Problem 38 - Chemistry in 30 days

Question

Which of the following is not linear? (a) \(\mathrm{I}_{3}^{-}\) (b) \(\mathrm{I}_{3}^{+}\) (c) \(\mathrm{CS}_{2}\) (d) \(\mathrm{XeF}_{2}\)

Step-by-Step Solution

Answer

The non-linear molecule is \\(\mathrm{I}_{3}^{+}\\).

Step 1: Understanding Molecular Geometry

Molecular geometry can be understood by analyzing the Lewis structure of the molecule or ion, which shows the arrangement of atoms and lone pairs. A linear molecule has a straight-line shape, typically characterized by an angle of 180°. We need to examine the electron groups around the central atom to predict its geometry.

Step 2: Analyze \\(\mathrm{I}_{3}^{-}\\)

The structure of \(\mathrm{I}_{3}^{-}\) consists of a central iodine atom with two bonded iodine atoms and three lone pairs. This results in a linear shape due to the trigonal bipyramidal electronic shape where lone pairs occupy the equatorial positions, leaving the bonded iodine atoms linear at 180°.

Step 3: Analyze \\(\mathrm{I}_{3}^{+}\\)

For \(\mathrm{I}_{3}^{+}\), the central iodine has one less lone pair than \(\mathrm{I}_{3}^{-}\), resulting in two bonded iodine atoms and two lone pairs. This leads to a bent configuration rather than linear.

Step 4: Analyze \\(\mathrm{CS}_{2}\\)

The molecular geometry of \(\mathrm{CS}_{2}\) involves a central carbon atom double bonded to two sulfur atoms. With no lone pairs on the carbon, the molecule maintains a linear structure at 180°.

Step 5: Analyze \\(\mathrm{XeF}_{2}\\)

\(\mathrm{XeF}_2\) has a linear structure due to the arrangement of two bonded fluorine atoms and three lone pairs on the xenon atom. The electronic geometry is trigonal bipyramidal, and the molecule is linear due to lone pairs occupying equatorial positions, minimizing repulsion.

Step 6: Conclusion

Calculating based on respective number of lone pairs and bonded atoms, \(\mathrm{I}_{3}^{+}\) has a bent structure due to its VSEPR configuration, creating a non-linear shape, while the others are linear.

Key Concepts

Linear Molecules

Linear molecules are entities where atoms sit in a straight line with a bond angle of 180°. This occurrence is frequent when central atoms bond with two atoms, and there's minimal electron repulsion to influence the shape.

• The structure is visually straightforward, resembling a line or a stick.
• Common examples include carbon disulfide (\(\mathrm{CS}_{2}\)) and xenon difluoride (\(\mathrm{XeF}_{2}\)).

Understanding linear molecules involves recognizing when lone pairs on central atoms allow for such symmetry, typically dispersing in a way to reduce repulsion.

VSEPR Theory

Valence Shell Electron Pair Repulsion (VSEPR) Theory is a model used to predict molecular shapes based on repulsion between electron pairs in an atom's valence shell. It stipulates that:

• Electron pairs (bonded and lone) arrange themselves to minimize repulsion.
• The geometry of a molecule is significantly impacted by the number of lone pairs versus bonded pairs.
• For example, in \(\mathrm{I}_{3}^{-}\), the molecule remains linear despite five electron groups because lone pairs in equatorial positions balance the shape.

VSEPR helps identify how different combinations of electron pairs affect molecular geometry, explaining why some molecules are non-linear despite seemingly similar structures.

Lewis Structures

Lewis structures are diagrammatic representations that show the arrangement of electrons in a molecule. They typically illustrate:

• How atoms within a molecule are bonded together.
• Lone pairs of electrons and their spatial disposition.
• Molecular shapes through the depiction of bonds and electron pairs.

Creating a Lewis structure involves placing electron pairs around atoms to impact the geometry, like in \(\mathrm{XeF}_{2}\) where xenon’s lone pairs and bonded fluorines form a linear arrangement. These visual tools are critical for predicting both shape and reactivity.

Bond Angles

Bond angles are the angles formed between bonds stemming from the central atom. In molecular geometry, bond angles are dictated by:

• Number and types of bonds present.
• Lone pairs on the central atom.

For instance, a linear geometry features bond angles of 180°, usually visible in molecules like \(\mathrm{CS}_{2}\). However, when electron density and lone pairs come into play, like in \(\mathrm{I}_{3}^{+}\), the bond angle can deviate, resulting in a bent geometry. Understanding bond angles involves comprehending how electron pair geometries influence molecular shape.