Question

Which of the following staternents is correct regarding the structure of \(\mathrm{PCl}_{5} ?\) (a) Three \(\mathrm{P}-\mathrm{Cl}\) bonds lie in one plane and two \(\mathrm{P}-\mathrm{Cl}\) bonds lieabove and below the equatorial plane (b) Five \(P-C l\) bonds lie in the same plane. (c) The bond angle in all P-Cl bonds is \(90^{\circ}\), (d) The bond length of all \(\mathrm{P}-\mathrm{Cl}\) bonds is same.

Short answer

Statement (a) is correct: Three (P-Cl) bonds lie in one plane (equatorial plane) and two (P-Cl) bonds lie above and below this plane (axial positions).

Step-by-step solution

Understand Molecular Geometry

Recognize that the molecular geometry of a compound depends on the number of bonding pairs and lone pairs around the central atom. Phosphorus pentachloride ((PCl_5)) has a total of 5 bonding pairs and no lone pairs on the central phosphorus (P) atom. This leads to a trigonal bipyramidal molecular geometry.

Identify the Location of Bonds

In a trigonal bipyramidal geometry, there are two distinct positions for the surrounding atoms: equatorial and axial. Three of the five chlorine (Cl) atoms form equatorial bonds with the central phosphorus (P) atom lying in the same plane, while the other two chlorine atoms form axial bonds, one above and one below the equatorial plane.

Determine Bond Angles

The bond angles for the equatorial bonds are approximately 120 degrees apart from each other in the same plane. The angles between the equatorial and axial bonds are approximately 90 degrees.

Analyze Bond Lengths

In a (PCl_5) molecule, the equatorial (P-Cl) bonds are slightly longer than the axial (P-Cl) bonds due to repulsion - the equatorial chlorine atoms are repelled by more bond pairs than the axial chlorines. Therefore, not all (P-Cl) bonds have the same length.

Select the Correct Statement

Based on the molecular geometry and properties of (PCl_5), identify the correct statement. (a) correctly describes the molecular geometry, (b) is incorrect because the bonds do not lie in the same plane, (c) is incorrect as not all bond angles are 90 degrees, and (d) is not true as there is a difference in bond lengths between axial and equatorial bonds.

Key concepts

Trigonal Bipyramidal Molecular Geometry

Understanding the structure of molecules is crucial in chemistry, and the phosphorus pentachloride ((PCl_5)) molecule is a classic example of trigonal bipyramidal molecular geometry. In this geometry, imagine a tripod with three legs spread out. These three legs represent the equatorial positions, which are spaced out evenly in a single plane, forming a triangle.
To complete the bipyramid shape, there are two additional axial positions, one pointing straight up and the other straight down, like the north and south poles on a globe. The central atom—phosphorus in the case of PCl_5—is at the center, equidistant from all the chlorine atoms, which minimizes the repulsion between their electron clouds. This arrangement is energetically favorable and is dictated by the Valence Shell Electron Pair Repulsion theory (VSEPR), which shapes the 3D structure of molecules based on electron repulsion.
It's important for students to visualize this structure, perhaps using models or 3D diagrams, to truly understand the spatial arrangement within PCl_5 and other molecules with similar geometries.

Bond Angles in PCl5

Bond angles are critical to understanding molecular shape and function. In the case of phosphorus pentachloride ((PCl_5)), the bond angles differ depending on the position of the chlorine atoms. For the three equatorial (Cl) atoms, they form an angle of 120 degrees with respect to each other, which is characteristic of the trigonal planar portion of the molecule.
On the other hand, the angles between an equatorial (Cl) and an axial (Cl) atom are about 90 degrees. These bond angles are a direct result of the trigonal bipyramidal geometry and the need to minimize repulsion between the electrons in the bond pairs. The configuration ensures that the atoms and their electron clouds are as far apart as possible, providing stability to the molecule. Remembering these angles will help to predict and understand the reactions and interactions that PCl_5 can engage in.

Equatorial and Axial Positions

The concept of equatorial and axial positions is integral to many molecular geometries, including the trigonal bipyramidal shape of PCl_5. Equatorial positions are those located around the 'equator' of the molecule, so to speak. In PCl_5, there are three equatorial chlorine atoms that form a triangle and lie in the same horizontal plane.

Axial Positions

The two other chlorine atoms occupy the axial positions and align along the 'axis' of the molecule, one above and one below the plane formed by the equatorial chlorines. These positions have different bond lengths due to the uneven distribution of electron repulsion. The axial bonds are shorter because they are surrounded by fewer electron pairs compared to the equatorial bonds, leading to less repulsion and allowing the atoms to be closer together.
For students, understanding how these positions dictate bond lengths and angles will greatly enhance the comprehension of molecular geometries and the predictions of molecular behavior in chemical reactions and interactions.