Question

Consider a series of molecules in which the \(\mathrm{C}\) atom is bonded to atoms of second-period elements: \(\mathrm{C}-\mathrm{O}\), \(\mathrm{C}-\mathrm{F}, \mathrm{C}-\mathrm{N}, \mathrm{C}-\mathrm{C},\) and \(\mathrm{C}-\mathrm{B}\). Place these bonds in order of increasing bond length.

Short answer

Order: \(\mathrm{C}-\mathrm{F} < \mathrm{C}-\mathrm{O} < \mathrm{C}-\mathrm{N} < \mathrm{C}-\mathrm{C} < \mathrm{C}-\mathrm{B}\).

Step-by-step solution

Understanding Bond Length

Bond length is the distance between the nuclei of two bonded atoms. Generally, bond length decreases with increasing bond order (single < double < triple) and with smaller atomic radii of the bonded atoms. In this exercise, we are comparing the bond lengths of carbon (C) with various second-period elements.

Analyze Atomic Sizes

The atomic size of an element influences the bond length. In the second period, the order by increasing atomic size is fluorine (F), oxygen (O), nitrogen (N), carbon (C), and boron (B). Smaller atomic size typically leads to shorter bond lengths.

Compare Electronegativity Effects

Electronegativity differences can affect bond length. Greater differences in electronegativity typically result in shorter, stronger bonds due to increased polarity and electron cloud distortion. Among the given atoms, fluorine has the highest electronegativity, followed by oxygen, nitrogen, carbon, and boron.

Arrange Bonds by Increasing Bond Length

Considering both atomic size and electronegativity effects, arrange the bonds by increasing bond length:- \( \mathrm{C}-\mathrm{F} \) (shortest)- \( \mathrm{C}-\mathrm{O} \)- \( \mathrm{C}-\mathrm{N} \)- \( \mathrm{C}-\mathrm{C} \)- \( \mathrm{C}-\mathrm{B} \) (longest).

Finalize the Order

Now combine the insights from atomic size and electronegativity to finalize the order of bond lengths, which is confirmed as:1. \( \mathrm{C}-\mathrm{F} \)2. \( \mathrm{C}-\mathrm{O} \)3. \( \mathrm{C}-\mathrm{N} \)4. \( \mathrm{C}-\mathrm{C} \)5. \( \mathrm{C}-\mathrm{B} \).

Key concepts

Second-Period Elements

The second period of the periodic table includes the elements from lithium ( Li ) to neon ( Ne ). These elements are crucial in understanding bond properties because they all share the same energy level (n=2). This similarity influences their atomic size and electronic configuration, which affect how they bond with other atoms.
For example, carbon (C) bonds with other second-period elements like oxygen (O), nitrogen (N), fluorine (F), and boron (B). The nature of these bonds varies due to differences in atomic size and electronegativity. When examining the bonds between carbon and these elements, such as C-F or C-O , understanding their position in the period helps predict bond length and strength.
Second-period elements have no more than 8 electrons in their outer shell, leading to varied bonding behaviors like strong covalent bonds seen in C-N and C-O . Recognizing this can assist in predicting molecular structures and reactions across different compounds.

Electronegativity

Electronegativity measures an atom's ability to attract shared electrons. It is a key player in determining the bond length and strength. In the context of the second-period elements, fluorine (F) is the most electronegative, while boron (B) is the least. This difference greatly impacts the bond characteristics with carbon (C).

• **C-F Bonds**: Fluorine's high electronegativity means it attracts electrons strongly, resulting in a shorter, polar bond, and hence, the shortest bond length among the given options.
• **C-O and C-N Bonds**: Oxygen and nitrogen also have high electronegativities, though less than fluorine, causing their bonds with carbon to be strong but slightly longer than C-F bonds.
• **C-C and C-B Bonds**: With similar or lower electronegativity values compared to carbon, these bonds are less polar, leading to longer bond lengths.

Electronegativity differences often provide insights into the reactivity and polarity of molecules, influencing real-world applications like material science and pharmaceuticals.

Atomic Size

The atomic size of an element is another factor that affects bond length. Atomic size is characterized by the distance from the nucleus to the outermost electrons. In the second period, atomic size increases from fluorine (F) to boron (B).
This trend is important when predicting bond length:

• **Smaller Atoms**: Fluorine, being the smallest, forms the shortest bond with carbon, followed by oxygen and nitrogen. This compact size allows their nuclei to be closer when bonded.
• **Larger Atoms**: Carbon and boron, being larger, lead to longer bonds due to the increased distance of their outermost electrons from the nucleus.

When analyzing molecules, considering atomic size alongside electronegativity provides a holistic view of bond characteristics. Understanding these principles aids in designing compounds with desired physical and chemical properties, crucial for innovation in chemistry and engineering.