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Chapter 9: Problem 13

\mathrm{An} \mathrm{} \mathrm{AB}_{2}\( molecule is described as linear, and the \)\mathrm{A}-\mathrm{B}\( bond length is known. (a) Does this information completely describe the geometry of the molecule? (b) Can you tell how many nonbonding pairs of electrons are around the \)A$ atom from this information?

Short Answer

Expert verified
(a) Yes, the information completely describes the geometry of the AB$_2$ molecule because the molecular shape is given as linear, the bond angle is 180 degrees, and the A-B bond length is provided. (b) No, we cannot tell how many nonbonding pairs of electrons are around the A atom from the given information, as the identity of the A and B atoms is not provided.

Step by step solution

01

Understanding the given information

We are given that the AB2 molecule is linear, which means that the three atoms A, B1, and B2 are arranged in a straight line. We are also given the bond length between A and B (A-B).
02

Part (a): Checking if the information completely describes the geometry

To understand whether the given information is enough to describe the geometry of the molecule, let's explore what is required to completely define a molecule's geometry. We need to know the following: 1. The arrangement of atoms (i.e., the molecular shape) 2. Bond lengths (distances between atoms) 3. Bond angles (angles between adjacent bonds) In our case, the molecular shape is given as linear, which means that the bond angle is 180 degrees. Since there are only 3 atoms in this molecule, the whole shape can be described by this bond angle. The A-B bond length has also been provided. Therefore, the given information does completely describe the geometry of the AB2 molecule. Answer to part (a): Yes, the information completely describes the geometry of the molecule.
03

Part (b): Determining nonbonding electron pairs

To find out how many nonbonding electron pairs are around the A atom, we need to know the total number of valence electrons for the A atom and the number of electrons involved in bonding with the two B atoms. However, the given information does not provide the identity of the A atom or the B atoms. Without knowing the type of atoms involved, it is not possible to determine the number of nonbonding electron pairs around the A atom. Answer to part (b): No, we cannot tell how many nonbonding pairs of electrons are around the A atom from the given information.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Bond Length
Bond length is a straightforward yet crucial concept in understanding molecular geometry. It refers to the distance between the nuclei of two bonded atoms. In a linear molecule like an AB鈧� formation, focusing on the bond length helps us understand molecular dimensions.
A bond length can vary:
  • Depending on the types of atoms involved. For example, longer bonds typically occur between larger atoms.
  • Based on the bond order. Generally, double bonds are shorter than single bonds, and triple bonds are shorter than double bonds.
In the context of the AB鈧� molecule described in the original exercise, the A-B bond length is given, which is key to defining its geometry. By knowing the bond length, we can predict spacing between atoms and gain a clearer picture of molecular structure. Bond length alone, though, cannot provide information on other elements like electron pairs or molecular symmetry without additional data on atom types or bond angles.
Nonbonding Electron Pairs
Nonbonding electron pairs, sometimes referred to as lone pairs, are valence electrons that are not involved in chemical bonding. They remain localized on a particular atom and can affect the molecule's geometry.
In a molecular structure, nonbonding electron pairs can influence:
  • The shape of the molecule by repelling bonded electron pairs, thereby altering bond angles.
  • Physical properties like polarity and reactivity due to their presence and arrangement.
For our linear AB鈧� molecule, determining the total number of nonbonding electron pairs requires knowing more about the atoms involved, particularly the A atom. When you know the identity of the A atom, you can calculate its valence electrons and discern how many participate in bonding versus those that remain unshared. Without this fundamental information, pinpointing nonbonding electron pairs remains speculative.
Linear Molecules
Linear molecules are characterized by an arrangement where atoms align in a straight line, typically resulting in a 180-degree bond angle. This geometry can arise in various types of linear molecules, including those in the form of AB鈧�.
Key features of linear molecules include:
  • Simplicity in geometry, as all bonds are collinear.
  • Predictable bond angles, typically 180 degrees due to the straight-line arrangement.
  • Varying physical and chemical properties depending on the participating atoms and their bond lengths.
The AB鈧� molecule discussed in the exercise exemplifies a linear molecule. The information provided confirms this geometry with the described bond length and geometry. However, aligning these atoms linearly does not automatically inform us about the presence or absence of nonbonding electron pairs or the full electron configuration, both of which require further atomic details.

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Most popular questions from this chapter

Sulfur tetrafluoride \(\left(\mathrm{SF}_{4}\right)\) reacts slowly with \(\mathrm{O}_{2}\) to form sulfur tetrafluoride monoxide \(\left(\mathrm{OSF}_{4}\right)\) according to the following unbalanced reaction: $$ \mathrm{SF}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{OSF}_{4}(g) $$ The \(\mathrm{O}\) atom and the four \(\mathrm{F}\) atoms in \(\mathrm{OSF}_{4}\) are bonded to a central \(\mathrm{S}\) atom. (a) Balance the equation. (b) Write a Lewis structure of \(\mathrm{OSF}_{4}\) in which the formal charges of all atoms are zero. (c) Use average bond enthalpies (Table 8.4) to estimate the enthalpy of the reaction. Is it endothermic or exothermic? (d) Determine the electron-domain geometry of \(\mathrm{OSF}_{4}\), and write two possible molecular geometries for the molecule based on this electron-domain geometry. (e) Which of the molecular geometries in part (d) is more likely to be observed for the molecule? Explain.

Draw sketches illustrating the overlap between the following orbitals on two atoms: (a) the \(2 s\) orbital on each atom, (b) the \(2 p_{z}\) orbital on each atom (assume both atoms are on the \(z\)-axis), (c) the \(2 s\) orbital on one atom and the \(2 p_{z}\) orbital on the other atom.

In which of these molecules or ions does the presence of nonbonding electron pairs produce an effect on molecular shape? (a) \(\mathrm{SiH}_{4}\), (b) \(\mathrm{PF}_{3}\), (c) \(\mathrm{HBr}\), (d) \(\mathrm{HCN}\), (e) \(\mathrm{SO}_{2}\).

(a) What is the physical basis for the VSEPR model? (b) When applying the VSEPR model, we count a double or triple bond as a single electron domain. Why is this justified?

Write the electron configuration for the first excited state for \(\mathrm{N}_{2}\), that is, the state with the highest-energy electron moved to the next available energy level. (a) Is the nitrogen in its first excited state diamagnetic or paramagnetic? (b) Is the \(\mathrm{N}-\mathrm{N}\) bond strength in the first excited state stronger or weaker compared to that in the ground state?
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