Question

For each statement, indicate whether it is true or false. (a) In order to make a covalent bond, the orbitals on each atom in the bond must overlap. (b) A p orbital on one atom cannot make a bond to an s orbital on another atom. (c) Lone pairs of electrons on an atom in a molecule influence the shape of a molecule. (d) The 1 s orbital has a nodal plane. (e) The \(2p\) orbital has a nodal plane.

Short answer

(a) True - Covalent bonds require orbital overlap. (b) False - p orbitals can bond with s orbitals. (c) True - Lone pairs affect the molecular shape. (d) False - 1s orbitals do not have nodal planes. (e) True - 2p orbitals have a nodal plane.

Step-by-step solution

Statement (a) - Covalent Bond Requirement

Statement (a) is true. In order to form a covalent bond, the orbitals on each atom in the bond must overlap. This overlap allows for the sharing of electrons between the two atoms, resulting in a stable covalent bond.

Statement (b) - Bonding Between p and s Orbitals

Statement (b) is false. A p orbital on one atom can indeed form a bond with an s orbital on another atom. This can occur, for example, in the formation of a sigma bond, where the probability of finding the shared electrons is highest along the axis that connects the two nuclei.

Statement (c) - Lone Pairs and Molecular Shape

Statement (c) is true. Lone pairs of electrons on an atom in a molecule have a significant influence on the shape of the molecule. This is because lone pairs of electrons still occupy space and create repulsion, pushing other atoms in the molecule away from them, ultimately affecting the overall geometry of the molecule.

Statement (d) - Nodal Plane in 1s Orbital

Statement (d) is false. The 1s orbital does not have a nodal plane. A nodal plane is a region in an orbital where the probability of finding an electron is zero. The 1s orbital is a spherical shape with uniform electron density, and there is no such region with zero electron probability.

Statement (e) - Nodal Plane in 2p Orbital

Statement (e) is true. The 2p orbital has a nodal plane. The 2p orbital has a dumbbell shape, with two lobes separated by a nodal plane. In this nodal plane, the probability of finding an electron is zero.

Key concepts

Orbital Overlap

When atoms come together to form covalent bonds, something interesting happens at the atomic level: orbital overlap. This is a key requirement for covalent bonding. Orbital overlap involves the sharing of electrons between two atoms' orbitals, which are the spaces where electrons are most likely to be found. The overlapping allows atoms to achieve a more stable electronic configuration by sharing electrons.
Some common types of overlaps include:

• s-s overlap: This occurs when two s orbitals from different atoms overlap. It's often seen in molecules like hydrogen gas ( H_2 ).
• s-p overlap: An example is seen in hydrogen fluoride ( HF ), where a hydrogen's 1s orbital overlaps with a fluorine's 2p orbital.
• p-p overlap: When two p orbitals overlap, electrons can be shared along the axis connecting the two nuclei, like in fluorine gas ( F_2 ).

Each type of orbital overlap contributes to the molecule's stability and dictates the type of bond—such as sigma or pi bonds—that forms.

Molecular Geometry

The shape of a molecule, also known as molecular geometry, is not just about how atoms are connected. It's influenced heavily by the presence of lone electron pairs. These lone pairs are pairs of valence electrons that are not shared with other atoms and occupy space around an atom.
These lonely pairs exert a repulsive force on nearby electrons, impacting the arrangement of atoms in a molecule. This concept is crucial when using the VSEPR (Valence Shell Electron Pair Repulsion) theory to predict molecular shapes. For example:

• Tetrahedral: A molecule like methane ( CH_4 ) where all four positions around the central carbon atom are occupied by hydrogen atoms.
• Trigonal Pyramidal: Ammonia ( NH_3 ) has one lone pair, which pushes the three hydrogen atoms into a trigonal pyramidal shape.
• Bent: Water ( H_2O ), with two lone pairs on oxygen, results in a bent molecular shape.

Overall, the distribution of lone pairs and bonding pairs determines the geometry, influencing properties like polarity and reactivity.

Nodal Planes

In atomic orbitals, a nodal plane is a fascinating concept. It refers to an area within an orbital where the chance of finding an electron is zero. The nature and number of nodal planes depend on the shape and type of the orbital.
The simplest orbital, the 1s, is spherical and has no nodal planes. Electrons are evenly distributed throughout, with no area of zero electron probability. However, higher energy levels introduce nodal planes.
In a 2p orbital, which is shaped like a dumbbell, there is a nodal plane between the two lobes. This plane means that an electron can't exist right in the middle of the 2p orbital. Such structures play a critical role in bonding and molecular formation by influencing how atoms interact.
Understanding nodal planes helps chemists appreciate and predict how orbitals might overlap and influence molecular geometry. Especially in higher orbitals, the number of nodal planes increases, becoming essential in complex molecular structures.