Question

Which of the following is a linear molecule? (a) \(\mathrm{SO}_{2}\) (b) \(\mathrm{CH}_{4}\) (c) \(\mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{BeCl}_{2}\)

Short answer

Molecule (d) BeCl[203 is linear.

Step-by-step solution

Determine molecular geometry options

Molecules can be linear, trigonal planar, tetrahedral, trigonal bipyramidal, etc. A linear molecule has atoms arranged in a straight line.

Analyze the electron geometry of each molecule

- SO[2082: Sulfur is bonded to two oxygen atoms but has lone pairs, making it bent rather than linear. - CH[204: Carbon forms four single bonds in a tetrahedral shape. - H[208[204: Oxygen forms two bonds and has lone pairs, resulting in a bent shape. - BeCl[203[204: Beryllium has two bonding pairs with no lone pairs, resulting in a linear shape.

Examine VSEPR Theory to confirm molecule shape

According to VSEPR Theory, a molecule can be linear if the central atom has no lone pairs and two bonds. - BeCl[203 uses sp hybridization to bond with chlorine atoms, without any lone pairs influencing the shape, confirming linear structure.

Key concepts

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) Theory is a fundamental concept used to predict the geometry of molecular structures. It posits that electron pairs surrounding a central atom will arrange themselves as far apart as possible to minimize repulsion and maximize stability. Here's a simple breakdown:

• Electron Groups: Each bond, whether it's single, double, or triple, as well as lone pairs around a central atom, counts as one electron group.
• Arrangement: These groups will orient themselves to be at maximum distances to reduce electron-pair repulsion.
• Shape Influence: This arrangement directly influences the molecular geometry, leading to shapes such as linear, tetrahedral, trigonal planar, etc.
• Lone Pairs: Lone pairs occupy more space than bonding pairs, which can affect the bond angles and alter the apparent geometry of the molecule.

Using VSEPR theory, you can predict that \(\text{BeCl}_2\) is linear because it has two bonding pairs and no lone pairs on the central atom. Hence, the electron pairs stay opposite each other in a 180-degree layout.

Linear Molecule

A linear molecule is the simplest molecular shape where atoms align in a straight line. This shape is typical when a central atom is connected to two other atoms with no lone electron pairs on the central atom. Key characteristics of linear molecules include:

• Straight Line Arrangement: The atoms are arranged in a straight line, which contributes to a 180-degree bond angle.
• Nonpolar Potential: If the atoms are identical on both sides, it can render the molecule nonpolar due to symmetrical charge distribution.
• Simplicity: Fewer interactions among atoms usually result in reduced molecular complexity.

For example, in \(\text{BeCl}_2\), beryllium bonds with two chlorine atoms, forming a symmetrical linear shape as there are no lone pairs to induce bending.This fundamental geometry enables easy prediction and identification of linear molecules when using VSEPR theory.

Hybridization

Hybridization is a central concept in understanding molecular geometry, describing the process by which atomic orbitals mix to form new hybrid orbitals. This helps explain molecular shapes and bond angles observed in three-dimensional space. Here's how hybridization works:

• Orbital Mixing: When atoms bond, their electron clouds overlap, blending atomic orbitals (s, p, d, etc.) to create hybrid orbitals.
• Types of Hybridization: Most common types are \(sp\), \(sp^2\), and \(sp^3\). The choice depends on the number and types of bonds:
• - \(sp\) involves the mixing of one s and one p orbital to form two equivalent \(sp\) orbitals, resulting in a linear shape.
• - \(sp^2\) includes one s and two p orbitals, leading to a trigonal planar shape.
• - \(sp^3\) involves one s and three p orbitals, shaping a tetrahedral structure.
• Bond Angles: The hybridization type influences expected bond angles, such as \(180^\circ\) for \(sp\), \(120^\circ\) for \(sp^2\), and \(109.5^\circ\) for \(sp^3\).

\(\text{BeCl}_2\) uses \(sp\) hybridization, which involves one s and one p orbital forming a linear geometry between beryllium and the two chlorines.