Question

The pair of species having identical shapes for molecules of both species is (a) \(\mathrm{CF}_{4}, \mathrm{SF}_{4}\) (b) \(\mathrm{XeF}_{2}, \mathrm{CO}_{2}\) (c) \(\mathrm{BF}_{3}^{4}, \mathrm{PCl}_{3}\) (d) \(\mathrm{PF}_{5}, \mathrm{IF}_{5}\)

Short answer

(b) \(\mathrm{XeF}_2\) and \(\mathrm{CO}_2\) are both linear.

Step-by-step solution

Determine the Molecular Geometry of Each Molecule

Let's first identify the molecular geometry of each molecule using the VSEPR theory. \(\mathrm{CF}_4\) is a tetrahedral molecule, \(\mathrm{SF}_4\) is a see-saw shaped molecule. \(\mathrm{XeF}_2\) is linear, whereas \(\mathrm{CO}_2\) is also linear. \(\mathrm{BF}_3\) is trigonal planar, which is not \(\mathrm{BF}_3^{4}\) and \(\mathrm{PCl}_3\) is trigonal pyramidal. \(\mathrm{PF}_5\) is trigonal bipyramidal, and \(\mathrm{IF}_{5}\) is square pyramidal.

Compare the Molecular Geometries

Identify which pairs have identical geometries. \(\mathrm{CF}_4\) and \(\mathrm{SF}_4\) do not match since they are tetrahedral and see-saw respectively. \(\mathrm{XeF}_2\) and \(\mathrm{CO}_2\) are both linear in shape, making them identical. \(\mathrm{BF}_3^{4}\) is incorrectly represented, but its structure would plausibly not match \(\mathrm{PCl}_3\). \(\mathrm{PF}_5\) and \(\mathrm{IF}_5\) have differing geometries, with trigonal bipyramidal and square pyramidal shapes.

Identify the Correct Pair

The only pair that has identical shapes is \(\mathrm{XeF}_2\) and \(\mathrm{CO}_2\), both having linear geometries. Thus, the answer is option (b).

Key concepts

VSEPR theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is a useful model to predict the shapes of molecules based on the repulsion between electron pairs in the valence shell of atoms. Its core idea is simple: electron pairs arrange themselves as far apart as possible to minimize repulsive forces.

This theory helps in determining the molecular geometry of a wide range of compounds. According to VSEPR, the shape of a molecule depends not only on the number of bond pairs (shared between atoms) but also on the number of lone pairs (unshared) around the central atom.

Here are the key points of the VSEPR theory:

• Electron pairs, whether bonding or non-bonding, repel each other.
• The shape of the molecule is determined by the positions where these electron pair repulsions are minimized.
• Non-bonding lone pairs exert a greater repulsive force than bonding pairs, often altering ideal bond angles.

Using the VSEPR model, we evaluate the molecular geometry by outlining Lewis structures and counting electron pairs. This can predict linear, trigonal planar, tetrahedral, and other structures, forming a basis for understanding more complex shapes like trigonal bipyramidal structures.

linear geometry

Linear geometry is one of the simplest molecular shapes, characterized by atoms arranged in a straight line. This shape occurs in molecules with two bonding pairs around the central atom with no lone pairs. The bond angle in a linear molecule is 180°.

For example, both \(\mathrm{XeF}_2\) and \(\mathrm{CO}_2\) adopt linear shapes. In \(\mathrm{XeF}_2\), the central xenon atom has three lone pairs and two bonding pairs causing a linear arrangement due to even distribution of electron density. Similarly, \(\mathrm{CO}_2\) arranges itself linearly as the oxygen atoms form double bonds with carbon, with no lone pairs on the central carbon atom.

Key features of linear molecules:

• Consist of three atoms where the central atom may contain lone pairs.
• Exhibit an electron pair geometry in straight line alignment to minimize repulsion.
• Typically associated with two bonding regions and zero lone pairs in simple diatomic molecules.

Understanding linear geometry allows us to predict the behavior and reactivity of molecular species, considering how such structures influence physical and chemical properties.

trigonal bipyramidal structure

The trigonal bipyramidal structure is a three-dimensional arrangement where a central atom is surrounded by five bonded regions. It combines both equatorial and axial positions, leading to unique molecular geometry.

In this shape, three atoms form an equatorial triangle in one plane, while the other two occupy axial positions perpendicularly, giving rise to different bond angles. For example, phosphorus pentafluoride (\(\text{PF}_5\)) forms a trigonal bipyramidal shape.

Characteristics of trigonal bipyramidal molecules:

• There are two distinct bond angles: 120° in the equatorial plane and 90° between axial and equatorial positions.
• This geometry arises from five shared electron pairs with no lone pairs on the central atom.
• It allows different shapes of distortions when lone pairs are present, leading structures like see-saw and T-shape.

The trigonal bipyramidal arrangement is a step up from simple models, showing more complex distribution of electrons and emphasizing the role of angles and symmetry in chemical bonding and reactions.