Problem 139 - General Chemistry: Principles and Modern Applications

Question

The greatest bond length is found in (a) \(\mathrm{O}_{2} ;\) (b) \(\mathrm{N}_{2}\) (c) \(\mathrm{Br}_{2} ;\) (d) BrCl.

Step-by-Step Solution

Answer

The compound with the greatest bond length is BrCl.

Step 1: Identifying atomic sizes

The first step involves identifying which atoms are larger. Oxygen, Nitrogen and Bromine. Bromine being in the 4th period of the periodic table is larger than Nitrogen and Oxygen which are in the 2nd period of the periodic table.

Step 2: Identify nature of bond

Next, look at the nature of the bonds in the compounds. \(\mathrm{O}_{2}\) and \(\mathrm{N}_{2}\) both have double and triple bonds respectively making them shorter. \(\mathrm{Br}_{2}\) has a single bond and BrCl involves two different larger atoms, possibly leading to a longer bond length.

Step 3: Compare and conclude

Comparing the bond lengths, the single bond between two larger bromine atoms in \(\mathrm{Br}_{2}\) and between bromine and chlorine in BrCl would be generally longer than the double bond in \(\mathrm{O}_{2}\) and the triple bond in \(\mathrm{N}_{2}\). However, between \(\mathrm{Br}_{2}\) and BrCl, the bond length of BrCl would likely be larger as bond lengths tend to increase with the increase in atomic size difference. Hence, BrCl has the greatest bond length among the given compounds.

Key Concepts

Atomic Sizes

Atomic sizes refer to the magnitude of an atom, often determined by the distance from the nucleus to the electron cloud boundary. Bigger atoms have electrons that are further from the nucleus. This influences many properties of elements, including bond length.

• Trend in the periodic table: As you move down a group, the atomic size increases. This is because each subsequent period adds a new outer electron shell. For example, Bromine is larger than both Oxygen and Nitrogen since Bromine is in the 4th period, while Oxygen and Nitrogen are in the 2nd period.
• Periodic trend in a period: Atomic sizes tend to decrease from left to right across a period. This happens because the additional protons increase the nuclear charge, pulling the electrons closer inward.

Understanding atomic size helps predict how long or short a bond might be, with larger atoms often leading to longer bonds.

Nature of Bonds

The nature of bonds heavily determines the length and strength of a chemical bond. Chemical bonds can be single, double, or triple, impacting how closely or far apart atoms are held together.

• Single Bonds: Consist of one pair of shared electrons and typically are the longest bond type. Think of a single bond as a simple bridge that spans two points.
• Double Bonds: Involve two pairs of shared electrons, making them shorter and stronger than single bonds. A double bond does a better job holding atoms tightly together because of the extra electron pair.
• Triple Bonds: Share three pairs of electrons, being the shortest and strongest of the bond types, almost like tying a rope three times for added stability.

When considering bond length in compounds, it’s important to note that - Br₂ (bromine-bromine) possesses a single bond, while - BrCl (bromine-chlorine) also typically presents a single bond, however, the variation in atom sizes can affect the bond length.

Periodic Table Trends

The periodic table is an essential tool in predicting the properties of elements like atomic sizes and bond behavior. Periodic trends offer simplified ways to foresee changes in properties when moving across a row or down a column.

• Trends in Atomic Radius: Down a group, atomic size increases, which can increase bond lengths when joining larger atoms.
• Bonds and Atomic Location: Moving across a period can influence bond characteristics due to changes in electronegativity and atomic size.
• Influence on Bond Length: Larger atoms or those on the same side of the periodic table typically form longer bonds, as seen in the case of bromine compounds vs nitrogen or oxygen compounds.

Understanding these trends assists in predicting which bonds will have greater lengths. The larger atomic sizes of bromine, compared to smaller atoms like nitrogen and oxygen, lead to typically longer bond lengths, especially evident in compounds like BrCl.