Problem 45 - Chemistry and Chemical Reactivity

Question

In each pair of bonds, predict which is shorter. (a) \(\mathrm{B}-\mathrm{Cl}\) or \(\mathrm{Ga}-\mathrm{Cl}\) (b) \(\mathrm{Sn}-\mathrm{O}\) or \(\mathrm{C}-\mathrm{O}\) (c) \(\mathrm{P}-\mathrm{S}\) or \(\mathrm{P}-\mathrm{O}\) (d) \(\mathrm{C}=\mathrm{O}\) or \(\mathrm{C}=\mathrm{N}\)

Step-by-Step Solution

Answer

(a) B-Cl, (b) C-O, (c) P-O, (d) C=O

Step 1: Consider Atomic Radii

Atomic radius is a primary factor in determining bond length; a larger radius leads to a longer bond. In pairs (a), (b), and (c), the element pair with the smaller atoms will typically form the shorter bond.

Step 2: Analyze Electron Negativity and Bond Type

Higher electronegativity usually leads to stronger, and thus shorter, bonds. Additionally, double bonds (c) are shorter than single bonds due to increased electron sharing between atoms.

Step 3: Compare Bonds in Part (a)

In pair (a) - Boron (B) has a smaller atomic radius than Gallium (Ga).- Thus, \(\mathrm{B}-\mathrm{Cl}\) bond is likely to be shorter than \(\mathrm{Ga}-\mathrm{Cl}\).

Step 4: Compare Bonds in Part (b)

In pair (b)- Carbon (C) has a smaller atomic radius than Tin (Sn). - Thus, \(\mathrm{C}-\mathrm{O}\) forms a shorter bond than \(\mathrm{Sn}-\mathrm{O}\) due to Carbon's smaller size and higher electronegativity.

Step 5: Compare Bonds in Part (c)

In pair (c)- Oxygen (O) is smaller and more electronegative than Sulfur (S). - Therefore, \(\mathrm{P}-\mathrm{O}\) bond is shorter than \(\mathrm{P}-\mathrm{S}\) bond.

Step 6: Compare Double Bonds in Part (d)

In pair (d)- Both \(\mathrm{C} = \mathrm{O}\) and \(\mathrm{C} = \mathrm{N}\) are double bonds.- Oxygen is more electronegative than Nitrogen, thus \(\mathrm{C} = \mathrm{O}\) bond tends to be shorter than \(\mathrm{C} = \mathrm{N}\).

Key Concepts

Atomic Radii

The atomic radius is a fundamental concept in chemistry that refers to the size of an atom. It plays a crucial role in determining the bond length between two atoms—the larger the atomic radii, the longer the bond will likely be. Imagine two people reaching out to hold hands; the farther apart they are (larger atomic radii), the longer their "arm span" (bond length). In our exercise, we're comparing bonds based on the size of different atoms. For instance:

• Boron (B) has a smaller atomic radius than Gallium (Ga), making the B-Cl bond shorter than the Ga-Cl bond.
• Similarly, Carbon (C) is smaller than Tin (Sn), resulting in the C-O bond being shorter than the Sn-O bond.

Understanding atomic radii helps us predict which bonds are shorter, crucial for chemistry studies.

Electronegativity

Electronegativity is the ability of an atom to attract electrons towards itself. It influences bond strength significantly. A high electronegativity means an atom pulls shared electrons more tightly, creating a stronger and hence shorter bond. Think of it like a tug of war; the atom with more electronegativity pulls the "rope" of electrons closer to itself.

• For example, in P-O versus P-S bonds, oxygen has a higher electronegativity than sulfur, resulting in a stronger, shorter P-O bond.
• In double bonds like C=O, oxygen's high electronegativity compared to nitrogen makes the C=O bond shorter than C=N.

Electronegativity provides insights into why some atoms form shorter bonds than others.

Bond Types

Bonds come in different types, primarily categorized into single, double, and triple bonds. Single bonds involve the sharing of one pair of electrons, making them longer and typically weaker than double or triple bonds. Double bonds share two pairs of electrons, making them stronger and shorter due to the increased electron density between two atoms.

• This is evident in our exercise with both C=O and C=N bonds being double, yet C=O is shorter due to oxygen's higher electronegativity.
• The presence of more shared electrons in double bonds naturally pulls the atoms closer, strengthening the bond.

Bond type is an essential factor when predicting bond length and strength.

Double Bonds

Double bonds are a fascinating concept in chemistry. They consist of two shared pairs of electrons between two atoms, implying more interaction and a closer approach compared to single bonds. This results in a shorter bond length and typically higher bond strength. Picture a double knot on a string; it holds much tighter than a simple single knot. In comparisons like C=O versus C=N, both bonds are double. However, the presence or absence of electronegative atoms impacts their length. A highly electronegative atom, such as oxygen, pulls electrons closer, making a C=O bond shorter and stronger than a C=N bond. Understanding double bonds is critical for grasping molecular shapes and properties, further reinforcing the importance of bond length comparisons.