometry? Do they have the same molecular shape? Name the geometry and the shape for both molecules. You know from Problem \(6.59\) that \(\mathrm{PH}_{3}\) is nonpolar. What about \(\mathrm{BH}_{3} ?\) Is it polar or nonpolar? Explain.

Short answer

\(\mathrm{BH}_{3}\) and \(\mathrm{PH}_{3}\) have different electron-group geometries and molecular shapes. \(\mathrm{BH}_{3}\) has a trigonal planar electron-group geometry and molecular shape, while \(\mathrm{PH}_{3}\) has a tetrahedral electron-group geometry and a trigonal pyramidal molecular shape. Both \(\mathrm{BH}_{3}\) and \(\mathrm{PH}_{3}\) are nonpolar molecules.

Step-by-step solution

1. Draw Lewis structures for \(\mathrm{BH}_{3}\) and \(\mathrm{PH}_{3}\)

To start, we need to draw the Lewis structures for both \(\mathrm{B}\) and \(\mathrm{P}\) atoms and find out the number of electron pairs surrounding them. In \(\mathrm{BH}_{3}\), the central \(\mathrm{B}\) atom has 3 valence electrons. Each \(\mathrm{H}\) atom contributes 1 electron, making a total of 6 electrons (3 from \(\mathrm{B}\) and 3 from the three \(\mathrm{H}\) atoms). In \(\mathrm{PH}_{3}\), the central \(\mathrm{P}\) atom has 5 valence electrons. Each \(\mathrm{H}\) atom contributes 1 electron, making a total of 8 electrons (5 from \(\mathrm{P}\) and 3 from the three \(\mathrm{H}\) atoms).

2. Determine electron-group geometry

Now, let's determine the electron-group geometry for each molecule. In \(\mathrm{BH}_{3}\), there are 3 bonding electron pairs around the central atom and no lone pairs. These electron pairs will arrange themselves in a trigonal planar geometry to minimize the repulsion between them. In \(\mathrm{PH}_{3}\), there are 3 bonding electron pairs around the central atom and 1 lone pair. The lone pair takes the position of an electron group, so the electron-group geometry will be tetrahedral. Therefore, the electron-group geometries of \(\mathrm{BH}_{3}\) and \(\mathrm{PH}_{3}\) are different.

3. Determine molecular shape

Now, let's determine the molecular shape, which is influenced by the electron-group geometry. In \(\mathrm{BH}_{3}\), the electron-group geometry is trigonal planar and all electron groups are bonding electron pairs. Therefore, the molecular shape of \(\mathrm{BH}_{3}\) is also trigonal planar. In \(\mathrm{PH}_{3}\), the electron-group geometry is tetrahedral, with one lone pair and three bonding electron pairs. The molecular shape is determined by the positions of the bonding electron pairs only, which take on a trigonal pyramidal shape in this case. Therefore, the molecular shapes of \(\mathrm{BH}_{3}\) and \(\mathrm{PH}_{3}\) are different.

4. Determine the polarity of \(\mathrm{BH}_{3}\)

To determine if \(\mathrm{BH}_{3}\) is polar or nonpolar, we need to consider the electronegativity difference between \(\mathrm{B}\) and \(\mathrm{H}\) and the molecular shape of the molecule. The electronegativity difference between \(\mathrm{B}\) and \(\mathrm{H}\) is small, so the \(\mathrm{B-H}\) bonds can be considered nonpolar. Furthermore, the molecular shape of \(\mathrm{BH}_{3}\) is trigonal planar, which has a symmetrical distribution of charge. Therefore, the polarity of the bonds cancels out, making \(\mathrm{BH}_{3}\) a nonpolar molecule. In conclusion: \(\mathrm{BH}_{3}\): Electron-group geometry - Trigonal planar. Molecular shape - Trigonal planar. Polarity - Nonpolar. \(\mathrm{PH}_{3}\): Electron-group geometry - Tetrahedral. Molecular shape - Trigonal pyramidal. Polarity - Nonpolar.

Key concepts

Lewis Structures

Lewis structures are diagrams that help illustrate the valence electrons surrounding atoms in a molecule. They are essential for predicting the shape and reactivity of molecules. For \(\mathrm{BH}_{3}\), the central \(\mathrm{B}\) atom has three valence electrons. Each hydrogen \(\mathrm{H}\) brings one electron, leading to a total of six valence electrons. The electrons are shared between the central boron and each hydrogen to form three single bonds. These bonds are shown as lines in the Lewis structure.
The Lewis structure for \(\mathrm{PH}_{3}\) is similar but involves a slightly different configuration. Phosphorus \(\mathrm{P}\) has five valence electrons, and with the addition of three electrons from the hydrogen atoms, the total is eight valence electrons. Unlike \(\mathrm{BH}_{3}\), \(\mathrm{PH}_{3}\)'s Lewis structure displays three phosphorus-hydrogen single bonds and one lone pair on the \(\mathrm{P}\) atom. This lone pair significantly influences the molecular shape and geometry.

Trigonal Planar Geometry

The concept of trigonal planar geometry is fundamental in understanding molecular configurations. It describes a molecule's shape where three atoms are evenly spaced around a central atom, all in a single plane, forming a triangle.
In \(\mathrm{BH}_{3}\), this electron-group geometry is achieved by the three \(\mathrm{B-H}\) bonds, with no lone pairs surrounding the central boron atom. This positioning is due to the desire to minimize electron pair repulsion, optimizing the structure into a flat, symmetrical shape.

• All bond angles in a trigonal planar arrangement are \(120^\circ\).
• This symmetry often leads to nonpolar molecules since the charges are evenly distributed.

Understanding trigonal planar arrangements aids in grasping why \(\mathrm{BH}_{3}\) is nonpolar, reflecting its symmetrical electron distribution.

Trigonal Pyramidal Shape

Unlike trigonal planar geometries, a trigonal pyramidal shape includes a central atom with three bonds pointing towards the vertices of a pyramid. The pivotal difference here is the lone pair of electrons that does not participate in bonding.
In \(\mathrm{PH}_{3}\), the lone pair on the phosphorus atom occupies a position similar to one of the `vertices` in a tetrahedral geometry, slightly pushing the three \(\mathrm{P-H}\) bonds downward into a trigonal pyramidal shape.

• The trigonal pyramidal shape involves bond angles around \(107^\circ\), slightly less than trigonally planar due to lone pair repulsion.
• Lone pairs significantly affect the shape and can increase molecular polarity compared to similar geometries without lone pairs.

Thus, even though \(\mathrm{PH}_{3}\) has a symmetric tetrahedral electron-group geometry, its shape is trigonal pyramidal and its impact on physical properties differs.

Molecular Polarity

Molecular polarity refers to the distribution of electrical charge around a molecule, significantly influenced by the shape and electronegativity differences between atoms. A molecule is polar if it has a net dipole moment.
In the case of \(\mathrm{BH}_{3}\), because of its trigonal planar geometry and equal \(\mathrm{B-H}\) bond distribution, the dipoles cancel out, resulting in a nonpolar molecule.
Alternatively, \(\mathrm{PH}_{3}\) has a trigonal pyramidal shape. Despite symmetry in bond angles, the lone pair on phosphorus pushes the \(\mathrm{P-H}\) bonds downward, creating a dipole moment.

• This lone pair-placement makes \(\mathrm{PH}_{3}\) appear \'almost polar,' though weak \(\mathrm{P-H}\) bonds produce very low polarity.

Understanding polarity is crucial for predicting molecular interactions in chemical reactions, biological systems, or material science applications.