Question

Consider the hypothetical molecule \(\mathrm{A}-\mathrm{A}=\mathrm{A}\) with a bent shape. Are the following statements true or false? (a) This molecule cannot exist. (b) If this molecule exists, it must possess an odd electron.

Short answer

In conclusion, for the hypothetical molecule A-A=A with a bent shape, the two statements are: (a) This molecule cannot exist: False. (b) If this molecule exists, it must possess an odd electron: True.

Step-by-step solution

The hypothetical molecule has a bent structure and is written as A-A=A. To better understand the molecule, we need to determine the type of bonds and the number of valence electrons involved for each atom in the molecule. #Step 2: Examine bonding and valence electrons#

For the A-A single bond, each A atom would contribute 1 valence electron resulting in a shared pair of electrons. Similarly, for the A=A double bond, each A atom would contribute 2 valence electrons, resulting in two shared pairs of electrons. In total, each A atom would need to share X, Y, and Z valence electrons: - X: Valence electrons for the A-A single bond - Y: Valence electrons for the A=A double bond - Z: Valence electrons for the bent shape #Step 3: Analyze the valence electron count#

According to the octet rule, an atom should have 8 valence electrons to achieve stability. In this hypothetical molecule, we can write the following equation for an A atom participating in both bonding and bent shape electron pairs: X+Y+Z = 8 Since X is the valence electron for the A-A single bond, it is equal to 1. Y is the valence electron for A=A double bond, which is equal to 2. The equation now becomes: 1+2+Z = 8 Solve for Z: Z = 5 #Step 4: Determine the validity of both statements#

Now that we have the valence electron count for this hypothetical molecule, let's examine both statements: (a) This molecule cannot exist: - There is no specific rule that states molecules with a valence electron arrangement like this cannot exist. Therefore, we cannot definitively say that this molecule cannot exist. So, this statement is False. (b) If this molecule exists, it must possess an odd electron: - The valence electron count Z for an 'A' atom in this hypothetical molecule is 5, which is an odd number. Therefore, if this molecule exists, it must possess an odd electron. So, this statement is True. In conclusion, the first statement is False, and the second statement is True.

Key concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. It plays a crucial role in determining the properties and reactivity of the molecule. In this case, the molecule is described with a bent shape, similar to well-known bent molecules like water (H\(_2\)O). A bent geometry arises when there are interactions between nonbonding electron pairs and bonded electron pairs that cause a deviation from the linear arrangement.

In bent structures, the central atom usually has lone pairs of electrons. These lone pairs occupy more space because they are not shared between atoms, which leads to repulsion and a bent shape instead of a straight one. Specifically in water, the combination of two lone pairs and two hydrogen atoms leads to a bond angle of about 104.5°. In our hypothetical A-A=A molecule, if we assume a similar presence of lone pairs, it results in a bent geometry as well.

• Bent geometry affects molecular polarity.
• Affects the molecular interactions, such as hydrogen bonding in water.
• Alters the dipole moment of the molecule.

Valence Electrons

Valence electrons are the outermost electrons of an atom and play a key role in chemical bonding. They are involved in the formation of chemical bonds and determine how atoms interact with each other. For our hypothetical molecule A-A=A, we must consider the valence electrons each A atom contributes to form the bonds.

In this molecule, A-A represents a single bond where each A contributes one valence electron, pairing to share a total of two electrons. For the A=A double bond, each A atom contributes two valence electrons, leading to the sharing of four electrons. To satisfy stable bonding in each atom's outer shell, especially following the octet rule, atoms will share or transfer electrons to fill their valence shell.

• Single bonds generally involve sharing one pair of electrons between two atoms.
• Double bonds involve sharing two pairs of electrons.
• Valence electrons help predict molecular shapes, reactivity, and bonding patterns.

Octet Rule

The octet rule is a chemical guideline that atoms tend to bond in such a way that they each have eight electrons in their valence shell, achieving a noble gas configuration. This rule is often applied to atoms within the main group of elements. In our hypothetical molecule, the incomplete electron sharing suggests an application of the octet rule.

Each A atom in the hypothetical molecule should ideally aim to have eight valence electrons around it, either through sharing or receiving electrons to fulfill this rule. The step-by-step solution demonstrates how the arrangement satisfies the octet rule's requirements, where X, Y, and Z denote the shared valence electrons through various bonds. With initial values of X and Y determined from single and double bonds, we find that each A atom fills up its octet when the extra five comes from the bent shape, implying lone pairs.

• The octet rule simplifies predicting the types of bonds atoms can form.
• It primarily applies to elements in the second period, particularly carbon, nitrogen, and oxygen.
• Exceptions exist, such as molecules with an odd number of electrons or those exceeding the octet.