Problem 29 - Chemistry The Molecular Science

Question

For each pair of bonds, predict which is the shorter. (a) \(\mathrm{B}-\mathrm{Cl}\) or \(\mathrm{Ga}-\mathrm{Cl}\) (b) \(\mathrm{C}-\mathrm{O}\) or \(\mathrm{Sn}-\mathrm{O}\) (c) \(\mathrm{P}-\mathrm{S}\) or \(\mathrm{P}-\mathrm{O}\) (d) The \(\mathrm{C}=\mathrm{C}\) or the \(\mathrm{C}=\mathrm{O}\) bond in acrolein

Step-by-Step Solution

Answer

(a) B-Cl, (b) C-O, (c) P-O, (d) C=O are shorter bonds.

Step 1: Understand Bond Length Basics

Bond length is the distance between the nuclei of two bonded atoms. Generally, bonds involving smaller atoms or multiple bonds (like double or triple bonds) are shorter. Elements that are higher up on the periodic table often have shorter bonds because their atomic radii are smaller.

Step 2: Compare B-Cl and Ga-Cl Bond Lengths

Boron (B) is higher on the periodic table than Gallium (Ga), which implies that the B–Cl bond is typically shorter than the Ga–Cl bond because boron is smaller than gallium.

Step 3: Compare C-O and Sn-O Bond Lengths

Carbon (C) is higher on the periodic table than Tin (Sn), indicating that the C–O bond is shorter than the Sn–O bond, as carbon is smaller and forms shorter bonds compared to tin.

Step 4: Compare P-S and P-O Bond Lengths

Oxygen is more electronegative and smaller than sulfur, which means that a P–O bond is shorter than a P–S bond, as oxygen forms shorter bonds than sulfur.

Step 5: Compare C=C and C=O Bond Lengths

Oxygen, being more electronegative and forming stronger bonds than carbon, typically results in a shorter C=O bond than a C=C bond, as observed in acrolein.

Key Concepts

Periodic Table Trends

The periodic table is a fundamental tool in chemistry, organizing elements based on their atomic number and electron configurations. One key trend you notice is that atomic size changes across the table. Atomic size generally decreases from left to right across a period due to increasing nuclear charge pulling electrons closer to the nucleus. It increases from top to bottom down a group because additional electron shells are added.
Understanding these trends helps predict several properties, including bond length.

• Smaller atoms, often seen higher on the periodic table, tend to form shorter bonds due to their reduced atomic radii.
• Greater electronegativities across periods result in varying bond strengths and lengths.

Observing these trends allows chemists to anticipate bond behaviors in chemical reactions.

Atomic Radii

Atomic radii refer to the size of an atom, typically defined as half the distance between two nuclei of the same element bonded together. This concept is essential in determining bond lengths in molecular structures.
Smaller atomic radii usually lead to shorter bonds, as the nuclei are closer together.

• The radii decrease across a period from left to right due to increasing positive charge, drawing electrons inward.
• Atomic radii increase down a group because of the addition of electron shells, which outweighs the increasing nuclear charge.
• Atoms higher up and to the right on the periodic table generally form shorter, tighter bonds.

Predicting bond lengths in molecules depends greatly on recognizing atomic radii trends.

Electronegativity

Electronegativity measures an atom's ability to attract and hold electrons in a bond. It is a crucial factor that affects bond length and bond strength.
Atoms with high electronegativity, like oxygen and fluorine, often form shorter and stronger covalent bonds because they attract bonding electrons more forcefully.

• Generally, electronegativity increases across a period from left to right, as atoms become more eager to complete their electron shells.
• It decreases down a group as the increased distance from the nucleus lessens the attractive force on bonding electrons.
• This concept helps explain why the \( \mathrm{C} = \mathrm{O} \) bond is typically shorter than the \( \mathrm{C} = \mathrm{C} \) bond because oxygen is more electronegative than carbon.

A strong grasp of electronegativity helps explain why certain bonds in molecules are shorter or longer.

Multiple Bonds

Multiple bonds, such as double and triple bonds, are stronger and shorter than single bonds. The presence of additional shared electrons in multiple bonds increases the attraction between the bonded atoms, drawing them closer together.

• For example, double bonds like \( \mathrm{C} = \mathrm{O} \) and \( \mathrm{C} = \mathrm{C} \) illustrate how multiple bonds are usually shorter and stronger due to more shared electrons.
• These bonds involve the overlapping of p-orbitals, resulting in increased electron density between the atoms.
• The bond order, or number of chemical bonds between a pair of atoms, is higher in multiple bonds, further contributing to the shortened bond length.

Thus, the difference in bond lengths in acrolein with \( \mathrm{C} = \mathrm{O} \) and \( \mathrm{C} = \mathrm{C} \) highlights the influence of bond multiplicity on bond length.